The document discusses the problem of finding the longest common subsequence (LCS) between two sequences. It presents a brute force algorithm that has exponential runtime complexity. It then introduces an dynamic programming approach that uses a table c[i,j] to store the length of the LCS between prefixes of the two sequences. The values in the table satisfy a recursive relationship, allowing the LCS to be found in polynomial time complexity. The approach exploits the optimal substructure property of the problem.
This document discusses the longest common subsequence (LCS) problem and how to solve it using dynamic programming. It begins by defining key terms like subsequence and common subsequence. It then describes the optimal substructure of LCS problems and how they can be broken down into overlapping subproblems. The document provides pseudocode that uses dynamic programming to fill a table to compute the length of the LCS between two sequences in O(mn) time and also construct the optimal LCS. An example is worked through and references are provided.
Definition: Sequence, Subsequence, Longest common subsequence.
Example of subsequence.
Using application details.
Lcs algorithm( Brief ).
LCS recursive solution.
Additional Information of lcs simulation.
CODE: LCS-LENGTH(H, Z, m, n).
Example of simulation.
Constructing a LCS
CODE:PRINT-LCS
Longest common subsequences in Algorithm AnalysisRajendran
The document discusses dynamic programming and the longest common subsequence (LCS) problem. It provides an example of using dynamic programming to find the LCS of two strings "ABCB" and "BDCAB" in multiple steps. The algorithm builds up the solution by filling a 2D array c[m,n] where m and n are the lengths of the two strings. Each entry c[i,j] represents the length of the LCS of the prefixes of length i and j of the two strings. The running time is O(mn).
The document describes the longest common subsequence (LCS) problem and its dynamic programming solution. It provides an example to illustrate how the LCS algorithm works by finding the LCS of strings "ABCB" and "BDCAB" in multiple steps. The algorithm runs in O(mn) time, where m and n are the lengths of the two strings, by filling a 2D array c[m+1][n+1] recursively. It can also be modified to recover the actual LCS by tracking the entries that were calculated as c[i-1,j-1]+1 while filling the array.
The document discusses the longest common subsequence (LCS) problem and how to solve it using dynamic programming. It begins by defining LCS as the longest sequence of characters that appear left-to-right in two given strings. It then describes solving LCS using a brute force method with exponential time complexity and using dynamic programming with polynomial time complexity. Finally, it provides an example of finding the LCS of two strings and discusses applications and references.
This document discusses the longest common subsequence problem and provides an example of how it can be solved using dynamic programming. It begins by defining the problem of finding the longest subsequence that is common to two input sequences. It then shows that this problem exhibits optimal substructure and can be solved recursively. However, a recursive solution is inefficient due to redundant subproblem computations. Instead, it presents an algorithm that uses dynamic programming to compute the length of the longest common subsequence in O(mn) time by filling out a 2D table in a bottom-up manner and returning the value at the last index. It also describes how to construct the actual longest common subsequence by tracing back through the table.
The document discusses dynamic programming and amortized analysis. It reviews how dynamic tables use amortized analysis to achieve an overall cost of O(1) per insertion by occasionally doubling the table size and reinserting all elements. This results in a worst case cost of O(n) for a single insertion but averages to O(1) over many insertions. It also discusses using an accounting method with a $3 charge per insertion to pay for future table resizes, achieving an amortized cost of O(1) per operation. Finally, it introduces dynamic programming and uses the longest common subsequence problem to illustrate how it breaks problems into optimal subrecurring subproblems.
The document discusses dynamic programming and its application to solving the longest common subsequence (LCS) problem. It presents the LCS algorithm, which uses dynamic programming to find the length and sequence of the longest subsequence common to two strings X and Y in O(mn) time, where m and n are the lengths of X and Y, respectively. It provides an example running the LCS algorithm on strings X="ABCB" and Y="BDCAB" to determine their longest common subsequence is "BCB".
This document discusses the longest common subsequence (LCS) problem and how to solve it using dynamic programming. It begins by defining key terms like subsequence and common subsequence. It then describes the optimal substructure of LCS problems and how they can be broken down into overlapping subproblems. The document provides pseudocode that uses dynamic programming to fill a table to compute the length of the LCS between two sequences in O(mn) time and also construct the optimal LCS. An example is worked through and references are provided.
Definition: Sequence, Subsequence, Longest common subsequence.
Example of subsequence.
Using application details.
Lcs algorithm( Brief ).
LCS recursive solution.
Additional Information of lcs simulation.
CODE: LCS-LENGTH(H, Z, m, n).
Example of simulation.
Constructing a LCS
CODE:PRINT-LCS
Longest common subsequences in Algorithm AnalysisRajendran
The document discusses dynamic programming and the longest common subsequence (LCS) problem. It provides an example of using dynamic programming to find the LCS of two strings "ABCB" and "BDCAB" in multiple steps. The algorithm builds up the solution by filling a 2D array c[m,n] where m and n are the lengths of the two strings. Each entry c[i,j] represents the length of the LCS of the prefixes of length i and j of the two strings. The running time is O(mn).
The document describes the longest common subsequence (LCS) problem and its dynamic programming solution. It provides an example to illustrate how the LCS algorithm works by finding the LCS of strings "ABCB" and "BDCAB" in multiple steps. The algorithm runs in O(mn) time, where m and n are the lengths of the two strings, by filling a 2D array c[m+1][n+1] recursively. It can also be modified to recover the actual LCS by tracking the entries that were calculated as c[i-1,j-1]+1 while filling the array.
The document discusses the longest common subsequence (LCS) problem and how to solve it using dynamic programming. It begins by defining LCS as the longest sequence of characters that appear left-to-right in two given strings. It then describes solving LCS using a brute force method with exponential time complexity and using dynamic programming with polynomial time complexity. Finally, it provides an example of finding the LCS of two strings and discusses applications and references.
This document discusses the longest common subsequence problem and provides an example of how it can be solved using dynamic programming. It begins by defining the problem of finding the longest subsequence that is common to two input sequences. It then shows that this problem exhibits optimal substructure and can be solved recursively. However, a recursive solution is inefficient due to redundant subproblem computations. Instead, it presents an algorithm that uses dynamic programming to compute the length of the longest common subsequence in O(mn) time by filling out a 2D table in a bottom-up manner and returning the value at the last index. It also describes how to construct the actual longest common subsequence by tracing back through the table.
The document discusses dynamic programming and amortized analysis. It reviews how dynamic tables use amortized analysis to achieve an overall cost of O(1) per insertion by occasionally doubling the table size and reinserting all elements. This results in a worst case cost of O(n) for a single insertion but averages to O(1) over many insertions. It also discusses using an accounting method with a $3 charge per insertion to pay for future table resizes, achieving an amortized cost of O(1) per operation. Finally, it introduces dynamic programming and uses the longest common subsequence problem to illustrate how it breaks problems into optimal subrecurring subproblems.
The document discusses dynamic programming and its application to solving the longest common subsequence (LCS) problem. It presents the LCS algorithm, which uses dynamic programming to find the length and sequence of the longest subsequence common to two strings X and Y in O(mn) time, where m and n are the lengths of X and Y, respectively. It provides an example running the LCS algorithm on strings X="ABCB" and Y="BDCAB" to determine their longest common subsequence is "BCB".
Dynamic programming is used to solve optimization problems by breaking them down into overlapping subproblems. It solves subproblems only once, storing the results in a table to lookup when the same subproblem occurs again, avoiding recomputing solutions. Key steps are characterizing optimal substructures, defining solutions recursively, computing solutions bottom-up, and constructing the overall optimal solution. Examples provided are matrix chain multiplication and longest common subsequence.
This document contains 38 multiple choice questions related to data structures and algorithms. The questions cover topics such as trees, graphs, hashing, sorting, algorithm analysis, and complexity classes. They assess knowledge of concepts like tree traversals, shortest paths, minimum spanning trees, asymptotic analysis, and resolving collisions in hash tables.
The document contains 16 multiple choice questions about algorithms, data structures, and graph theory. Each question has 4 possible answers and the correct answer is provided. The maximum number of comparisons needed to merge sorted sequences is 358, and depth first search on a graph represented with an adjacency matrix has a worst case time complexity of O(n^2).
This document contains a 30 question mid-semester exam for a data structures and algorithms course. The exam covers topics like asymptotic analysis, sorting algorithms, hashing, binary search trees, and recursion. It provides multiple choice questions to test understanding of algorithm time complexities, worst-case inputs, and recursive functions. Students are instructed to attempt all questions in the 2 hour time limit and notify the proctor if any electronic devices other than calculators are used.
This document provides an introduction to support vector machines (SVMs). It discusses how SVMs can be used for binary classification, regression, and multi-class problems. SVMs find the optimal separating hyperplane that maximizes the margin between classes. Soft margins allow for misclassified points by introducing slack variables. Kernels are discussed for mapping data into higher dimensional feature spaces to perform linear separation. The document outlines the formulation of SVMs for classification and regression and discusses model selection and different kernel functions.
The document discusses dynamic programming and provides examples of problems that can be solved using dynamic programming including unidirectional traveling salesman problem, coin change, longest common subsequence, and longest increasing subsequence. Source code is presented for solving these problems using dynamic programming including dynamic programming tables, tracing optimal solutions, and time complexity analysis. Various online judges are listed that contain sample problems relating to these dynamic programming techniques.
This document discusses functions, limits, and continuity. It begins by defining functions, domains, ranges, and some standard real functions like constant, identity, modulus, and greatest integer functions. It then covers limits of functions including one-sided limits and properties of limits. Examples are provided to illustrate evaluating limits using substitution and factorization methods. The overall objectives are to understand functions, domains, ranges, limits of functions and methods to evaluate limits.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
(1) Jacobson's theorem states that if a division ring D satisfies the property that for every element a in D there exists an integer n(a)>1 such that an(a)=a, then D is a commutative field.
(2) The proof proceeds by showing that if a division ring D satisfies the given property, then D has characteristic p for some prime p. This implies D contains a subring W which is a finite field.
(3) It is then shown that if a,b are elements of D, they must also be elements of the subfield W. But W is a commutative field, so a and b must commute. This is a contradiction unless D=W,
ON THE COVERING RADIUS OF CODES OVER Z4 WITH CHINESE EUCLIDEAN WEIGHTijitjournal
In this paper, we give lower and upper bounds on the covering radius of codes over the ring Z4 with respect to chinese euclidean distance. We also determine the covering radius of various Repetition codes, Simplex codes Type α and Type β and give bounds on the covering radius for MacDonald codes of both types over Z4
1. The document discusses probability concepts related to single and multivariate random variables including probability density functions, cumulative distribution functions, expected value, variance, and common distributions.
2. It also covers topics related to bivariate and multivariate random variables such as joint probability, marginal probability, conditional probability, and the bivariate normal distribution.
3. The document then discusses random signals and linear estimation methods, including maximum likelihood estimation and mean square error estimation. It provides an example of estimating a signal using mean square error minimization.
The document discusses various concepts related to digital image processing including:
1) The relationships between pixels in an image including 4-neighbors, 8-neighbors, and m-neighbors of a pixel.
2) The concepts of adjacency and connectivity between pixels based on their intensity values and whether they are neighbors.
3) Computing the shortest path between two pixels using 4, 8, or m-adjacency and examples calculating these paths.
Iit jam 2016 physics solutions BY TrajectoryeducationDev Singh
1. The electric field at a point (a, b, 0) due to an infinitely long wire with uniform line charge density λ is given by E=λ/(2πε0)(a/r2)ex+(b/r2)ey, where r2=a2+b2.
2. For a 1W point source emitting light uniformly in all directions, the Poynting vector at the point (1, 1, 0) is 1/(8π)ex+(y/e)ey W/cm2.
3. A charged particle starting from the origin with velocity 3/2ex+2ez m/s in a uniform magnetic field B=B
This document provides information about a theoretical physics course, including the course code, homepage, lecturer contact information, textbook, main topics covered, and assessment details. The course covers complex variables and their applications in theoretical physics. Topics include Cauchy's integral formula, calculus of residues, partial differential equations, special functions, and Fourier series. Students will be assessed through a 3-hour written exam worth 80% and a course assessment worth 20%.
IIT Jam math 2016 solutions BY TrajectoryeducationDev Singh
The document contains a mathematics exam question paper with 10 single mark questions (Q1-Q10) and 20 two mark questions (Q11-Q30). The questions cover topics like sequences, linear transformations, integrals, permutations, differential equations etc. Some key questions asked about the nature of a sequence involving sines, order of a permutation, evaluating a limit, checking if a differential equation is exact etc. and provided solutions to them.
The document discusses various backtracking techniques including bounding functions, promising functions, and pruning to avoid exploring unnecessary paths. It provides examples of problems that can be solved using backtracking including n-queens, graph coloring, Hamiltonian circuits, sum-of-subsets, 0-1 knapsack. Search techniques for backtracking problems include depth-first search (DFS), breadth-first search (BFS), and best-first search combined with branch-and-bound pruning.
1) The document discusses double trace flows in dS/CFT correspondence by calculating the time-evolving wavefunction Ψ in de Sitter space.
2) It derives the beta function for the double trace coupling λ in the dual CFT using holographic renormalization group techniques. The beta function matches expectations from large N field theory arguments.
3) It also shows the beta function derivation matches that obtained from the AdS/CFT correspondence upon analytic continuation, providing evidence that dS/CFT may describe the dual of quantum gravity in de Sitter space.
This document discusses dynamic programming and provides examples for solving problems related to longest common subsequences and optimal binary search trees using dynamic programming. It begins with an introduction to dynamic programming as an algorithm design technique for optimization problems. It then provides steps for solving problems with dynamic programming, including characterizing the optimal structure, defining the problem recursively, computing optimal values in a table, and constructing the optimal solution. The document uses the problems of longest common subsequence and optimal binary search tree to demonstrate how to apply these steps with examples.
This document discusses dynamic programming and provides examples for solving problems related to longest common subsequences and optimal binary search trees using dynamic programming. It begins with defining the longest common subsequence problem and providing a naive recursive solution. It then shows that the problem exhibits optimal substructure and can be solved using dynamic programming by computing a table of values in a bottom-up manner. A similar approach is taken for the optimal binary search tree problem, characterizing its optimal substructure and computing an expected search cost table to find the optimal tree configuration.
Dynamic programming is used to solve optimization problems by breaking them down into overlapping subproblems. It solves subproblems only once, storing the results in a table to lookup when the same subproblem occurs again, avoiding recomputing solutions. Key steps are characterizing optimal substructures, defining solutions recursively, computing solutions bottom-up, and constructing the overall optimal solution. Examples provided are matrix chain multiplication and longest common subsequence.
This document contains 38 multiple choice questions related to data structures and algorithms. The questions cover topics such as trees, graphs, hashing, sorting, algorithm analysis, and complexity classes. They assess knowledge of concepts like tree traversals, shortest paths, minimum spanning trees, asymptotic analysis, and resolving collisions in hash tables.
The document contains 16 multiple choice questions about algorithms, data structures, and graph theory. Each question has 4 possible answers and the correct answer is provided. The maximum number of comparisons needed to merge sorted sequences is 358, and depth first search on a graph represented with an adjacency matrix has a worst case time complexity of O(n^2).
This document contains a 30 question mid-semester exam for a data structures and algorithms course. The exam covers topics like asymptotic analysis, sorting algorithms, hashing, binary search trees, and recursion. It provides multiple choice questions to test understanding of algorithm time complexities, worst-case inputs, and recursive functions. Students are instructed to attempt all questions in the 2 hour time limit and notify the proctor if any electronic devices other than calculators are used.
This document provides an introduction to support vector machines (SVMs). It discusses how SVMs can be used for binary classification, regression, and multi-class problems. SVMs find the optimal separating hyperplane that maximizes the margin between classes. Soft margins allow for misclassified points by introducing slack variables. Kernels are discussed for mapping data into higher dimensional feature spaces to perform linear separation. The document outlines the formulation of SVMs for classification and regression and discusses model selection and different kernel functions.
The document discusses dynamic programming and provides examples of problems that can be solved using dynamic programming including unidirectional traveling salesman problem, coin change, longest common subsequence, and longest increasing subsequence. Source code is presented for solving these problems using dynamic programming including dynamic programming tables, tracing optimal solutions, and time complexity analysis. Various online judges are listed that contain sample problems relating to these dynamic programming techniques.
This document discusses functions, limits, and continuity. It begins by defining functions, domains, ranges, and some standard real functions like constant, identity, modulus, and greatest integer functions. It then covers limits of functions including one-sided limits and properties of limits. Examples are provided to illustrate evaluating limits using substitution and factorization methods. The overall objectives are to understand functions, domains, ranges, limits of functions and methods to evaluate limits.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
(1) Jacobson's theorem states that if a division ring D satisfies the property that for every element a in D there exists an integer n(a)>1 such that an(a)=a, then D is a commutative field.
(2) The proof proceeds by showing that if a division ring D satisfies the given property, then D has characteristic p for some prime p. This implies D contains a subring W which is a finite field.
(3) It is then shown that if a,b are elements of D, they must also be elements of the subfield W. But W is a commutative field, so a and b must commute. This is a contradiction unless D=W,
ON THE COVERING RADIUS OF CODES OVER Z4 WITH CHINESE EUCLIDEAN WEIGHTijitjournal
In this paper, we give lower and upper bounds on the covering radius of codes over the ring Z4 with respect to chinese euclidean distance. We also determine the covering radius of various Repetition codes, Simplex codes Type α and Type β and give bounds on the covering radius for MacDonald codes of both types over Z4
1. The document discusses probability concepts related to single and multivariate random variables including probability density functions, cumulative distribution functions, expected value, variance, and common distributions.
2. It also covers topics related to bivariate and multivariate random variables such as joint probability, marginal probability, conditional probability, and the bivariate normal distribution.
3. The document then discusses random signals and linear estimation methods, including maximum likelihood estimation and mean square error estimation. It provides an example of estimating a signal using mean square error minimization.
The document discusses various concepts related to digital image processing including:
1) The relationships between pixels in an image including 4-neighbors, 8-neighbors, and m-neighbors of a pixel.
2) The concepts of adjacency and connectivity between pixels based on their intensity values and whether they are neighbors.
3) Computing the shortest path between two pixels using 4, 8, or m-adjacency and examples calculating these paths.
Iit jam 2016 physics solutions BY TrajectoryeducationDev Singh
1. The electric field at a point (a, b, 0) due to an infinitely long wire with uniform line charge density λ is given by E=λ/(2πε0)(a/r2)ex+(b/r2)ey, where r2=a2+b2.
2. For a 1W point source emitting light uniformly in all directions, the Poynting vector at the point (1, 1, 0) is 1/(8π)ex+(y/e)ey W/cm2.
3. A charged particle starting from the origin with velocity 3/2ex+2ez m/s in a uniform magnetic field B=B
This document provides information about a theoretical physics course, including the course code, homepage, lecturer contact information, textbook, main topics covered, and assessment details. The course covers complex variables and their applications in theoretical physics. Topics include Cauchy's integral formula, calculus of residues, partial differential equations, special functions, and Fourier series. Students will be assessed through a 3-hour written exam worth 80% and a course assessment worth 20%.
IIT Jam math 2016 solutions BY TrajectoryeducationDev Singh
The document contains a mathematics exam question paper with 10 single mark questions (Q1-Q10) and 20 two mark questions (Q11-Q30). The questions cover topics like sequences, linear transformations, integrals, permutations, differential equations etc. Some key questions asked about the nature of a sequence involving sines, order of a permutation, evaluating a limit, checking if a differential equation is exact etc. and provided solutions to them.
The document discusses various backtracking techniques including bounding functions, promising functions, and pruning to avoid exploring unnecessary paths. It provides examples of problems that can be solved using backtracking including n-queens, graph coloring, Hamiltonian circuits, sum-of-subsets, 0-1 knapsack. Search techniques for backtracking problems include depth-first search (DFS), breadth-first search (BFS), and best-first search combined with branch-and-bound pruning.
1) The document discusses double trace flows in dS/CFT correspondence by calculating the time-evolving wavefunction Ψ in de Sitter space.
2) It derives the beta function for the double trace coupling λ in the dual CFT using holographic renormalization group techniques. The beta function matches expectations from large N field theory arguments.
3) It also shows the beta function derivation matches that obtained from the AdS/CFT correspondence upon analytic continuation, providing evidence that dS/CFT may describe the dual of quantum gravity in de Sitter space.
This document discusses dynamic programming and provides examples for solving problems related to longest common subsequences and optimal binary search trees using dynamic programming. It begins with an introduction to dynamic programming as an algorithm design technique for optimization problems. It then provides steps for solving problems with dynamic programming, including characterizing the optimal structure, defining the problem recursively, computing optimal values in a table, and constructing the optimal solution. The document uses the problems of longest common subsequence and optimal binary search tree to demonstrate how to apply these steps with examples.
This document discusses dynamic programming and provides examples for solving problems related to longest common subsequences and optimal binary search trees using dynamic programming. It begins with defining the longest common subsequence problem and providing a naive recursive solution. It then shows that the problem exhibits optimal substructure and can be solved using dynamic programming by computing a table of values in a bottom-up manner. A similar approach is taken for the optimal binary search tree problem, characterizing its optimal substructure and computing an expected search cost table to find the optimal tree configuration.
The document discusses the longest common subsequence (LCS) problem and presents a dynamic programming approach to solve it. It defines key terms like subsequence and common subsequence. It then presents a theorem that characterizes an LCS and shows it has optimal substructure. A recursive solution and algorithm to compute the length of an LCS are provided, with a running time of O(mn). The b table constructed enables constructing an LCS in O(m+n) time.
Longest common subsequence(dynamic programming).munawerzareef
The document discusses the longest common subsequence (LCS) problem. It defines key terms like subsequence and common subsequence. It presents the dynamic programming solution to find the longest common subsequence of two input sequences in O(nm) time using two nested for loops over the sequences' lengths, storing results in a 2D table and using pointers to recover the subsequence. It also provides pseudocode for the algorithm and discusses applications in biology.
This document discusses amortized analysis, which is a technique for analyzing algorithms where the average cost per operation is small even if some operations are more expensive. It presents three methods for amortized analysis: aggregate analysis, accounting analysis, and potential analysis. As an example, it analyzes the cost of dynamic table resizing using these three amortized analysis methods and shows that the amortized cost per operation is O(1) even though individual operations may cost more.
This document summarizes a lecture on asymptotic notation and analyzing recurrences. It introduces O, Ω, and Θ notation for describing asymptotic upper bounds, lower bounds, and tight bounds of functions. It also discusses methods for solving recurrences like the substitution method and recursion tree method. Examples are provided to illustrate analyzing recurrences to determine tight asymptotic bounds.
Dynamical models are widely used to describe chemical, physical and biochemical processes. The main challenge for this class of problems is the identification of kinetic parameters from given measurement data, the so called parameter estimation. However, parameters of such models are never exactly determined, due to measurement noise and the limited amount of data, but remain uncertain. This uncertainty can be captured by a probability density over the parameter space. Unfortunately, studying this probability density is often computationally demanding as this requires the repeated simulation of the underlying model. In this talk we will present a novel method for analysis of such probability densities using networks of radial basis functions.
A particular characteristic of radial basis function approximation schemes is meshless nature, which allows for the free choice of sampling nodes. We will show that root lattices have optimality properties and propose a novel algorithm for the generation of lattices restricted to superlevel-sets. Furthermore we introduce an adaptive method for the generation of nodes based on interacting particles.
Numerical examples show that our method can yield an expected L2 approximation error that is several orders of magnitude lower compared to classical approximations. This allows a drastic reduction of sampling points, which in turn facilitates the analysis of uncertainty for problems with high computational complexity.
Tensor Decomposition and its ApplicationsKeisuke OTAKI
This document discusses tensor factorizations and decompositions and their applications in data mining. It introduces tensors as multi-dimensional arrays and covers 2nd order tensors (matrices) and 3rd order tensors. It describes how tensor decompositions like the Tucker model and CANDECOMP/PARAFAC (CP) model can be used to decompose tensors into core elements to interpret data. It also discusses singular value decomposition (SVD) as a way to decompose matrices and reduce dimensions while approximating the original matrix.
Supervised learning is a category of machine learning that uses labeled datasets to train algorithms to predict outcomes and recognize patterns. Unlike unsupervised learning, supervised learning algorithms are given labeled training to learn the relationship between the input and the outputs.
Supervised machine learning algorithms make it easier for organizations to create complex models that can make accurate predictions. As a result, they are widely used across various industries and fields, including healthcare, marketing, financial services, and more.
Here, we’ll cover the fundamentals of supervised learning in AI, how supervised learning algorithms work, and some of its most common use cases.
Get started for free
How does supervised learning work?
The data used in supervised learning is labeled — meaning that it contains examples of both inputs (called features) and correct outputs (labels). The algorithms analyze a large dataset of these training pairs to infer what a desired output value would be when asked to make a prediction on new data.
For instance, let’s pretend you want to teach a model to identify pictures of trees. You provide a labeled dataset that contains many different examples of types of trees and the names of each species. You let the algorithm try to define what set of characteristics belongs to each tree based on the labeled outputs. You can then test the model by showing it a tree picture and asking it to guess what species it is. If the model provides an incorrect answer, you can continue training it and adjusting its parameters with more examples to improve its accuracy and minimize errors.
Once the model has been trained and tested, you can use it to make predictions on unknown data based on the previous knowledge it has learned.
How does supervised learning work?
The data used in supervised learning is labeled — meaning that it contains examples of both inputs (called features) and correct outputs (labels). The algorithms analyze a large dataset of these training pairs to infer what a desired output value would be when asked to make a prediction on new data.
For instance, let’s pretend you want to teach a model to identify pictures of trees. You provide a labeled dataset that contains many different examples of types of trees and the names of each species. You let the algorithm try to define what set of characteristics belongs to each tree based on the labeled outputs. You can then test the model by showing it a tree picture and asking it to guess what species it is. If the model provides an incorrect answer, you can continue training it and adjusting its parameters with more examples to improve its accuracy and minimize errors.
Once the model has been trained and tested, you can use it to make predictions on unknown data based on the previous knowledge it has learned.
Types of supervised learning
Supervised learning in machine learning is generally divided into two categories: classification and regre
This document contains lecture notes on evaluating definite integrals. It introduces the definition of the definite integral as a limit of Riemann sums, and properties of integrals such as additivity and comparison properties. It also states the Second Fundamental Theorem of Calculus, which relates definite integrals to indefinite integrals via the derivative of the integrand function. Examples are provided to illustrate how to use these properties and theorems to evaluate definite integrals.
This document discusses various methods for estimating normalizing constants that arise when evaluating integrals numerically. It begins by noting there are many computational methods for approximating normalizing constants across different communities. It then lists the topics that will be covered in the upcoming workshop, including discussions on estimating constants using Monte Carlo methods and Bayesian versus frequentist approaches. The document provides examples of estimating normalizing constants using Monte Carlo integration, reverse logistic regression, and Xiao-Li Meng's maximum likelihood estimation approach. It concludes by discussing some of the challenges in bringing a statistical framework to constant estimation problems.
New Mathematical Tools for the Financial SectorSSA KPI
AACIMP 2010 Summer School lecture by Gerhard Wilhelm Weber. "Applied Mathematics" stream. "Modern Operational Research and Its Mathematical Methods with a Focus on Financial Mathematics" course. Part 5.
More info at http://summerschool.ssa.org.ua
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
The document discusses L1-convergence of the Rees-Stanojević modified cosine sum. It contains the following key points:
1. The author obtains a necessary and sufficient condition for L1-convergence of the Rees-Stanojević sum under the condition that the Fourier coefficients satisfy a certain limit.
2. This generalizes a previous result by Garrett and Stanojević which proved convergence in the L-metric for quasi-convex sequences.
3. As a corollary, the author shows that the L1-convergence of the partial sums of the cosine series is equivalent to the condition that the product of the largest neglected coefficient and log n approaches 0 as n approaches
The document summarizes Manindra Agrawal's presentation on the arithmetic complexity of the Euler function. It discusses two families of polynomials (EΣ,n(x) and EΠ,n(x)) that can be used to compute the Euler function. It presents two main theorems: the first states that a lower bound on circuits for EΣ,n(x) implies a lower bound for computing the permanent polynomial; the second states a similar result for EΠ,n(x). The document also describes a multilinear version of EΣ,n(x) that is equivalent to computing the permanent of a small matrix.
This document summarizes a seminar on kernels and support vector machines. It begins by explaining why kernels are useful for increasing flexibility and speed compared to direct inner product calculations. It then covers definitions of positive definite kernels and how to prove a function is a kernel. Several kernel families are discussed, including translation invariant, polynomial, and non-Mercer kernels. Finally, the document derives the primal and dual problems for support vector machines and explains how the kernel trick allows non-linear classification.
The document discusses the divide-and-conquer algorithm design paradigm and several examples that use this paradigm. It begins by outlining the three main steps of divide-and-conquer: 1) divide the problem into subproblems, 2) conquer the subproblems recursively, and 3) combine the subproblem solutions. It then provides examples that use divide-and-conquer, including merge sort, binary search, powering a number, computing Fibonacci numbers, and matrix multiplication. For each example, it describes how the problem is divided and conquered recursively and analyzes the running time.
The document discusses low-rank matrix optimization problems and heuristics for solving rank minimization problems. It covers the following key points in 3 sentences:
The document outlines motivation for extracting low-dimensional structures from high-dimensional data using rank minimization. It then discusses several heuristics for approximating the non-convex rank minimization problem, including replacing the rank with the nuclear norm, using the log-det heuristic as a smooth surrogate, matrix factorization methods, and iteratively solving a sequence of rank-constrained convex problems. Applications mentioned include the Netflix Prize and video intrusion detection.
A T(1)-type theorem for entangled multilinear Calderon-Zygmund operatorsVjekoslavKovac1
This document summarizes a talk given by Vjekoslav Kovač at a joint mathematics conference. The talk concerned establishing T(1)-type theorems for entangled multilinear Calderón-Zygmund operators. Specifically, Kovač discussed studying multilinear singular integral forms where the functions partially share variables, known as an "entangled structure." He outlined establishing generalized modulation invariance and Lp estimates for such operators. The talk motivated further studying related problems involving bilinear ergodic averages and forms with more complex graph structures. Kovač specialized his techniques to bipartite graphs, multilinear Calderón-Zygmund kernels, and "perfect" dyadic models.
This document provides an overview of several topics related to relations and functions:
- It defines relations, domains, and ranges using examples.
- It identifies which examples represent functions and which do not using the vertical line test.
- It outlines tasks to be completed on days 59 and 60, including expressing a relation as a mapping and determining if it is a function, as well as an assignment on relations and functions.
First-order logic (FOL) is a formal system used in mathematics, philosophy, linguistics, and computer science to represent knowledge about domains involving objects and relations. FOL extends propositional logic with quantifiers and predicates to describe properties of and relations between objects. Well-formed formulas in FOL involve constants, variables, functions, predicates, quantifiers, and logical connectives. The meaning and truth of FOL statements is determined with respect to a structure called a model that specifies a domain of objects and interpretations of symbols. FOL can be used to represent knowledge about many different domains and perform logical inference.
This document discusses improving the usability of inserting Bible verses into blog posts on a church website. Currently, verses are inserted with no line breaks, causing issues if the user wants to add text above the verse. To solve this, the system should insert one line break above the verse box when embedded, allowing text to be added above if desired.
The document requests several changes to media pages on a church website:
1) Remove the Activity tab from pages for adding documents, audio, and video.
2) Enable upload buttons on those pages once the user inputs a file path or YouTube URL.
3) Display a validation message after uploading a document, as is done for videos.
4) Investigate why documents uploaded via API take longer than expected to appear, when direct uploads are faster.
The document retells the classic fable of the tortoise and the hare through multiple races that teach lessons about teamwork, strengths, strategy, and perseverance. In the initial race, the hare loses by being overconfident and sleeping. Subsequent races demonstrate the value of relying on strengths, changing strategies to utilize those strengths, and working as a team by combining competencies. The moral is that individual brilliance is less powerful than harnessing each other's talents through cooperative teamwork.
The document proposes several changes to a user profile page on a website:
1) Remove certain links and lines from the top of the profile; add the user's name in bold above their photo.
2) Rename some section titles by removing "My" (e.g. "Blog" instead of "My Blog").
3) Add a new "Prayer Requests" section between "Photos" and "Blog" showing prayer details for that user.
4) Remove certain fields from the user's profile box and move other sections up to fill the empty space.
This document is a registration form for the National Aptitude Test (NAT) administered by the National Testing Service (NTS) of Pakistan. It collects basic information from candidates such as name, father's name, education level, desired test city, test type, contact information, and academic records. Candidates are instructed to choose one test city and test type, attach required documents including photographs and deposit slip, and send the completed form via postal service or courier to the NTS office in Islamabad.
The document discusses several issues with uploading and displaying media like videos, documents, and pictures on a church website. It requests that the media tab be highlighted on three specific pages and that the "Add Video" button be enabled when a YouTube URL is entered. It also reports problems with uploading documents where the progress bar does not update or errors occur. It asks for a validation message to be displayed after document uploads and looks into why documents take longer to display when uploaded via the API versus uploading directly on SlideShare.
This document contains a PHP script command to execute a PHP file located in a projects directory. The PHP interpreter is being called to run code stored in the /home/aryhbea3/projects/ path on the system. In summary, this command will run a PHP script from the specified location.
The document is a registration form for the National Aptitude Test (NAT) administered by the National Testing Service (NTS) of Pakistan. The 2-page form collects information from candidates such as personal details, bank deposit slip, desired test city, education level, and test type. It provides instructions on how to correctly fill out and submit the form along with required documents and payment.
This document contains a PHP script command to execute a PHP file located in a projects directory. The PHP interpreter is being called to run code stored in the /home/aryhbea3/projects/ path on the system. In summary, this command will run a PHP script from the specified location.
This document contains a PHP script command to execute a PHP file located in a projects directory. The PHP interpreter is being called to run code stored in the /home/aryhbea3/projects/ path on the system. In summary, this command will run a PHP script from the specified location.
The mychurch.org/_admin page will be overhauled by removing certain reports and links and replacing them with new metrics. Specifically, all links circled in red and the links and underlying code for two reports circled in blue will be removed to improve database performance. A calendar will replace the dates on the Viral Marketing Stats report to allow specifying a custom date range. A new Retention Metrics report will be added with three sections showing total posts and comments broken down by type, and active churches.
This document contains a PHP script command to execute a PHP file located in a projects directory. The PHP interpreter is being called to run code stored in the /home/aryhbea3/projects/ path on the system. In summary, this command will run a PHP script from the specified location.
This document contains a PHP script command to execute a PHP file located in a projects directory. The PHP interpreter is being called to run code stored in the /home/aryhbea3/projects/ path on the system. In summary, this command will run a PHP script from the specified location.
This document contains a PHP script command to execute a PHP file located in a projects directory. The PHP interpreter is being called to run code stored in the /home/aryhbea3/projects/ path on the system. In summary, this command will run a PHP script from the specified location.
This document contains a PHP script command to execute a PHP file located in a projects directory. The PHP interpreter is being called to run code stored in the /home/aryhbea3/projects/ path on the system. In summary, this command will run a PHP script from the specified location.
The document retells the classic fable of the Tortoise and the Hare through multiple races between them. Each race highlights a different lesson: slow and steady wins; being fast and reliable is better; changing the playing field to suit your strengths; and teamwork allows you to harness different strengths. The moral is that there are many approaches to success, including working harder individually, changing strategies, and cooperating as a team by situational leadership.
This document contains a PHP script command to execute a PHP file located in a projects directory. The PHP interpreter is being called to run code stored in the /home/aryhbea3/projects/ path on the system. In summary, this command will run a PHP script from the specified location.
The document is a registration form for the National Aptitude Test (NAT) administered by the National Testing Service (NTS) of Pakistan. The 2-page form collects information from candidates such as personal details, academic qualifications, test type and location preferences. It provides instructions on how to correctly fill out and submit the form along with payment and photographs.
The document is a registration form for the National Aptitude Test (NAT) administered by the National Testing Service (NTS) of Pakistan. The 2-page form collects information from candidates such as personal details, academic qualifications, test type and location preferences. It provides instructions on how to correctly fill out and submit the form along with payment and photos.
This document contains a PHP script command to execute a PHP file located in a projects directory. The PHP interpreter is being called to run code stored in the /home/aryhbea3/projects/ path on the system. In summary, this command will run a PHP script from the specified location.