The document describes Hidden Markov Models (HMMs). It discusses how the problem of finding CG-islands in DNA sequences can be modeled as the "Fair Bet Casino" problem of determining which coin (fair or biased) was used to generate a sequence of coin flips. An HMM is presented to model this problem, consisting of hidden states (fair/biased coins), observed emissions (heads/tails), and transition and emission probabilities. Algorithms for decoding (finding the most likely hidden state sequence) and parameter estimation are discussed, including the Viterbi algorithm and Forward-Backward algorithm.
The document discusses different methods for representing and filling polygons in computer graphics, including:
1) Solid-fill and pattern-fill for filling polygon interiors.
2) Representing polygons by listing vertex coordinates or relative positions to simplify translation.
3) Using the odd-parity rule to test if a point is interior or exterior to a polygon.
4) The scan-line polygon fill algorithm which horizontally scans a polygon, identifies intersecting edges, and draws interior lines.
The document discusses computer graphics viewing in 2D. It covers windowing concepts, clipping lines and areas to a window using algorithms like Cohen-Sutherland for lines and Sutherland-Hodgman for areas. When displaying a scene, objects must be clipped to only show those within the window using efficient algorithms to avoid drawing parts outside the window.
Clipping Algorithm In Computer Graphicsstudent(MCA)
This document discusses window clipping techniques for computer graphics. It introduces point and line clipping, describing a brute force approach and the more efficient Cohen-Sutherland clipping algorithm. It then explains the Sutherland-Hodgman area clipping algorithm. Key concepts covered include using region codes to efficiently determine which lines and portions of lines need to be clipped to a window.
This document discusses different techniques for clipping graphics objects to a viewing window, including:
- Point and line clipping, where points and line segments outside the window are "clipped" and not drawn.
- The Cohen-Sutherland and Liang-Barsky line clipping algorithms, which use outcodes and parametric equations to efficiently determine which portions of lines are inside the window.
- Area clipping techniques like the Sutherland-Hodgman algorithm, which successively clips a polygon against each boundary of the window by comparing vertices and finding intersection points.
The document summarizes a lecture on multi-party computation protocols. It defines multi-party computation where multiple parties want to compute a function on their private inputs while keeping the inputs secret. It discusses security against threshold adversaries who can corrupt up to t parties. It overviews classical results on the thresholds for secure computation and constructions using secret sharing and arithmetic circuits over fields.
The document discusses the Sutherland-Hodgeman polygon clipping algorithm. It clips a polygon by considering it against each boundary edge of the window. It passes the polygon's vertices to clipping procedures for the left, right, bottom and top edges. At each stage, it generates a new set of vertices for the clipped polygon which is passed to the next stage. There are four cases considered - when vertices are inside/outside the window boundary and their intersection points are determined and stored in the output vertex list. Once all vertices are clipped against one boundary, the result is passed to the next boundary for further clipping until the fully clipped polygon is produced.
The document discusses algorithms for finding the convex hull of a set of points in two dimensions. It describes the Jarvis march (also called the gift wrapping algorithm) and the Graham scan algorithm. The Jarvis march finds the convex hull by iterating through points and finding the next point that forms the smallest interior angle with the last two points on the hull. The Graham scan sorts points by angle and then iterates through, eliminating any point that forms an obtuse angle with the last three points. Both algorithms run in O(n log n) time.
The document discusses 2D and 3D rendering pipelines. It describes techniques for clipping geometric primitives to a viewing window, including Cohen-Sutherland line clipping and Sutherland-Hodgeman polygon clipping. It also covers viewport transformation to map from screen to image coordinates, and scan conversion algorithms to determine which pixels are inside primitives like triangles and polygons.
The document discusses different methods for representing and filling polygons in computer graphics, including:
1) Solid-fill and pattern-fill for filling polygon interiors.
2) Representing polygons by listing vertex coordinates or relative positions to simplify translation.
3) Using the odd-parity rule to test if a point is interior or exterior to a polygon.
4) The scan-line polygon fill algorithm which horizontally scans a polygon, identifies intersecting edges, and draws interior lines.
The document discusses computer graphics viewing in 2D. It covers windowing concepts, clipping lines and areas to a window using algorithms like Cohen-Sutherland for lines and Sutherland-Hodgman for areas. When displaying a scene, objects must be clipped to only show those within the window using efficient algorithms to avoid drawing parts outside the window.
Clipping Algorithm In Computer Graphicsstudent(MCA)
This document discusses window clipping techniques for computer graphics. It introduces point and line clipping, describing a brute force approach and the more efficient Cohen-Sutherland clipping algorithm. It then explains the Sutherland-Hodgman area clipping algorithm. Key concepts covered include using region codes to efficiently determine which lines and portions of lines need to be clipped to a window.
This document discusses different techniques for clipping graphics objects to a viewing window, including:
- Point and line clipping, where points and line segments outside the window are "clipped" and not drawn.
- The Cohen-Sutherland and Liang-Barsky line clipping algorithms, which use outcodes and parametric equations to efficiently determine which portions of lines are inside the window.
- Area clipping techniques like the Sutherland-Hodgman algorithm, which successively clips a polygon against each boundary of the window by comparing vertices and finding intersection points.
The document summarizes a lecture on multi-party computation protocols. It defines multi-party computation where multiple parties want to compute a function on their private inputs while keeping the inputs secret. It discusses security against threshold adversaries who can corrupt up to t parties. It overviews classical results on the thresholds for secure computation and constructions using secret sharing and arithmetic circuits over fields.
The document discusses the Sutherland-Hodgeman polygon clipping algorithm. It clips a polygon by considering it against each boundary edge of the window. It passes the polygon's vertices to clipping procedures for the left, right, bottom and top edges. At each stage, it generates a new set of vertices for the clipped polygon which is passed to the next stage. There are four cases considered - when vertices are inside/outside the window boundary and their intersection points are determined and stored in the output vertex list. Once all vertices are clipped against one boundary, the result is passed to the next boundary for further clipping until the fully clipped polygon is produced.
The document discusses algorithms for finding the convex hull of a set of points in two dimensions. It describes the Jarvis march (also called the gift wrapping algorithm) and the Graham scan algorithm. The Jarvis march finds the convex hull by iterating through points and finding the next point that forms the smallest interior angle with the last two points on the hull. The Graham scan sorts points by angle and then iterates through, eliminating any point that forms an obtuse angle with the last three points. Both algorithms run in O(n log n) time.
The document discusses 2D and 3D rendering pipelines. It describes techniques for clipping geometric primitives to a viewing window, including Cohen-Sutherland line clipping and Sutherland-Hodgeman polygon clipping. It also covers viewport transformation to map from screen to image coordinates, and scan conversion algorithms to determine which pixels are inside primitives like triangles and polygons.
Clipping is a technique that identifies parts of an image that are inside or outside a defined clipping region or window. There are different types of clipping including point, line, polygon, curve, and text clipping. The Cohen-Sutherland algorithm is commonly used for line clipping. It assigns 4-bit codes to line endpoints to determine if they are fully inside, outside, or intersect the clipping window boundary. Intersecting line segments are then subdivided and clipped. Midpoint subdivision is another algorithm that divides partially visible lines at their midpoint into shorter segments.
The document discusses different techniques for thickening lines and clipping primitives during rasterization. It describes Cohen-Sutherland and Sutherland-Hodgman algorithms for clipping lines and polygons against viewing windows. Clipping removes parts of primitives that fall outside the viewport, reducing unnecessary computation during rasterization. Various approaches are discussed for thickening lines during drawing and clipping lines, polygons, and other primitives efficiently.
The document discusses different algorithms for polygon clipping, which is a process that identifies the visible portions of a polygon through a clipping window. It describes the Sutherland-Hodgeman algorithm, which clips polygons by extending the edges of a convex clip polygon and selecting only visible vertices. The Weiler-Atherton algorithm modifies this approach to correctly display concave polygons. Polygon clipping is important for video games to maximize frame rate by avoiding rendering calculations for invisible portions of polygons.
1. Clipping is a procedure that identifies parts of an image that are inside or outside a specified region, called the clip window. Parts inside the window are displayed, while outside parts are discarded.
2. There are different types of clipping like point, curve, text, and line clipping. Line clipping involves testing if line segments are fully inside/outside the window, and calculating intersections if they cross window boundaries.
3. Popular line clipping algorithms like Cohen-Sutherland and Liang-Barsky assign codes to line endpoints to quickly determine if lines are fully in/out of the window without calculating intersections. They find intersection points to clip lines that cross window edges.
This document discusses windowing and clipping in computer graphics. It defines the world coordinate system, which stores graphical information, and the screen coordinate system, which is used for display. A window selects a portion of the model for viewing in the viewport, which is the area on screen where the window is displayed. The window to viewport transformation maps the model from world to screen coordinates using scaling and translation. Clipping removes portions of lines and curves outside the window boundaries. The Sutherland-Cohen algorithm clips lines by calculating intersection points with the window edges.
Definition of Viewing & Clipping?
Viewing pipeline
Viewing the transformation system
Several types of clipping
Cohen-Sutherland Line Clipping
Application of Clipping
Conclusion
The document discusses 2D viewing and clipping techniques in computer graphics. It describes how clipping is used to select only a portion of an image to display by defining a clipping region. It also discusses 2D viewing transformations which involve operations like translation, rotation and scaling to map coordinates from a world coordinate system to a device coordinate system. It specifically describes the Cohen-Sutherland line clipping algorithm which uses region codes to quickly determine if lines are completely inside, outside or intersect the clipping region to optimize the clipping calculation.
Clipping algorithms identify portions of an image that are inside or outside a specified clipping region. They are used to extract a defined scene for viewing, identify visible surfaces, and perform other drawing and display operations. Common types of clipping include point, line, polygon, and curve clipping. Algorithms like Cohen-Sutherland and mid-point subdivision use codes and binary subdivision to efficiently determine which image portions are visible and should be displayed.
Clipping is a process that extracts portions of data or scenes inside a specified clipping region. It uses endpoint codes, which assign a 4-bit code to line endpoints to indicate if they are inside or outside the clipping window. One algorithm is the Cohen-Sutherland algorithm which uses these endpoint codes to test if lines are completely inside, completely outside, or intersect the clipping window. Another is the Mid-Point Subdivision algorithm which avoids directly calculating line-window intersections by performing a binary search via dividing lines at their midpoint.
Polygon clipping involves taking a polygon and clipping it against another shape to produce one or more smaller polygons. The Sutherland-Hodgman algorithm handles polygon clipping by testing each edge of the clipping polygon against each edge of the clip shape. There are four cases for how an edge can be clipped - wholly inside, exit, wholly outside, enter - and the algorithm saves or discards vertices based on these cases. Repeatedly clipping against each edge of the clip shape handles all cases and produces the final clipped polygon(s).
The document discusses two algorithms for polygon clipping:
1. The Sutherland-Hodgeman algorithm clips polygons by processing vertices against window boundaries from left to right, bottom to top. It works for convex polygons but can produce extraneous lines with concave polygons.
2. The Weiler-Atherton algorithm modifies this by following either the polygon or window boundary depending on if the vertex pair is entering or exiting the clip region. This correctly handles concave polygons by producing separated clipped sections rather than extraneous lines.
Lec12 Intro to Computer Engineering by Hsien-Hsin Sean Lee Georgia Tech -- Ad...Hsien-Hsin Sean Lee, Ph.D.
This document summarizes key concepts in combinational logic building blocks including adders, subtractors, and parity checkers. It describes half adders, full adders, ripple carry adders, carry lookahead adders, subtraction using 2's complement, and even parity generation and detection. The document discusses issues like carry propagation delay in ripple carry adders and improved delay in carry lookahead adders. It also covers overflow/underflow detection in signed arithmetic and examples of parity error detection.
The document discusses several algorithms for clipping lines and polygons in computer graphics:
1. The Cohen-Sutherland and Cyrus-Back algorithms are described for clipping lines, with Cohen-Sutherland using outcodes to determine if lines can be trivially accepted or rejected from the clipping region.
2. The Cyrus-Back algorithm uses the concepts of potentially entering and leaving to iteratively calculate intersection points and clip line segments.
3. The Sutherland-Hodgeman algorithm is described for polygon clipping, using iterative clipping of vertices against clipping boundaries.
4. Both Cohen-Sutherland and Cyrus-Back extend readily to 3D clipping through additional bits for the
Encoder for (7,3) cyclic code using matlabSneheshDutta
This document provides an overview of cyclic codes including:
- What cyclic codes are and their properties of error detection and correction.
- The method of generating cyclic codes by multiplying message polynomials by a generator polynomial.
- How to systematically encode cyclic codes in three steps.
- The encoding and decoding circuits including Meggitt decoder.
- An example of a (7,3) cyclic code implemented in Matlab showing the encoding, corruption with errors, and decoding.
- How cyclic codes can detect errors through syndrome computation and lookup tables.
- Applications of cyclic codes in message identification.
This document discusses parallelizing loops to compute pi through numerical integration. It begins by describing how pi can be computed by approximating the integral of 1/(1+x^2) from 0 to 1. It then shows C++ and Fortran code that performs this computation sequentially with increasing numbers of steps to improve the approximation of pi. The document discusses variable scopes in C++ and Fortran and how OpenMP parallelization works by dividing the loop workload across threads. It demonstrates parallelizing the loops in both languages using the reduction clause to correctly sum values across threads. Finally, it discusses considerations for parallelizing loops and challenges like data dependencies.
Curve clipping involves using polygon clipping to test if a curved object's bounding rectangle overlaps a clipping window. If there is no overlap, the object is discarded. If there is overlap, the simultaneous curve and boundary equations are solved to find intersection points. Special cases like circles are considered, such as discarding a circle if its center is outside the clipping window plus/minus the radius. Bezier and spline curves can also be clipped by approximating them as polylines or using their convex hull properties.
Clipping polygons is more complex than clipping lines because it involves considering the polygon as a whole rather than just its individual line segments. The Sutherland-Hodgman algorithm clips polygons by considering each edge of the clipping region individually and clipping the subject polygon against that edge, resulting in a new clipped polygon. This process is repeated for each clipping region edge until the polygon is fully clipped. The algorithm takes as input a list of polygon vertices and outputs a new list of clipped polygon vertices.
The document discusses distance formula and its applications. It defines distance formula as the formula used to find the distance between two points (x1, y1) and (x2, y2). The formula is the square root of (x2 - x1)2 + (y2 - y1)2. It provides a proof of the formula using the Pythagorean theorem. Examples are given to demonstrate calculating distances between points using the formula. The key aspects are defining distance formula, proving it, and providing examples of its application.
This document discusses algorithms for clipping circles and curves to a bounding region. It describes a fast circle clipping algorithm that uses an accept/reject test to determine whether points are inside or outside the clipping region. It also discusses a midpoint circle algorithm that uses incremental steps to scan convert circles. Finally, it explains that curved objects can be clipped by first testing if their bounding rectangles overlap the clipping region before solving nonlinear equations to find curve-window intersection points.
The document discusses different algorithms for clipping polygons and lines to a viewing window, including the Sutherland-Hodgman and Weiler-Atherton polygon clipping algorithms. The Sutherland-Hodgman algorithm clips polygons by processing edges against each window boundary edge but can result in disconnected line segments or extraneous lines for concave polygons. The Weiler-Atherton algorithm addresses this by following either the polygon or window boundary depending on if the vertex pair is outside to inside or vice versa.
Hidden Markov Models with applications to speech recognitionbutest
This document provides an introduction to hidden Markov models (HMMs). It discusses how HMMs can be used to model sequential data where the underlying states are not directly observable. The key aspects of HMMs are: (1) the model has a set of hidden states that evolve over time according to transition probabilities, (2) observations are emitted based on the current hidden state, (3) the four basic problems of HMMs are evaluation, decoding, training, and model selection. Examples discussed include modeling coin tosses, balls in urns, and speech recognition. Learning algorithms for HMMs like Baum-Welch and Viterbi are also summarized.
In this presentation we describe the formulation of the HMM model as consisting of states that are hidden that generate the observables. We introduce the 3 basic problems: Finding the probability of a sequence of observation given the model, the decoding problem of finding the hidden states given the observations and the model and the training problem of determining the model parameters that generate the given observations. We discuss the Forward, Backward, Viterbi and Forward-Backward algorithms.
Clipping is a technique that identifies parts of an image that are inside or outside a defined clipping region or window. There are different types of clipping including point, line, polygon, curve, and text clipping. The Cohen-Sutherland algorithm is commonly used for line clipping. It assigns 4-bit codes to line endpoints to determine if they are fully inside, outside, or intersect the clipping window boundary. Intersecting line segments are then subdivided and clipped. Midpoint subdivision is another algorithm that divides partially visible lines at their midpoint into shorter segments.
The document discusses different techniques for thickening lines and clipping primitives during rasterization. It describes Cohen-Sutherland and Sutherland-Hodgman algorithms for clipping lines and polygons against viewing windows. Clipping removes parts of primitives that fall outside the viewport, reducing unnecessary computation during rasterization. Various approaches are discussed for thickening lines during drawing and clipping lines, polygons, and other primitives efficiently.
The document discusses different algorithms for polygon clipping, which is a process that identifies the visible portions of a polygon through a clipping window. It describes the Sutherland-Hodgeman algorithm, which clips polygons by extending the edges of a convex clip polygon and selecting only visible vertices. The Weiler-Atherton algorithm modifies this approach to correctly display concave polygons. Polygon clipping is important for video games to maximize frame rate by avoiding rendering calculations for invisible portions of polygons.
1. Clipping is a procedure that identifies parts of an image that are inside or outside a specified region, called the clip window. Parts inside the window are displayed, while outside parts are discarded.
2. There are different types of clipping like point, curve, text, and line clipping. Line clipping involves testing if line segments are fully inside/outside the window, and calculating intersections if they cross window boundaries.
3. Popular line clipping algorithms like Cohen-Sutherland and Liang-Barsky assign codes to line endpoints to quickly determine if lines are fully in/out of the window without calculating intersections. They find intersection points to clip lines that cross window edges.
This document discusses windowing and clipping in computer graphics. It defines the world coordinate system, which stores graphical information, and the screen coordinate system, which is used for display. A window selects a portion of the model for viewing in the viewport, which is the area on screen where the window is displayed. The window to viewport transformation maps the model from world to screen coordinates using scaling and translation. Clipping removes portions of lines and curves outside the window boundaries. The Sutherland-Cohen algorithm clips lines by calculating intersection points with the window edges.
Definition of Viewing & Clipping?
Viewing pipeline
Viewing the transformation system
Several types of clipping
Cohen-Sutherland Line Clipping
Application of Clipping
Conclusion
The document discusses 2D viewing and clipping techniques in computer graphics. It describes how clipping is used to select only a portion of an image to display by defining a clipping region. It also discusses 2D viewing transformations which involve operations like translation, rotation and scaling to map coordinates from a world coordinate system to a device coordinate system. It specifically describes the Cohen-Sutherland line clipping algorithm which uses region codes to quickly determine if lines are completely inside, outside or intersect the clipping region to optimize the clipping calculation.
Clipping algorithms identify portions of an image that are inside or outside a specified clipping region. They are used to extract a defined scene for viewing, identify visible surfaces, and perform other drawing and display operations. Common types of clipping include point, line, polygon, and curve clipping. Algorithms like Cohen-Sutherland and mid-point subdivision use codes and binary subdivision to efficiently determine which image portions are visible and should be displayed.
Clipping is a process that extracts portions of data or scenes inside a specified clipping region. It uses endpoint codes, which assign a 4-bit code to line endpoints to indicate if they are inside or outside the clipping window. One algorithm is the Cohen-Sutherland algorithm which uses these endpoint codes to test if lines are completely inside, completely outside, or intersect the clipping window. Another is the Mid-Point Subdivision algorithm which avoids directly calculating line-window intersections by performing a binary search via dividing lines at their midpoint.
Polygon clipping involves taking a polygon and clipping it against another shape to produce one or more smaller polygons. The Sutherland-Hodgman algorithm handles polygon clipping by testing each edge of the clipping polygon against each edge of the clip shape. There are four cases for how an edge can be clipped - wholly inside, exit, wholly outside, enter - and the algorithm saves or discards vertices based on these cases. Repeatedly clipping against each edge of the clip shape handles all cases and produces the final clipped polygon(s).
The document discusses two algorithms for polygon clipping:
1. The Sutherland-Hodgeman algorithm clips polygons by processing vertices against window boundaries from left to right, bottom to top. It works for convex polygons but can produce extraneous lines with concave polygons.
2. The Weiler-Atherton algorithm modifies this by following either the polygon or window boundary depending on if the vertex pair is entering or exiting the clip region. This correctly handles concave polygons by producing separated clipped sections rather than extraneous lines.
Lec12 Intro to Computer Engineering by Hsien-Hsin Sean Lee Georgia Tech -- Ad...Hsien-Hsin Sean Lee, Ph.D.
This document summarizes key concepts in combinational logic building blocks including adders, subtractors, and parity checkers. It describes half adders, full adders, ripple carry adders, carry lookahead adders, subtraction using 2's complement, and even parity generation and detection. The document discusses issues like carry propagation delay in ripple carry adders and improved delay in carry lookahead adders. It also covers overflow/underflow detection in signed arithmetic and examples of parity error detection.
The document discusses several algorithms for clipping lines and polygons in computer graphics:
1. The Cohen-Sutherland and Cyrus-Back algorithms are described for clipping lines, with Cohen-Sutherland using outcodes to determine if lines can be trivially accepted or rejected from the clipping region.
2. The Cyrus-Back algorithm uses the concepts of potentially entering and leaving to iteratively calculate intersection points and clip line segments.
3. The Sutherland-Hodgeman algorithm is described for polygon clipping, using iterative clipping of vertices against clipping boundaries.
4. Both Cohen-Sutherland and Cyrus-Back extend readily to 3D clipping through additional bits for the
Encoder for (7,3) cyclic code using matlabSneheshDutta
This document provides an overview of cyclic codes including:
- What cyclic codes are and their properties of error detection and correction.
- The method of generating cyclic codes by multiplying message polynomials by a generator polynomial.
- How to systematically encode cyclic codes in three steps.
- The encoding and decoding circuits including Meggitt decoder.
- An example of a (7,3) cyclic code implemented in Matlab showing the encoding, corruption with errors, and decoding.
- How cyclic codes can detect errors through syndrome computation and lookup tables.
- Applications of cyclic codes in message identification.
This document discusses parallelizing loops to compute pi through numerical integration. It begins by describing how pi can be computed by approximating the integral of 1/(1+x^2) from 0 to 1. It then shows C++ and Fortran code that performs this computation sequentially with increasing numbers of steps to improve the approximation of pi. The document discusses variable scopes in C++ and Fortran and how OpenMP parallelization works by dividing the loop workload across threads. It demonstrates parallelizing the loops in both languages using the reduction clause to correctly sum values across threads. Finally, it discusses considerations for parallelizing loops and challenges like data dependencies.
Curve clipping involves using polygon clipping to test if a curved object's bounding rectangle overlaps a clipping window. If there is no overlap, the object is discarded. If there is overlap, the simultaneous curve and boundary equations are solved to find intersection points. Special cases like circles are considered, such as discarding a circle if its center is outside the clipping window plus/minus the radius. Bezier and spline curves can also be clipped by approximating them as polylines or using their convex hull properties.
Clipping polygons is more complex than clipping lines because it involves considering the polygon as a whole rather than just its individual line segments. The Sutherland-Hodgman algorithm clips polygons by considering each edge of the clipping region individually and clipping the subject polygon against that edge, resulting in a new clipped polygon. This process is repeated for each clipping region edge until the polygon is fully clipped. The algorithm takes as input a list of polygon vertices and outputs a new list of clipped polygon vertices.
The document discusses distance formula and its applications. It defines distance formula as the formula used to find the distance between two points (x1, y1) and (x2, y2). The formula is the square root of (x2 - x1)2 + (y2 - y1)2. It provides a proof of the formula using the Pythagorean theorem. Examples are given to demonstrate calculating distances between points using the formula. The key aspects are defining distance formula, proving it, and providing examples of its application.
This document discusses algorithms for clipping circles and curves to a bounding region. It describes a fast circle clipping algorithm that uses an accept/reject test to determine whether points are inside or outside the clipping region. It also discusses a midpoint circle algorithm that uses incremental steps to scan convert circles. Finally, it explains that curved objects can be clipped by first testing if their bounding rectangles overlap the clipping region before solving nonlinear equations to find curve-window intersection points.
The document discusses different algorithms for clipping polygons and lines to a viewing window, including the Sutherland-Hodgman and Weiler-Atherton polygon clipping algorithms. The Sutherland-Hodgman algorithm clips polygons by processing edges against each window boundary edge but can result in disconnected line segments or extraneous lines for concave polygons. The Weiler-Atherton algorithm addresses this by following either the polygon or window boundary depending on if the vertex pair is outside to inside or vice versa.
Hidden Markov Models with applications to speech recognitionbutest
This document provides an introduction to hidden Markov models (HMMs). It discusses how HMMs can be used to model sequential data where the underlying states are not directly observable. The key aspects of HMMs are: (1) the model has a set of hidden states that evolve over time according to transition probabilities, (2) observations are emitted based on the current hidden state, (3) the four basic problems of HMMs are evaluation, decoding, training, and model selection. Examples discussed include modeling coin tosses, balls in urns, and speech recognition. Learning algorithms for HMMs like Baum-Welch and Viterbi are also summarized.
In this presentation we describe the formulation of the HMM model as consisting of states that are hidden that generate the observables. We introduce the 3 basic problems: Finding the probability of a sequence of observation given the model, the decoding problem of finding the hidden states given the observations and the model and the training problem of determining the model parameters that generate the given observations. We discuss the Forward, Backward, Viterbi and Forward-Backward algorithms.
This document provides an introduction to hidden Markov models (HMMs). It defines HMMs as an extension of Markov models that allows for observations that are probabilistic functions of hidden states. The core problems of HMMs are finding the probability of an observed sequence and determining the most probable hidden state sequence that produced an observation. HMMs have applications in areas like speech recognition by finding the most likely string of words given acoustic input using the Viterbi and forward algorithms.
This document discusses Hidden Markov Models (HMMs) and Markov chains. It begins with an introduction to Markov processes and how HMMs are used in various domains like natural language processing. It then describes the properties of a Markov chain, which has a set of states that the system transitions between randomly at discrete time steps based on transition probabilities. The Markov property is explained as the conditional independence of future states from past states given the present state. HMMs extend Markov chains by making the state sequence hidden and only allowing observation of the output states.
- Hidden Markov models (HMMs) are statistical models where the system is assumed to be a Markov process with hidden states. Each state has a number of possible transitions to other states, each with an assigned probability.
- There are three main issues in HMMs: model evaluation, decoding the most probable path, and model training.
- HMMs have applications in areas like speech recognition, gesture recognition, language modeling, and video analysis.
Basic knowledge of antenna and antenna selectionswatisabnis87
This document provides an overview of antenna basics, including:
1) A description of common antenna types and structures used in mobile communication networks.
2) Explanations of key antenna parameters and measurement techniques.
3) Guidelines for antenna selection and installation in different environments.
4) Details on antenna radiation theory, development trends, and the state of the Chinese antenna industry.
This document discusses various algorithms for polygon scan conversion and filling, including:
- The scan line polygon fill algorithm which determines pixel color by calculating polygon edge intersections with scan lines and using an odd-even rule.
- Methods for handling special cases like horizontal edges and vertex intersections.
- Using a sorted edge table and active edge list to incrementally calculate edge intersections across scan lines.
- Flood fill and depth/z-buffer algorithms for hidden surface removal when rendering overlapping polygons.
The document discusses various 2D geometric transformations including reflections, shears, and their matrix representations. It also covers 2D viewing pipelines including coordinate systems, clipping techniques like Cohen-Sutherland and Liang-Barsky line clipping, and Sutherland-Hodgeman polygon clipping. Reflections are described as 180 degree rotations about an axis. Shearing shifts points along an axis proportional to their coordinate on the other axis. Clipping algorithms discard or shorten line/polygon segments that fall outside the clip region.
Linear feedback shift registers (LFSRs) are circuits that can generate pseudo-random sequences of bits. They consist of a shift register with XOR logic gates in a feedback path. LFSRs can be used for random number generation, error detection and correction codes, and counting applications. They are efficient in that they require little hardware and operate at high speeds. The document then provides examples of 4-bit and 8-bit LFSR circuits and discusses how LFSRs can implement finite field arithmetic over Galois fields using polynomial representations. It also describes how LFSRs can be used to generate parity bits for error detection codes.
The document discusses techniques for clipping and rasterization in computer graphics. It covers line segment clipping algorithms like Cohen-Sutherland and Liang-Barsky. It also discusses polygon clipping, including brute force, triangulation, and a black box pipeline approach. Finally, it covers rasterization techniques for points, lines, and polygons, including inside-outside testing methods, fill algorithms like flood fill and scanline fill.
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Elliptic Curve Cryptography uses elliptic curves over finite fields for public-key encryption, digital signatures, and other applications. The talk introduces elliptic curves, defines their properties like being an abelian group, and explains how to perform point addition graphically. It then discusses how elliptic curve groups can be used in cryptosystems like Elliptic Curve Diffie-Hellman key exchange and Elliptic Curve Digital Signature Algorithm. The talk concludes by outlining how to implement an elliptic curve cryptosystem analogously to El Gamal encryption.
A polygon is a closed two-dimensional shape with straight or curved sides. It can be defined by an ordered sequence of vertices and edges connecting consecutive vertices. The scan line polygon fill algorithm uses an odd-even rule to determine if a point is inside or outside the polygon by counting edge crossings along a scan line from that point to infinity. Boundary fill and flood fill are two area filling algorithms that color the interior of a polygon or region by recursively filling neighboring pixels of the same color.
Elliptic Curve Cryptography (ECC) uses elliptic curves over finite fields for public-key encryption, digital signatures, and key exchanges. ECC provides the same security as other cryptosystems but with smaller key sizes. The talk introduced elliptic curves, defined their properties as abelian groups, and explained how to add points on a curve. It then discussed how ECC works analogously to other cryptosystems like El Gamal but using point multiplication on elliptic curves instead of exponentiation in finite fields.
I am Josh U. I am a Probabilistic Systems Exam Helper at statisticsexamhelp.com. I hold a Masters' Degree in Statistics, from the University of Southampton, UK. I have been helping students with their exams for the past 5 years. You can hire me to take your exam in Probabilistic Systems.
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Here are the steps to solve this ODE problem:
1. Define the ODE function:
function dydt = odefun(t,y)
dydt = -t.*y/10;
end
2. Solve the ODE:
[t,y] = ode45(@odefun,[0 10],10);
3. Plot the result:
plot(t,y)
xlabel('t')
ylabel('y(t)')
This uses ode45 to solve the ODE dy/dt = -t*y/10 on the interval [0,10] with initial condition y(0)=10.
Alice wants to teleport an unknown quantum state ψ to Bob using prior entanglement and classical communication. They share one half of an entangled Bell state β each. Alice combines her half of β with ψ and performs a teleportation circuit involving CNOT and Hadamard gates. She then measures her two qubits and sends the results to Bob. Based on the received classical bits, Bob applies a Pauli operator to reconstruct the state ψ exactly at his location.
This Presentation Elliptical Curve Cryptography give a brief explain about this topic, it will use to enrich your knowledge on this topic. Use this ppt for your reference purpose and if you have any queries you'll ask questions.
The document summarizes the Count-Min Sketch streaming algorithm. It uses a two-dimensional array and d independent hash functions to estimate item frequencies in a data stream using sublinear space. It works by incrementing the appropriate counters in each row when an item arrives. The estimated frequency of an item is the minimum value across the rows. Analysis shows that for an array width w proportional to 1/ε, the estimate will be within an additive error of ε times the total frequency with high probability.
Quantum computing uses quantum bits (qubits) that can exist in superpositions of states. A controlled-NOT (CN) gate inverts the target qubit if the control qubit is 1. A controlled-controlled-NOT (CCN) gate inverts the target qubit if both control qubits are 1. Shor's algorithm uses quantum Fourier transforms and modular exponentiation to factor integers into prime factors exponentially faster than classical computers. It finds the period of the function x raised to a power (mod N), from which the factors can be derived.
The document describes an algorithm for estimating the probability distribution of travel demand forecasts that are subject to uncertainty. It involves identifying variables that influence forecast error, determining probability distributions for each variable, defining scenarios that combine the discrete outcomes of each variable, calculating the probability and predicted revenue for each scenario, and plotting the revenue cumulative distribution function. Key variables of uncertainty identified for a toll road project include truck value of time, travel demand, and growth rates of car and truck value of time. Probability distributions assumed for these variables include lognormal, normal, and triangular. The algorithm allows assessment of the uncertainty and risk associated with toll revenue forecasts.
This document summarizes key points from Lecture 2 of the Introduction to Programming in MATLAB course. It discusses user-defined functions, including function declarations and overloading functions. Flow control statements like if/else and for loops are explained. Various plotting functions and options are covered, such as line, image, surface, and 3D plots. Advanced plotting exercises demonstrate modifying a plotting function to include conditionals and subplotting multiple axes. Specialized plotting functions like polar, bar, and quiver are also mentioned.
This document introduces hidden Markov models (HMMs). It defines the key components of HMMs, including states, observations, transition probabilities, and observation probabilities. It provides an example of an HMM for weather prediction with hidden states of "Rain" and "Dry" and observations of the weather. It also discusses the main problems in using HMMs, including evaluation, decoding, and learning problems. Forward-backward and Viterbi algorithms are introduced for efficiently solving the evaluation and decoding problems, respectively.
The document discusses different techniques for filling polygons, including boundary fill, flood fill, and scan-line fill methods. It explains that boundary fill and flood fill work by recursively filling neighboring pixels of the same color until reaching the polygon boundary. Scan-line fill works by drawing pixels between edge intersections on each scan line from top to bottom of the polygon. Special cases like handling vertices and updating edge positions are important to the scan-line fill algorithm.
This document provides information on combinational logic circuits and summarizes steps for analyzing combinational logic problems using truth tables and Karnaugh maps. It begins by defining combinational circuits as those whose outputs solely depend on current inputs, as opposed to sequential circuits which use memory elements. It then provides examples of writing truth tables and deriving Boolean expressions from problem statements. The document also covers standard forms of sum of products and product of sums, and methods for simplifying expressions using Karnaugh maps including grouping cells and rules for grouping.
This document provides information on combinational logic circuits and techniques for analyzing them, including:
1. Combinational circuits have outputs that solely depend on current inputs, unlike sequential circuits which use memory elements.
2. Truth tables are used to represent the relationships between inputs and outputs, and techniques like Karnaugh maps can simplify Boolean expressions.
3. Karnaugh maps arrange minterms or maxterms in a grid, allowing groups of redundant variables to be identified and simplified. Standard forms like sum of products can be plotted and minimized on the map.
The document describes string comparison techniques using matrix algebra and seaweed matrices. It introduces the concept of semi-local string comparison, which involves comparing a whole string to substrings of another string. The key idea is representing string comparison matrices implicitly using seaweed matrices, which represent unit-Monge matrices. This allows developing algebraic techniques for efficiently multiplying such matrices using the algebra of braids and the seaweed monoid. These multiplication techniques can then be applied to problems like dynamic programming string comparison and comparing compressed strings.
The document provides an overview of the KNIME analytics platform and its capabilities. It discusses:
- KNIME's origins, offices, codebase, and application areas including pharma, healthcare, finance, retail, and more.
- The key components of the KNIME platform including data access, transformation, analysis, visualization, and deployment capabilities.
- Integrations with tools like R, Weka, databases, and file formats.
- Community contributions expanding KNIME's functionality in areas like bioinformatics, chemistry, image processing, and more.
Ядерный век прошел, и становится все понятнее, что в фокусе науки 21-го века будут живые системы, медицина, и человек во всех его проявлениях. Здесь осуществляются самые масштабные финансовые вливания, и на эту отрасль человечество возлагает самые большие надежды. Все чаще слышатся предметные обсуждения тем, казавшихся еще недавно научной фантастикой: сможет ли человечество победить старение, рак, и другие смертельные заболевания? Сможет ли менять свой геном по собственному желанию? Будем ли мы хозяевами своим телам в той же мере, как мы хозяйничаем на Земле?
Многие десятилетия биология и медицина развивались как описательные науки. Однако по мере созревания и накопления информации, любая наука рано или поздно переходит на более точный язык - язык математики. Проект "Геном человека" обеспечил технологический прорыв, который будет питать науку о живом еще много лет - но который также поставил много новых глобальных вопросов перед современными учеными.
Иммунотерапия раковых опухолей: взгляд со стороны системной биологии. Максим ...BioinformaticsInstitute
This document summarizes recent advances in cancer immunotherapy from the perspective of systems biology. It discusses how checkpoint blockade immunotherapy works by addressing the second co-inhibitory checkpoint signal needed for T cell activation. Computational methods are now able to identify tumor-specific neoantigens that can be targeted by immunotherapy. Mouse model studies showed that certain tumors are naturally rejected due to expression of a mutant antigen recognized by T cells, and that antigen-specific T cells are present before immunotherapy treatment. The high mutational load in melanoma makes it particularly responsive to checkpoint blockade. Early work in the 19th century by William Coley observed tumor regression following bacterial infection, which led to development of a toxin mixture that resembled modern vaccine formulations. Members of
http://bioinformaticsinstitute.ru/guests
В пятницу 10 октября в 19.00 Мария Шутова (ИоГЕН РАН) выступала в Институте биоинформатики с открытой лекцией, посвященной изучению рака.
Рак -- одна из наиболее распространенных причин смерти по всему миру. В лекции рассматривается, как знания об эволюции, работе генома, репрограммировании, а также использование биоинформатических методов помогли лучше понять, как развивается раковая опухоль и предложить новые методы лечения разнообразных типов рака. Рассмотрены мышиные модели развития рака и интересные результаты, которые были получены с их помощью.
http://bioinformaticsinstitute.ru/lectures
Гостевая лекция Института биоинформатики, 9 октября 2014. Лектор -- Мария Шутова (ИоГЕН РАН).
За последние десять лет плюрипонтентные клетки стали героями двух Нобелевских премий и многих тысяч научных и научно-популярных статей. Их уникальная возможность превращаться в любую клетку взрослого организма до сих пор дает пищу для ума как биологам развития, так и ученым, ищущим способы лечения генетических заболеваний. В лекции будет рассказано о двух типах плюрипотентных клеток: "естественных" (эмбриональные стволовые клетки) и "искусственных" (индуцированные плюрипотентные стволовые клетки). Отдельно мы остановимся на том, как знания о работе транскрипционных факторов помогли репрограммировать клетки, и как эти "искусственные" плюрипотентные клетки можно использовать в медицине.
Секвенирование как инструмент исследования сложных фенотипов человека: от ген...BioinformaticsInstitute
This document summarizes genetic analyses of complex human phenotypes. It describes whole genome sequencing of individuals from bipolar disorder families and finding an association between genetic variation in a chromosome 6 region and amygdala volume. It also discusses rare variant sequencing of metabolic syndrome-related genes in Finnish cohorts, identifying new signals beyond existing GWAS hits. Additionally, it outlines exome and targeted sequencing of Tourette syndrome pedigrees, with a genome-wide significant result in a long non-coding RNA gene linked to the trait.
В своей лекции Андрей Афанасьев рассказал о стартапах в биотехе и биоинформатике и своем биоинформатическом проекте iBinom, разобрал несколько биотехнологических проектов глазами инноваторов и инвесторов, а также коснулся вопроса поиска инвестиций и поделился личным опытом взаимодействия с венчурными фондами и институтами развития.
This document provides an overview of the ENCODE project and how its data can be accessed through the UCSC Genome Browser. It discusses the different types of ENCODE data available, including mapping data, gene annotations, expression data, regulatory information, and genetic variation. It also explains how to find, view, and download ENCODE tracks from the Genome Browser and where to get more information about ENCODE. The overall goal of the ENCODE project is to identify all functional elements in the human genome.
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?Speck&Tech
ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...SOFTTECHHUB
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
“An Outlook of the Ongoing and Future Relationship between Blockchain Technologies and Process-aware Information Systems.” Invited talk at the joint workshop on Blockchain for Information Systems (BC4IS) and Blockchain for Trusted Data Sharing (B4TDS), co-located with with the 36th International Conference on Advanced Information Systems Engineering (CAiSE), 3 June 2024, Limassol, Cyprus.
Maruthi Prithivirajan, Head of ASEAN & IN Solution Architecture, Neo4j
Get an inside look at the latest Neo4j innovations that enable relationship-driven intelligence at scale. Learn more about the newest cloud integrations and product enhancements that make Neo4j an essential choice for developers building apps with interconnected data and generative AI.
Essentials of Automations: The Art of Triggers and Actions in FMESafe Software
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
Dr. Sean Tan, Head of Data Science, Changi Airport Group
Discover how Changi Airport Group (CAG) leverages graph technologies and generative AI to revolutionize their search capabilities. This session delves into the unique search needs of CAG’s diverse passengers and customers, showcasing how graph data structures enhance the accuracy and relevance of AI-generated search results, mitigating the risk of “hallucinations” and improving the overall customer journey.
Communications Mining Series - Zero to Hero - Session 1DianaGray10
This session provides introduction to UiPath Communication Mining, importance and platform overview. You will acquire a good understand of the phases in Communication Mining as we go over the platform with you. Topics covered:
• Communication Mining Overview
• Why is it important?
• How can it help today’s business and the benefits
• Phases in Communication Mining
• Demo on Platform overview
• Q/A
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AIVladimir Iglovikov, Ph.D.
Presented by Vladimir Iglovikov:
- https://www.linkedin.com/in/iglovikov/
- https://x.com/viglovikov
- https://www.instagram.com/ternaus/
This presentation delves into the journey of Albumentations.ai, a highly successful open-source library for data augmentation.
Created out of a necessity for superior performance in Kaggle competitions, Albumentations has grown to become a widely used tool among data scientists and machine learning practitioners.
This case study covers various aspects, including:
People: The contributors and community that have supported Albumentations.
Metrics: The success indicators such as downloads, daily active users, GitHub stars, and financial contributions.
Challenges: The hurdles in monetizing open-source projects and measuring user engagement.
Development Practices: Best practices for creating, maintaining, and scaling open-source libraries, including code hygiene, CI/CD, and fast iteration.
Community Building: Strategies for making adoption easy, iterating quickly, and fostering a vibrant, engaged community.
Marketing: Both online and offline marketing tactics, focusing on real, impactful interactions and collaborations.
Mental Health: Maintaining balance and not feeling pressured by user demands.
Key insights include the importance of automation, making the adoption process seamless, and leveraging offline interactions for marketing. The presentation also emphasizes the need for continuous small improvements and building a friendly, inclusive community that contributes to the project's growth.
Vladimir Iglovikov brings his extensive experience as a Kaggle Grandmaster, ex-Staff ML Engineer at Lyft, sharing valuable lessons and practical advice for anyone looking to enhance the adoption of their open-source projects.
Explore more about Albumentations and join the community at:
GitHub: https://github.com/albumentations-team/albumentations
Website: https://albumentations.ai/
LinkedIn: https://www.linkedin.com/company/100504475
Twitter: https://x.com/albumentations
Removing Uninteresting Bytes in Software FuzzingAftab Hussain
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Building RAG with self-deployed Milvus vector database and Snowpark Container...Zilliz
This talk will give hands-on advice on building RAG applications with an open-source Milvus database deployed as a docker container. We will also introduce the integration of Milvus with Snowpark Container Services.
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
2. Outline
1. CG-Islands
2. The “Fair Bet Casino”
3. Hidden Markov Model
4. Decoding Algorithm
5. Forward-Backward Algorithm
6. Profile HMMs
7. HMM Parameter Estimation
8. Viterbi Training
9. Baum-Welch Algorithm
3. Outline - CHANGE
• The “Fair Bet Casino” – improve graphics in “HMM for Fair
Bet Casino (con‟d)”
• Decoding Algorithm – SHOW the two-row graph for casino
problem
• Forward-Backward Algorithm – SHOW the similarity in
dynamic programming equation between Viterbi and forward-
backward algorithm
• HMM Parameter Estimation – explain the idea of Baum-
Welch
• Profile HMM Alignment SHOW “Profile HMM” slide more
slowly – show M states first and add I and D slides later on –
SHOW an alignment in terms of M, I, D states
• it is not clear how p(xi) term appears after / in “Profile HMM
alignment: Dynamic Programming” – MAKE a dynamic
5. CG-Islands
• Given 4 nucleotides: probability of any one‟s occurrence is ~
1/4.
• Thus, probability of occurrence of a given dinucleotide (pair
of successive nucleotides is ~ 1/16.
• However, the frequencies of dinucleotides in DNA sequences
vary widely.
• In particular, CG is typically underepresented (frequency of CG
is typically < 1/16)
6. CG-Islands
• CG is the least frequent dinucleotide because the C in CG is
easily methylated and has the tendency to mutate into T
afterwards.
• However, methylation is suppressed around genes in a
genome. So, CG appears at relatively high frequency within
these CG-islands.
• So, finding the CG-islands in a genome is an important
biological problem.
8. The “Fair Bet Casino”
• The CG-islands problem can be modeled after a problem
named The Fair Bet Casino.
• The game is to flip two coins, which results in only two
possible outcomes: Head (H) or Tail(T).
• The Fair coin (F) will give H and T each with probability
½, which is written P(H | F) = P(T | F) = ½.
• The Biased coin (B) will give H with probability ¾, which
we write as P(H | B) = ¾, P(T | B) = ¼.
• The crooked dealer changes between F and B coins with
probability 10%.
• How can we tell when the dealer is using F and when he is
using B?
9. The Fair Bet Casino Problem
• Input: A sequence x = x1x2x3…xn of coin tosses made by two
possible coins (F or B).
• Output: A sequence π = π1 π2 π3… πn, with each πi being either
F or B and indicating that xi is the result of tossing the Fair or
Biased coin respectively.
10. Problem…
• Any observed outcome of coin tosses could have been
generated by any sequence of states!
• Example: HHHHHHHHHH could be generated by
BBBBBBBBBB, FFFFFFFFFF, FBFBFBFBFB, etc.
• We need to incorporate a way to grade different sequences
differently.
• This provides us with the decoding problem.
11. Simple Case: The Dealer Never Switches Coins
• We assume first that the dealer never changes coins:
• P(x | F): probability of the dealer using F and generating the
outcome x.
• P(x | B): probability of the dealer using the B coin and
generating outcome x.
• Example: Say that in x we observe k heads and n – k tails:
P x F
1
2
1
2
n
i1
n
P ( x B)
3
4
k
1
4
n k
3
k
4
n
12. When Does P(x | F) = P(x | B)?
P(x F) P(x B)
1
2
n
3
k
4
n
2
n
3
k
n log 2
3
k
n k log 2 3
k
n
log 2 3
13. Log-odds Ratio
• We define the log-odds ratio (L) as follows:
• From the previous slide, if L > 0 we have reason to believe that
the coin is fair, and if L < 0 we think the coin is biased.
L log 2
P x F
P x B
log 2
1
2
n
log 2
3
k
4
n
n log 2 3
k
log 2 4
n
n k log 2 3 2n
n k log 2
3
14. • Consider a sliding window of the outcome sequence and find
the log-odds ratio for this short window.
x1x2x3x4x5x6x7x8…xn
Computing Log-odds Ratio in Sliding Windows
Log-odds value
0
Fair coin most likely
used
Biased coin most likely
used
• Key Disadvantages:
• The length of the CG-island is not known in advance.
• Different windows may classify the same position differently.
15. • Consider a sliding window of the outcome sequence and find
the log-odds ratio for this short window.
x1x2x3x4x5x6x7x8…xn
Computing Log-odds Ratio in Sliding Windows
Log-odds value
0
Fair coin most likely
used
Biased coin most likely
used
• Key Disadvantages:
• The length of the CG-island is not known in advance.
• Different windows may classify the same position differently.
16. • Consider a sliding window of the outcome sequence and find
the log-odds ratio for this short window.
x1x2x3x4x5x6x7x8…xn
Computing Log-odds Ratio in Sliding Windows
Log-odds value
0
Fair coin most likely
used
Biased coin most likely
used
• Key Disadvantages:
• The length of the CG-island is not known in advance.
• Different windows may classify the same position differently.
17. • Consider a sliding window of the outcome sequence and find
the log-odds ratio for this short window.
x1x2x3x4x5x6x7x8…xn
Computing Log-odds Ratio in Sliding Windows
Log-odds value
0
Fair coin most likely
used
Biased coin most likely
used
• Key Disadvantages:
• The length of the CG-island is not known in advance.
• Different windows may classify the same position differently.
18. • Consider a sliding window of the outcome sequence and find
the log-odds ratio for this short window.
x1x2x3x4x5x6x7x8…xn
Computing Log-odds Ratio in Sliding Windows
Log-odds value
0
Fair coin most likely
used
Biased coin most likely
used
• Key Disadvantages:
• The length of the CG-island is not known in advance.
• Different windows may classify the same position differently.
20. Hidden Markov Model (HMM)
• Can be viewed as an abstract machine with k hidden states that
emits symbols from an alphabet Σ.
• Each state has its own probability distribution, and the
machine switches between states and chooses characters
according to this probability distribution.
• While in a certain state, the machine makes two decisions:
1. What state should I move to next?
2. What symbol - from the alphabet Σ - should I emit?
21. Why “Hidden”?
• Observers can see the emitted symbols of an HMM but have
no ability to know which state the HMM is currently in.
• The goal is to infer the most likely hidden states of an HMM
based on the given sequence of emitted symbols.
22. HMM Parameters
• Σ: set of emission characters.
• Q: set of hidden states, each emitting symbols from Σ.
• A = (akl): a |Q| x |Q| matrix containing the probabilities of
changing from state k to state l.
• E = (ek(b)): a |Q| x |Σ| matrix of probability of emitting symbol
b while being in state k.
23. HMM Parameters
• A = (akl): a |Q| x |Q| matrix containing the probabilities of
changing from state k to state l.
• aFF = 0.9 aFB = 0.1
• aBF = 0.1 aBB = 0.9
• E = (ek(b)): a |Q| x |Σ| matrix of probability of emitting symbol
b while being in state k.
• eF(0) = ½ eF(1) = ½
• eB(0) = ¼ eB(1) = ¾
24. HMM for the Fair Bet Casino
Fair Biased
Fair aFF = 0.9 aFB = 0.1
Biased aBF = 0.1 aBB = 0.9
Tails(0) Heads(1)
Fair eF(0) = ½ eF(1) = ½
Biased eB(0) =
¼
eB(1) =
¾
• The Fair Bet Casino in HMM terms:
• Σ = {0, 1} (0 for T and 1 for H)
• Q = {F, B}
Transition Probabilities (A) Emission Probabilities (E)
25. HMM for the Fair Bet Casino
• HMM model for the Fair Bet Casino Problem:
26. Hidden Paths
x 0 1 0 1 1 1 0 1 0 0 1
π = F F F B B B B B F F F
P(xi|πi)
P(πi-1 πi)
Transition probability from state πi-1 to state πi
Probability that xi was emitted from state πi
• A path π = π1… πn in the HMM is defined as a sequence of
states.
• Consider path π = FFFBBBBBFFF and sequence x =
01011101001
27. Hidden Paths
x 0 1 0 1 1 1 0 1 0 0 1
π = F F F B B B B B F F F
P(xi|πi) ½ ½ ½ ¾ ¾ ¾ ¼ ¾ ½ ½ ½
P(πi-1 πi)
Transition probability from state πi-1 to state πi
Probability that xi was emitted from state πi
• A path π = π1… πn in the HMM is defined as a sequence of
states.
• Consider path π = FFFBBBBBFFF and sequence x =
01011101001
28. Hidden Paths
x 0 1 0 1 1 1 0 1 0 0 1
π = F F F B B B B B F F F
P(xi|πi) ½ ½ ½ ¾ ¾ ¾ ¼ ¾ ½ ½ ½
P(πi-1 πi) ½ 9/10
9/10
1/10
9/10
9/10
9/10
9/10
1/10
9/10
9/10
Transition probability from state πi-1 to state πi
Probability that xi was emitted from state πi
• A path π = π1… πn in the HMM is defined as a sequence of
states.
• Consider path π = FFFBBBBBFFF and sequence x =
01011101001
29. P(x | π) Calculation
• P(x | π): Probability that sequence x was generated if we know
that we have the path π.
P x P 0 1 P xi
i1
n
P i i1
a 0 , 1
e i
x a i , i 1
i1
n
30. P(x | π) Calculation
• P(x | π): Probability that sequence x was generated if we know
that we have the path π.
P x P 0 1 P xi
i1
n
P i i1
a 0 , 1
e i
x a i , i 1
i1
n
e i
x a i , i 1
i 0
n
32. Decoding Problem
• Goal: Find an optimal hidden path of states given observations.
• Input: Sequence of observations x = x1…xn generated by an
HMM M(Σ, Q, A, E).
• Output: A path that maximizes P(x | π) over all possible paths π.
33. Building Manhattan for Decoding Problem
• Andrew Viterbi used the Manhattan edit graph model to solve
the Decoding Problem.
• Vertices are composed of n “levels” with |Q| vertices in each
level; each vertex represents a different state.
• We connect each vertex in level i to each vertex in level i + 1
via a directed edge, giving |Q|2(n – 1) edges.
• Therefore every choice of π = π1… πn corresponds to a path in
the graph.
35. Decoding Problem vs. Alignment Problem
Valid Directions in
Alignment Valid Directions in Decoding
36. Decoding Problem
• Every path in the graph has the probability P(x | π).
• The Viterbi algorithm finds the path that maximizes P(x | π)
among all possible paths.
• The Viterbi algorithm runs in O(n |Q|2) time.
38. • The weight w is given by: ?
Decoding Problem: Weights of Edges
w
(k, i) (l, i+1)
P x e i 1
xi1 a i , i 1
i 0
n 1
39. • The weight w is given by: ?
Decoding Problem: Weights of Edges
w
(k, i) (l, i+1)
P x e i 1
xi1 a i , i 1
i 0
n 1
i
th
term e i 1
xi1 a i , i 1
40. • The weight w is given by: el (xi+1) . ak, l
Decoding Problem: Weights of Edges
w
(k, i) (l, i+1)
P x e i 1
xi1 a i , i 1
i 0
n 1
i
th
term e i 1
xi1 a i , i 1
41. Decoding Problem and Dynamic Programming
• sl, i+1 = max probability of all paths of length i + 1 ending in
state l (for the first i + 1 observations).
• Recursion:
sl, i1 max
kQ
sk, i weight of edge between k, i and l, i 1
max
kQ
sk, i ak, l el xi1
el xi1 max
kQ
sk, i ak, l
42. • The value of the product can become extremely small, which
leads to overflow.
• A computer has only finite storage to store any given
number, and if the number is too small it runs out of room.
• To avoid overflow, take the logarithm of the right side instead.
Decoding Problem and Dynamic Programming
sl, i1 log el xi1 max
kQ
log sk, i log ak, l
43. Decoding Problem and Dynamic Programming
• Initialization:
• Let π* be the optimal path. Then,
P x
max
kQ
sk, n ak, end
sk, 0
1 if k begin
0 otherwise
45. Forward-Backward Problem
• Given: a sequence of coin tosses generated by an HMM.
• Goal: Find the probability that the dealer was using a biased
coin at a particular time.
46. Forward Probability
• Define fk,i (forward probability) as the probability of
emitting the prefix x1…xi and reaching the state π = k.
• The recurrence for the forward algorithm:
fk,i ek xi fl, i1 al,k
lQ
47. Backward Probability
• However, forward probability is not the only factor affecting
P(πi = k | x).
• The sequence of transitions and emissions that the HMM
undergoes between πi+1 and πn also affect P(πi = k | x).
• Define the backward probability bk,i as the probability of
being in state πi = k and emitting the suffix xi+1…xn. Recurrence:
Forward Backwardxi
bk,i el xi1
lQ
bl,i1 ak,l
48. Backward-Forward Probability
• The probability that HMM is in a certain state k at any
moment i, given that we observe the output x, is therefore
influenced by both the forward and backward probabilities.
• We use the mathematical definition of conditional
probability to calculate P(πi = k | x):
P i k x
P x, i k
P x
fk, i bk, i
P x
50. Finding Distant Members of a Protein Family
• A distant cousin of functionally related sequences in a protein
family may have weak pairwise similarities with each member
of the family and thus fail a significance test.
• However, they may have these weak similarities with many
members of the family, indicating a correlation.
• The goal is to align a sequence to all members of the family at
once.
• A family of related proteins can be represented by their
multiple alignment and the corresponding profile.
51. Profile Representation of Protein Families
• Aligned DNA sequences can be represented by a 4 x n profile
matrix reflecting the frequencies of nucleotides in every aligned
position.
• Example:
• Similarly, a protein family can be represented by a 20 x n
profile representing frequencies of amino acids.
52. • Multiple alignment of a protein family shows variations in
conservation along the length of a protein.
• Example: After aligning many globin proteins, biologists
recognized that the helices region in globins are more
conserved than others.
Protein Family Classification
53. • A profile HMM is a probabilistic representation of a multiple
alignment.
• A given multiple alignment (of a protein family) is used to
build a profile HMM.
• This model then may be used to find and score less obvious
potential matches of new protein sequences.
What Is a Profile HMM?
54. Profile HMM
• A profile HMM has three sets of states:
• Match states: M1 ,…, Mn (plus begin/end states)
• Insertion states: I0 , I1 ,…, In
• Deletion states: D1 ,…, Dn
55. 1. Multiple alignment is used to construct the HMM model.
2. Assign each column to a Match state in HMM. Add Insertion
and Deletion state.
3. Estimate the emission probabilities according to amino acid
counts in column. Different positions in the protein will have
different emission probabilities.
4. Estimate the transition probabilities between Match, Deletion
and Insertion states.
Building a Profile HMM
56. Transition Probabilities in a Profile HMM
• Gap Initiation Penalty: The cost of beginning a gap, which
means that we must have transitions from match state to insertion
state and vice versa.
• Penalty:
• Gap Extension Penalty: The cost of extending a gap, which
corresponds to maintaining the insertion state for one period.
• Penalty:
log aMI log aIM
log aII
57. Emission Probabilities in a Profile HMM
• Probabilty of emitting a symbol a at an insertion state Ij:
• Here p(a) is the frequency of the occurrence of the symbol a
in all the sequences.
eI j
a p a
58. Profile HMM Alignment
• Define vM
j (i) as the logarithmic likelihood score of the best
path for matching x1..xi to the profile HMM ending with xi
emitted by the state Mj.
• vI
j (i) and vD
j (i) are defined similarly.
59. Profile HMM Alignment: Dynamic Programming
v j
M
i log
eM j
xi
p xi
max
v j 1
M
i 1 log aM j 1 , M j
v j 1
I
i 1 log aI j 1 , M j
v j 1
D
i 1 log aD j 1 , M j
60. Profile HMM Alignment: Dynamic Programming
v j
I
i log
eI j
xi
p xi
max
v j
M
i 1 log aM j , I j
v j
I
i 1 log aI j , I j
v j
D
i 1 log aD j , I j
61. Paths in Edit Graph and Profile HMM
• At right is a path
through an edit graph
and the corresponding
path through a profile
HMM.
• Observe:
• Diagonalmatch
• Verticalinsertion
• Horizontaldeletion
62. 1. Use BLAST to separate a protein database into families of related
proteins.
2. Construct a multiple alignment for each protein family.
3. Construct a profile HMM model and optimize the parameters of the
model (transition and emission probabilities).
4. Align the target sequence against each HMM to find the best fit
between a target sequence and an HMM.
Making a Collection of HMM for Protein Families
63. Profile HMMs and Modeling Globin Proteins
• Globins represent a large collection of protein sequences.
• 400 globin sequences were randomly selected from all globins
and used to construct a multiple alignment.
• Multiple alignment was used to assign an HMM.
• 625 remaining globin sequences were aligned to the HMM,
resulting in a multiple alignment. This multiple alignment was
in a good agreement with the structurally derived alignment.
• Other proteins, were randomly chosen from the database and
compared against the globin HMM.
• This experiment resulted in an excellent separation between
globin and non-globin families.
64. • Pfam decribes protein domains.
• Each protein domain family in Pfam has:
• Seed alignment: Manually verified multiple alignment of a
representative set of sequences.
• HMM: Built from the seed alignment for further searches.
• Full alignment: Generated automatically from the HMM.
• The distinction between seed and full alignments facilitates
Pfam updates.
• Seed alignments are stable resources.
• HMM profiles and full alignments can be updated with
newly found amino acid sequences.
PFAM
65. • Pfam HMMs span entire domains that include both well-
conserved motifs and less-conserved regions with insertions
and deletions.
• It results in modeling complete domains that facilitates better
sequence annotation and leads to more sensitive detection.
PFAM Uses
67. HMM Parameter Estimation
• So far, we have assumed that the transition and emission
probabilities are known.
• However, in most HMM applications, the probabilities are not
known. It is very difficult to estimate the probabilities.
68. HMM Parameter Estimation Problem
• Given: HMM with states and alphabet (emission characters),
as well as independent training sequences x1, … xm.
• Goal: Find HMM parameters Θ (that is, ak,,b , ek(b) that
maximize the joint probability of the training sequences, which
is given by the following:
P x
1
,K , x
m
69. • P(x1, …, xm | Θ) as a function of Θ is called the likelihood of
the model.
• The training sequences are assumed independent; therefore,
• The parameter estimation problem seeks Θ that realizes
• In practice the log likelihood is computed to avoid underflow
errors.
i
i
xP )|(max
Maximize the Likelihood
P x
1
,K , x
m
P x
i
i1
m
70. 1. Known paths for training sequences:
• CpG islands marked on training sequences
• Casino analogue: One evening the dealer allows us to see when
he changes the dice.
2. Unknown paths for training sequences:
• CpG islands are not marked
• We do not see when the casino dealer changes dice
Two Situations
71. • Akl = # of times each k l is taken in the training sequences.
• Ek(b) = # of times b is emitted from state k in the training
sequences.
• Compute akl and ek(b) as maximum likelihood estimators:
Known Paths
ak, l
Ak, l
Ak, l'
l'
ek b
E k b
E k b'
b '
72. • Some state k may not appear in any of the training sequences. This
means Ak, l = 0 for every state l and ak, l cannot be computed with
the given equation.
• To avoid this overfitting, use predetermined pseudocounts rkl and
rk(b) which reflect prior biases about the probability values:
• Ak, l = number of transitions kl + rk, l
• Ek(b) = number of emissions of b from k + rk(b)
Pseudocounts
74. Unknown Paths Method 1: Viterbi Training
• Idea: Use Viterbi decoding to compute the most probable path
for training sequence x.
• Method:
1. Start with some guess for initial parameters and compute
π* = the most probable path for x using initial parameters.
2. Iterate until no change in π*.
3. Determine Ak, l and Ek(b) as before.
4. Compute new parameters ak, l and ek(b) using the same
formulas as before.
5. Compute new π* for x and the current parameters.
75. • The algorithm converges precisely.
• There are finitely many possible paths.
• New parameters are uniquely determined by the current π*.
• There may be several paths for x with the same probability, hence
we must compare the new π* with all previous paths having highest
probability.
• Does not maximize the likelihood Πx P(x | Θ) but rather the
contribution to the likelihood of the most probable path,
Πx P(x | Θ, π*).
• In general, performs less well than Baum-Welch (below).
Viterbi Training Analysis
77. • Idea: Guess initial values for parameters.
• This is art and experience, not science.
• We then estimate new (better) values for parameters.
• How?
• We repeat until stopping criterion is met.
• What criterion?
Unknown Paths Method 2: Baum-Welch
78. • We would need the Ak,l and Ek(b) values, but the path is unknown,
and we do not want to use a most probable path.
• Therefore for all states k, l, symbols b, and training sequences x:
• Compute Ak,l and Ek(b) as expected values, given the current
parameters.
Improved Parameters
79. Probabilistic Setting for Ak,l
• Given our training sequences x1, … ,xm consider a discrete
probability space with elementary events εk,l, = “k l is taken in
x1, …, xm.”
• For each x in {x1,…,xm} and each position i in x let Yx,i be a
random variable defined by
• Define Y = Σx Σi Yx,i as the random variable which counts the
number of times the event εk,l happens in x1,…,xm.
Yx, i (k, l )
1 if i k and i1 l
0 otherwise
80. The meaning of Ak,l
• Let Akl be the expectation of Y:
• We therefore need to compute P(πi = k, πi+1 = l | x).
Ak, l E Y
E Yx, i
i
x
P Yx, i
1
i
x
P x, l
i
k and i1
l i
x
P i k, i1 l x
i
x
81. Probabilistic setting for Ek(b)
• Given x1, … ,xm , consider a discrete probability space with
elementary events εk,b = “b is emitted in state k in x1, … ,xm.”
• For each x in {x1,…,xm} and each position i in x, let Yx,i be a
random variable defined by
• Define Y = Σx Σi Yx,i as the random variable which counts the
number of times the event εk,b happens in x1,…,xm.
Yx, i k, b
1 if xi b and i k
0 otherwise
82. Computing New Parameters
• Consider a training sequence x = x1, … , xm.
• Concentrate on positions i and i + 1:
• Use the forward-backward values:
fk, i P x1 L xi i k
bk, i P xi1 L xn i k
83. Compute Ak,l (1)
• The probability k l is taken at position i of x:
• Compute P(x) using either forward or backward values.
• Expected number of times k l is used in training sequences:
P i k, i1 l x1 L xn
P x, i k, i1 l
P x
P x, i k, i1 l bl, i1 el xi1 ak, l fk, i
Ak, l
bl, i1 el xi1 ak, l fk, i
i
x
P x
84. Compute Akl(2)
P x, i k, i1 l P x1L xi, i k, i1 l, xi1L xn
P i1 l, xi1L xn x1L xi, i k P x1L xi, i k
P i1
l, xi1
L xn
i
k fk, i
P xi1L xn i k, i1 l P i1 l i k fk, i
P xi1L xn i1 l ak, l fk, i
P xi 2 L xn xi1, i1 l P xi1 i1 l ak, l fk, i
P xi 2 L xn i1 l el xi1 ak, l fk, i
bl, i1 el xi1 ak, l fk, i
85. Compute Ek(b)
• Probability that xi of x is emitted in state k:
• Expected number of times b is emitted in state k:
E k (b)
fk, i bk, i
P x i : xi b
x
P i k x1 L xn
P i k, x1 L xn
P x
P i k, x1 L xn P x1 L xi, i k, xi1 L xn
P xi1 L xn x1 L xi, i k P x1 L xi, i k
P xi1 L xn i k fk, i
bk, i fk, i
86. Finally, new parameters
• We can then add pseudocounts as before.
ak, l
Ak, l
Ak, l'
l'
ek (b)
E k b
E k b'
b'
• These methods allow us to calculate our new parameters ak, l
and ek(b):
87. Stopping criteria
• We cannot actually reach maximum (property of optimization of
continuous functions).
• Therefore we need stopping criteria.
• Compute the log likelihood of the model for current Θ :
• Compare with previous log likelihood.
• Stop if small difference.
• Stop after a certain number of iterations to avoid infinite loop.
log P x
x
88. • Initialization: Pick the best-guess for model parameters (or
arbitrary).
• Iteration:
1. Forward for each x
2. Backward for each x
3. Calculate Ak, l , Ek(b)
4. Calculate new ak, l , ek(b)
5. Calculate new log-likelihood
• Repeat until log-likelihood does not change much.
The Baum-Welch Algorithm Summarized
89. • Log-likelihood is increased by iterations.
• Baum-Welch is a particular case of the expectation
maximization (EM) algorithm.
• Convergence is to local maximum. The choice of initial
parameters determines local maximum to which the algorithm
converges.
Baum-Welch Analysis
90. Additional Application: Speech Recognition
• Create an HMM of the words in a language.
• Each word is a hidden state in Q.
• Each of the basic sounds in the language is a symbol in Σ.
• Input: Fragment of speech.
• Goal: Find the most probable sequence of states.
91. Speech Recognition: Building the Model
• Analyze some large source of English sentences, such as a
database of newspaper articles, to form probability matrices.
• A0i: The chance that word i begins a sentence.
• Aij: The chance that word j follows word i.
• Analyze English speakers to determine what sounds are
emitted with what words.
• Ek(b): the chance that sound b is spoken in word k. Allows for
alternate pronunciation of words.
92. Speech Recognition: Using the Model
• Use the same dynamic programming algorithm as before.
• Weave the spoken sounds through the model the same way
we wove the rolls of the die through the casino model.
• π will therefore represent the most likely set of words.
93. Using the Model
• How well does the model work?
• Common words, such as „the‟, „a‟, „of‟ make prediction less
accurate, since there are so many words that follow normally.
94. Improving Speech Recognition
• Initially, we were using a bigram, or a graph connecting every
two words.
• Expand that to a trigram.
• Each state represents two words spoken in succession.
• Each edge joins those two words (A B) to another state
representing (B C).
• Requires n3 vertices and edges, where n is the number of
words in the language.
• Much better, but still limited context.