The document discusses linear regression and logistic regression. Linear regression finds the best-fitting linear relationship between independent and dependent variables. Logistic regression applies a sigmoid function to the linear combination of inputs to output a probability between 0 and 1, fitting a logistic curve rather than a straight line. It works by first transforming the probabilities into log-odds (logits) and then performing linear regression on the transformed data. This allows predicting probabilities while ensuring outputs remain between 0 and 1.
This document provides an overview of linear programming and the simplex method for solving linear programming problems. It begins with defining the basic linear programming problem as having an objective function and a set of constraints. It then describes how to formulate a sample linear programming problem as a set of equations in standard form. The document explains how to find the feasible region and optimal solution graphically. It introduces the concept of basic feasible solutions and shows how the simplex method works by iteratively moving from one basic feasible solution to an adjacent better solution until the optimal solution is found. Key steps like choosing entering and leaving variables are demonstrated.
Episode 50 : Simulation Problem Solution Approaches Convergence Techniques S...SAJJAD KHUDHUR ABBAS
Episode 50 : Simulation Problem Solution Approaches Convergence Techniques Simulation Strategies
3.2.3.3. Quasi-Newton (QN) Methods
These methods represent a very important class of techniques because of their extensive use in practical alqorithms. They attempt to use an approximation to the Jacobian and then update this at each step thus reducing the overall computational work.
The QN method uses an approximation Hk to the true Jacobian i and computes the step via a Newton-like iteration. That is,
SAJJAD KHUDHUR ABBAS
Ceo , Founder & Head of SHacademy
Chemical Engineering , Al-Muthanna University, Iraq
Oil & Gas Safety and Health Professional – OSHACADEMY
Trainer of Trainers (TOT) - Canadian Center of Human
Development
The document provides an overview of the simplex algorithm for solving linear programming problems. It begins with an introduction and defines the standard format for representing linear programs. It then describes the key steps of the simplex algorithm, including setting up the initial simplex tableau, choosing the pivot column and pivot row, and pivoting to move to the next basic feasible solution. It notes that the algorithm terminates when an optimal solution is reached where all entries in the objective row are non-negative. The document also briefly discusses variants like the ellipsoid method and cycling issues addressed by Bland's rule.
Linear regression aims to fit a linear model to training data to predict continuous output variables. It works by minimizing the squared error between predicted and actual outputs. Regularization is important to prevent overfitting, with ridge regression being a common approach that adds an L2 penalty on the weights. Linear regression can be viewed as solving a system of linear equations, with various methods available to handle over- or under-determined systems without expensive matrix inversions. The next lecture will cover iterative optimization methods for solving linear regression.
Wk 6 part 2 non linearites and non linearization april 05Charlton Inao
The document discusses linearization of nonlinear systems. It begins by defining linear and nonlinear systems, and their properties of superposition and homogeneity. Nonlinearities can arise in physical systems due to effects like saturation, dead zones, and backlash. The document then presents methods for linearizing nonlinear systems by approximating them locally as linear systems, using techniques like linearization rules, Taylor series expansions, and deriving linearized differential equations. Several examples are provided to demonstrate linearizing functions and nonlinear differential equations around an operating point. The overall summary is that nonlinear systems can be approximated as linear near a point by deriving their linear representation.
Linear regression [Theory and Application (In physics point of view) using py...ANIRBANMAJUMDAR18
Machine-learning models are behind many recent technological advances, including high-accuracy translations of the text and self-driving cars. They are also increasingly used by researchers to help in solving physics problems, like Finding new phases of matter, Detecting interesting outliers
in data from high-energy physics experiments, Founding astronomical objects are known as gravitational lenses in maps of the night sky etc. The rudimentary algorithm that every Machine Learning enthusiast starts with is a linear regression algorithm. In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent
variables). Linear regression analysis (least squares) is used in a physics lab to prepare the computer-aided report and to fit data. In this article, the application is made to experiment: 'DETERMINATION OF DIELECTRIC CONSTANT OF NON-CONDUCTING LIQUIDS'. The entire computation is made through Python 3.6 programming language in this article.
- Dimensionality reduction techniques assign instances to vectors in a lower-dimensional space while approximately preserving similarity relationships. Principal component analysis (PCA) is a common linear dimensionality reduction technique.
- Kernel PCA performs PCA in a higher-dimensional feature space implicitly defined by a kernel function. This allows PCA to find nonlinear structure in data. Kernel PCA computes the principal components by finding the eigenvectors of the normalized kernel matrix.
- For a new data point, its representation in the lower-dimensional space is given by projecting it onto the principal components in feature space using the kernel trick, without explicitly computing features.
This document provides an overview of linear programming and the simplex method for solving linear programming problems. It begins with defining the basic linear programming problem as having an objective function and a set of constraints. It then describes how to formulate a sample linear programming problem as a set of equations in standard form. The document explains how to find the feasible region and optimal solution graphically. It introduces the concept of basic feasible solutions and shows how the simplex method works by iteratively moving from one basic feasible solution to an adjacent better solution until the optimal solution is found. Key steps like choosing entering and leaving variables are demonstrated.
Episode 50 : Simulation Problem Solution Approaches Convergence Techniques S...SAJJAD KHUDHUR ABBAS
Episode 50 : Simulation Problem Solution Approaches Convergence Techniques Simulation Strategies
3.2.3.3. Quasi-Newton (QN) Methods
These methods represent a very important class of techniques because of their extensive use in practical alqorithms. They attempt to use an approximation to the Jacobian and then update this at each step thus reducing the overall computational work.
The QN method uses an approximation Hk to the true Jacobian i and computes the step via a Newton-like iteration. That is,
SAJJAD KHUDHUR ABBAS
Ceo , Founder & Head of SHacademy
Chemical Engineering , Al-Muthanna University, Iraq
Oil & Gas Safety and Health Professional – OSHACADEMY
Trainer of Trainers (TOT) - Canadian Center of Human
Development
The document provides an overview of the simplex algorithm for solving linear programming problems. It begins with an introduction and defines the standard format for representing linear programs. It then describes the key steps of the simplex algorithm, including setting up the initial simplex tableau, choosing the pivot column and pivot row, and pivoting to move to the next basic feasible solution. It notes that the algorithm terminates when an optimal solution is reached where all entries in the objective row are non-negative. The document also briefly discusses variants like the ellipsoid method and cycling issues addressed by Bland's rule.
Linear regression aims to fit a linear model to training data to predict continuous output variables. It works by minimizing the squared error between predicted and actual outputs. Regularization is important to prevent overfitting, with ridge regression being a common approach that adds an L2 penalty on the weights. Linear regression can be viewed as solving a system of linear equations, with various methods available to handle over- or under-determined systems without expensive matrix inversions. The next lecture will cover iterative optimization methods for solving linear regression.
Wk 6 part 2 non linearites and non linearization april 05Charlton Inao
The document discusses linearization of nonlinear systems. It begins by defining linear and nonlinear systems, and their properties of superposition and homogeneity. Nonlinearities can arise in physical systems due to effects like saturation, dead zones, and backlash. The document then presents methods for linearizing nonlinear systems by approximating them locally as linear systems, using techniques like linearization rules, Taylor series expansions, and deriving linearized differential equations. Several examples are provided to demonstrate linearizing functions and nonlinear differential equations around an operating point. The overall summary is that nonlinear systems can be approximated as linear near a point by deriving their linear representation.
Linear regression [Theory and Application (In physics point of view) using py...ANIRBANMAJUMDAR18
Machine-learning models are behind many recent technological advances, including high-accuracy translations of the text and self-driving cars. They are also increasingly used by researchers to help in solving physics problems, like Finding new phases of matter, Detecting interesting outliers
in data from high-energy physics experiments, Founding astronomical objects are known as gravitational lenses in maps of the night sky etc. The rudimentary algorithm that every Machine Learning enthusiast starts with is a linear regression algorithm. In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent
variables). Linear regression analysis (least squares) is used in a physics lab to prepare the computer-aided report and to fit data. In this article, the application is made to experiment: 'DETERMINATION OF DIELECTRIC CONSTANT OF NON-CONDUCTING LIQUIDS'. The entire computation is made through Python 3.6 programming language in this article.
- Dimensionality reduction techniques assign instances to vectors in a lower-dimensional space while approximately preserving similarity relationships. Principal component analysis (PCA) is a common linear dimensionality reduction technique.
- Kernel PCA performs PCA in a higher-dimensional feature space implicitly defined by a kernel function. This allows PCA to find nonlinear structure in data. Kernel PCA computes the principal components by finding the eigenvectors of the normalized kernel matrix.
- For a new data point, its representation in the lower-dimensional space is given by projecting it onto the principal components in feature space using the kernel trick, without explicitly computing features.
The document provides an overview of the simplex method for solving linear programming problems. It discusses:
- The simplex method is an iterative algorithm that generates a series of solutions in tabular form called tableaus to find an optimal solution.
- It involves writing the problem in standard form, introducing slack variables, and constructing an initial tableau.
- The method then performs iterations involving selecting a pivot column and row, and applying row operations to generate new tableaus until an optimal solution is found.
- It also discusses how artificial variables are introduced for problems with non-strict inequalities and provides an example solved using the simplex method.
The document discusses the simplex method for solving linear programming problems. It introduces some key terminology used in the simplex method like slack variables, surplus variables, and artificial variables. It then provides an overview of how the simplex method works for maximization problems, including forming the initial simplex table, testing for optimality and feasibility, pivoting to find an optimal solution. Finally, it provides an example application of the simplex method to a sample maximization problem.
The document provides an overview of power flow analysis using the Gauss-Seidel and Newton-Raphson methods. It discusses key concepts such as different bus types, stopping criteria, and examples to illustrate the iterative process. The Gauss-Seidel method is introduced and examples are shown to demonstrate its use in solving power flows. Limitations of Gauss-Seidel are also outlined. The Newton-Raphson method is then presented as an alternative approach using sequential linear approximations to iteratively find the solution.
The document discusses algorithms for drawing lines and circles on a discrete pixel display. It begins by describing what characteristics an "ideal line" would have on such a display. It then introduces several algorithms for drawing lines, including the simple line algorithm, digital differential analyzer (DDA) algorithm, and Bresenham's line algorithm. The Bresenham algorithm is described in detail, as it uses only integer calculations. Next, a simple potential circle drawing algorithm is presented and its shortcomings discussed. Finally, the more accurate and efficient mid-point circle algorithm is introduced. This algorithm exploits the eight-way symmetry of circles and only calculates points in one octant.
The document discusses algorithms for drawing lines and circles on a discrete pixel display. It begins by describing what characteristics an "ideal line" would have on such a display. It then introduces several algorithms for drawing lines, including the simple line algorithm, digital differential analyzer (DDA) algorithm, and Bresenham's line algorithm. The Bresenham algorithm is described in detail, as it uses only integer calculations. Next, a simple potential circle drawing algorithm is presented and its shortcomings discussed. Finally, the more accurate and efficient mid-point circle algorithm is described. This algorithm exploits the eight-way symmetry of circles and uses incremental calculations to determine the next pixel point.
1. The document discusses various machine learning classification algorithms including neural networks, support vector machines, logistic regression, and radial basis function networks.
2. It provides examples of using straight lines and complex boundaries to classify data with neural networks. Maximum margin hyperplanes are used for support vector machine classification.
3. Logistic regression is described as useful for binary classification problems by using a sigmoid function and cross entropy loss. Radial basis function networks can perform nonlinear classification with a kernel trick.
The document describes the bisection method for finding roots of equations. It provides an introduction to the bisection method and its graphical representation. It also presents the algorithm, a C program implementing the method, and examples finding roots of polynomial and trigonometric equations using bisection.
The document discusses the simplex algorithm for solving linear programming problems. It begins with an introduction and overview of the simplex algorithm. It then describes the key steps of the algorithm, which are: 1) converting the problem into slack format, 2) constructing the initial simplex tableau, 3) selecting the pivot column and calculating the theta ratio to determine the departing variable, 4) pivoting to create the next tableau. The document provides examples to illustrate these steps. It also briefly discusses cycling issues, software implementations, efficiency considerations and variants of the simplex algorithm.
This document provides an overview of regression analysis and compares regression to neural networks. It defines regression as estimating the relationship between variables. The main types covered are linear, nonlinear, simple, multiple and logistic regression. Examples are given to illustrate simple linear regression and least squares methods. The document also discusses best practices like avoiding overfitting and dealing with multicollinearity. Finally, it provides examples comparing regression and deep learning approaches.
Digital control systems (dcs) lecture 18-19-20Ali Rind
This document discusses digital control systems and related topics such as difference equations, z-transforms, and mapping between the s-plane and z-plane. It begins with an outline of topics to be covered including difference equations, z-transforms, inverse z-transforms, and the relationship between the s-plane and z-plane. Examples are provided to illustrate difference equations, z-transforms, and mapping poles between the two planes. Standard z-transforms of discrete-time signals like the unit impulse and sampled step are also defined.
- Linear regression is a predictive modeling technique used to establish a relationship between two variables, known as the predictor and response variables.
- The residuals are the errors between predicted and actual values, and the optimal regression line is the one that minimizes the sum of squared residuals.
- Linear regression can be used to predict variables like salary based on experience, or housing prices based on features like crime rates or school quality. Co-relation analysis examines the relationships between predictor variables.
This document provides an overview of optimization techniques. It defines optimization as identifying variable values that minimize or maximize an objective function subject to constraints. It then discusses various applications of optimization in finance, engineering, and data modeling. The document outlines different types of optimization problems and algorithms. It provides examples of unconstrained optimization algorithms like gradient descent, conjugate gradient, Newton's method, and BFGS. It also discusses the Nelder-Mead simplex algorithm for constrained optimization and compares the performance of these algorithms on sample problems.
GlobalLogic Machine Learning Webinar “Advanced Statistical Methods for Linear...GlobalLogic Ukraine
31 травня відбувся вебінар для ML-спеціалістів - “Advanced Statistical Methods for Linear Regression” від спікера Віталія Мірошниченка! Ця доповідь для тих, хто добре ознайомлений із найпоширенішими моделями даних та підходами у машинному навчанні і хоче розширити знання іншими підходами.
У доповіді ми розглянули:
- Нагадування. Модель лінійної регресії і підгонка параметрів;
- Навчання батчами (великі об’єми вибірок);
- Оптимізація розрахунків у каскаді моделей;
- Модель суміші лінійних регресій;
- Оцінки методом складеного ножа матриць коваріацій.
Про спікера:
Віталій Мірошниченко — Senior ML Software Engineer, GlobalLogic. Має більше 6 років досвіду, який отримав здебільшого на проєктах, пов’язаних із Telecom, Cyber security, Retail. Активний учасник змагань Kaggle, та Аспірант КНУ.
Деталі заходу: https://bit.ly/3HkqhDB
Відкриті ML позиції у GlobalLogic: https://bit.ly/3MPC9yo
The security of the RSA algorithm depends on the difficulty of factoring large numbers. The best known factoring algorithms are trial division, Dixon's algorithm, the quadratic sieve, and the number field sieve. The quadratic sieve and number field sieve are parallelizable algorithms that improve on Dixon's algorithm by using a "sieving" technique to more efficiently find relations between factors. While factoring performance improves incrementally over time, a large key size (over 300 bits) is still considered secure against the best known factoring methods.
1) The document discusses simple linear regression using a scatter diagram and data from a study of employees' years of working experience and income.
2) It presents the scatter diagram and shows how to draw a trend line to roughly estimate dependent variable (income) values from the independent variable (years experience).
3) Equations for the least squares linear regression line are provided, including how to calculate the standard error of estimate, which is interpreted as the standard deviation around the regression line.
The document discusses different algorithms for drawing lines and circles on a discrete pixel grid, including approaches to reduce aliasing effects. It covers the digital differential analyzer (DDA) algorithm, Bresenham's algorithm, techniques for antialiasing such as area sampling and weighted area filtering using a conical filter. The Gupta-Sproull algorithm is highlighted as a method for antialiasing lines that calculates pixel intensities based on the distance from the line center using features of Bresenham's algorithm.
I am Jayson L. I am a Signals and Systems Homework Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, from the University of Sheffield. I have been helping students with their homework for the past 7 years. I solve homework related to Signals and Systems.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Signals and Systems homework.
This document provides an overview of machine learning techniques for classification and regression, including decision trees, linear models, and support vector machines. It discusses key concepts like overfitting, regularization, and model selection. For decision trees, it explains how they work by binary splitting of space, common splitting criteria like entropy and Gini impurity, and how trees are built using a greedy optimization approach. Linear models like logistic regression and support vector machines are covered, along with techniques like kernels, regularization, and stochastic optimization. The importance of testing on a holdout set to avoid overfitting is emphasized.
Cs6402 design and analysis of algorithms may june 2016 answer keyappasami
The document discusses algorithms and complexity analysis. It provides Euclid's algorithm for computing greatest common divisor, compares the orders of growth of n(n-1)/2 and n^2, and describes the general strategy of divide and conquer methods. It also defines problems like the closest pair problem, single source shortest path problem, and assignment problem. Finally, it discusses topics like state space trees, the extreme point theorem, and lower bounds.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
The document provides an overview of the simplex method for solving linear programming problems. It discusses:
- The simplex method is an iterative algorithm that generates a series of solutions in tabular form called tableaus to find an optimal solution.
- It involves writing the problem in standard form, introducing slack variables, and constructing an initial tableau.
- The method then performs iterations involving selecting a pivot column and row, and applying row operations to generate new tableaus until an optimal solution is found.
- It also discusses how artificial variables are introduced for problems with non-strict inequalities and provides an example solved using the simplex method.
The document discusses the simplex method for solving linear programming problems. It introduces some key terminology used in the simplex method like slack variables, surplus variables, and artificial variables. It then provides an overview of how the simplex method works for maximization problems, including forming the initial simplex table, testing for optimality and feasibility, pivoting to find an optimal solution. Finally, it provides an example application of the simplex method to a sample maximization problem.
The document provides an overview of power flow analysis using the Gauss-Seidel and Newton-Raphson methods. It discusses key concepts such as different bus types, stopping criteria, and examples to illustrate the iterative process. The Gauss-Seidel method is introduced and examples are shown to demonstrate its use in solving power flows. Limitations of Gauss-Seidel are also outlined. The Newton-Raphson method is then presented as an alternative approach using sequential linear approximations to iteratively find the solution.
The document discusses algorithms for drawing lines and circles on a discrete pixel display. It begins by describing what characteristics an "ideal line" would have on such a display. It then introduces several algorithms for drawing lines, including the simple line algorithm, digital differential analyzer (DDA) algorithm, and Bresenham's line algorithm. The Bresenham algorithm is described in detail, as it uses only integer calculations. Next, a simple potential circle drawing algorithm is presented and its shortcomings discussed. Finally, the more accurate and efficient mid-point circle algorithm is introduced. This algorithm exploits the eight-way symmetry of circles and only calculates points in one octant.
The document discusses algorithms for drawing lines and circles on a discrete pixel display. It begins by describing what characteristics an "ideal line" would have on such a display. It then introduces several algorithms for drawing lines, including the simple line algorithm, digital differential analyzer (DDA) algorithm, and Bresenham's line algorithm. The Bresenham algorithm is described in detail, as it uses only integer calculations. Next, a simple potential circle drawing algorithm is presented and its shortcomings discussed. Finally, the more accurate and efficient mid-point circle algorithm is described. This algorithm exploits the eight-way symmetry of circles and uses incremental calculations to determine the next pixel point.
1. The document discusses various machine learning classification algorithms including neural networks, support vector machines, logistic regression, and radial basis function networks.
2. It provides examples of using straight lines and complex boundaries to classify data with neural networks. Maximum margin hyperplanes are used for support vector machine classification.
3. Logistic regression is described as useful for binary classification problems by using a sigmoid function and cross entropy loss. Radial basis function networks can perform nonlinear classification with a kernel trick.
The document describes the bisection method for finding roots of equations. It provides an introduction to the bisection method and its graphical representation. It also presents the algorithm, a C program implementing the method, and examples finding roots of polynomial and trigonometric equations using bisection.
The document discusses the simplex algorithm for solving linear programming problems. It begins with an introduction and overview of the simplex algorithm. It then describes the key steps of the algorithm, which are: 1) converting the problem into slack format, 2) constructing the initial simplex tableau, 3) selecting the pivot column and calculating the theta ratio to determine the departing variable, 4) pivoting to create the next tableau. The document provides examples to illustrate these steps. It also briefly discusses cycling issues, software implementations, efficiency considerations and variants of the simplex algorithm.
This document provides an overview of regression analysis and compares regression to neural networks. It defines regression as estimating the relationship between variables. The main types covered are linear, nonlinear, simple, multiple and logistic regression. Examples are given to illustrate simple linear regression and least squares methods. The document also discusses best practices like avoiding overfitting and dealing with multicollinearity. Finally, it provides examples comparing regression and deep learning approaches.
Digital control systems (dcs) lecture 18-19-20Ali Rind
This document discusses digital control systems and related topics such as difference equations, z-transforms, and mapping between the s-plane and z-plane. It begins with an outline of topics to be covered including difference equations, z-transforms, inverse z-transforms, and the relationship between the s-plane and z-plane. Examples are provided to illustrate difference equations, z-transforms, and mapping poles between the two planes. Standard z-transforms of discrete-time signals like the unit impulse and sampled step are also defined.
- Linear regression is a predictive modeling technique used to establish a relationship between two variables, known as the predictor and response variables.
- The residuals are the errors between predicted and actual values, and the optimal regression line is the one that minimizes the sum of squared residuals.
- Linear regression can be used to predict variables like salary based on experience, or housing prices based on features like crime rates or school quality. Co-relation analysis examines the relationships between predictor variables.
This document provides an overview of optimization techniques. It defines optimization as identifying variable values that minimize or maximize an objective function subject to constraints. It then discusses various applications of optimization in finance, engineering, and data modeling. The document outlines different types of optimization problems and algorithms. It provides examples of unconstrained optimization algorithms like gradient descent, conjugate gradient, Newton's method, and BFGS. It also discusses the Nelder-Mead simplex algorithm for constrained optimization and compares the performance of these algorithms on sample problems.
GlobalLogic Machine Learning Webinar “Advanced Statistical Methods for Linear...GlobalLogic Ukraine
31 травня відбувся вебінар для ML-спеціалістів - “Advanced Statistical Methods for Linear Regression” від спікера Віталія Мірошниченка! Ця доповідь для тих, хто добре ознайомлений із найпоширенішими моделями даних та підходами у машинному навчанні і хоче розширити знання іншими підходами.
У доповіді ми розглянули:
- Нагадування. Модель лінійної регресії і підгонка параметрів;
- Навчання батчами (великі об’єми вибірок);
- Оптимізація розрахунків у каскаді моделей;
- Модель суміші лінійних регресій;
- Оцінки методом складеного ножа матриць коваріацій.
Про спікера:
Віталій Мірошниченко — Senior ML Software Engineer, GlobalLogic. Має більше 6 років досвіду, який отримав здебільшого на проєктах, пов’язаних із Telecom, Cyber security, Retail. Активний учасник змагань Kaggle, та Аспірант КНУ.
Деталі заходу: https://bit.ly/3HkqhDB
Відкриті ML позиції у GlobalLogic: https://bit.ly/3MPC9yo
The security of the RSA algorithm depends on the difficulty of factoring large numbers. The best known factoring algorithms are trial division, Dixon's algorithm, the quadratic sieve, and the number field sieve. The quadratic sieve and number field sieve are parallelizable algorithms that improve on Dixon's algorithm by using a "sieving" technique to more efficiently find relations between factors. While factoring performance improves incrementally over time, a large key size (over 300 bits) is still considered secure against the best known factoring methods.
1) The document discusses simple linear regression using a scatter diagram and data from a study of employees' years of working experience and income.
2) It presents the scatter diagram and shows how to draw a trend line to roughly estimate dependent variable (income) values from the independent variable (years experience).
3) Equations for the least squares linear regression line are provided, including how to calculate the standard error of estimate, which is interpreted as the standard deviation around the regression line.
The document discusses different algorithms for drawing lines and circles on a discrete pixel grid, including approaches to reduce aliasing effects. It covers the digital differential analyzer (DDA) algorithm, Bresenham's algorithm, techniques for antialiasing such as area sampling and weighted area filtering using a conical filter. The Gupta-Sproull algorithm is highlighted as a method for antialiasing lines that calculates pixel intensities based on the distance from the line center using features of Bresenham's algorithm.
I am Jayson L. I am a Signals and Systems Homework Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, from the University of Sheffield. I have been helping students with their homework for the past 7 years. I solve homework related to Signals and Systems.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Signals and Systems homework.
This document provides an overview of machine learning techniques for classification and regression, including decision trees, linear models, and support vector machines. It discusses key concepts like overfitting, regularization, and model selection. For decision trees, it explains how they work by binary splitting of space, common splitting criteria like entropy and Gini impurity, and how trees are built using a greedy optimization approach. Linear models like logistic regression and support vector machines are covered, along with techniques like kernels, regularization, and stochastic optimization. The importance of testing on a holdout set to avoid overfitting is emphasized.
Cs6402 design and analysis of algorithms may june 2016 answer keyappasami
The document discusses algorithms and complexity analysis. It provides Euclid's algorithm for computing greatest common divisor, compares the orders of growth of n(n-1)/2 and n^2, and describes the general strategy of divide and conquer methods. It also defines problems like the closest pair problem, single source shortest path problem, and assignment problem. Finally, it discusses topics like state space trees, the extreme point theorem, and lower bounds.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
1. CS 472 - Regression 1
Regression
For classification the output(s) is nominal
In regression the output is continuous
– Function Approximation
Many models could be used – Simplest is linear regression
– Fit data with the best hyper-plane which "goes through" the points
y
dependent
variable
(output)
x – independent variable (input)
2. CS 472 - Regression 2
Regression
For classification the output(s) is nominal
In regression the output is continuous
– Function Approximation
Many models could be used – Simplest is linear regression
– Fit data with the best hyper-plane which "goes through" the points
y
dependent
variable
(output)
x – independent variable (input)
3. CS 472 - Regression 3
Regression
For classification the output(s) is nominal
In regression the output is continuous
– Function Approximation
Many models could be used – Simplest is linear regression
– Fit data with the best hyper-plane which "goes through" the points
– For each point the difference between the predicted point and the
actual observation is the residue
y
x
4. Simple Linear Regression
For now, assume just one (input) independent variable x,
and one (output) dependent variable y
– Multiple linear regression assumes an input vector x
– Multivariate linear regression assumes an output vector y
We "fit" the points with a line (i.e. hyper-plane)
Which line should we use?
– Choose an objective function
– For simple linear regression we choose sum squared error (SSE)
S (predictedi – actuali)2 = S (residuei)2
– Thus, find the line which minimizes the sum of the squared
residues (e.g. least squares)
– This exactly mimics the case assuming data points were sampled
from the actual hyperplane with Gaussian noise added
CS 472 - Regression 4
5. How do we "learn" parameters
For the 2-d problem (line) there are coefficients for the
bias and the independent variable (y-intercept and slope)
To find the values for the coefficients which minimize the
objective function we take the partial derivates of the
objective function (SSE) with respect to the coefficients.
Set these to 0, and solve.
CS 472 - Regression 5
Y = b0 +b1X
b1 =
n xy
å - x y
å
å
n x2
- x
å
( )
2
å
b0 =
y
å - b1 x
å
n
6. Multiple Linear Regression
There is a closed form for finding multiple linear regression
weights which requires matrix inversion, etc.
There are also iterative techniques to find weights
One is the delta rule. For regression we use an output node
which is not thresholded (just does a linear sum) and iteratively
apply the delta rule – For regression net is the output
Where c is the learning rate and xi is the input for that weight
Delta rule will update towards the objective of minimizing the
SSE, thus solving multiple linear regression
There are other regression approaches that give different results
by trying to better handle outliers and other statistical anomalies
CS 472 - Regression 6
Dwi = c(t -net)xi
7. SSE and Linear Regression
SSE chooses to square the difference of
the predicted vs actual.
Don't want residues to cancel each other
Could use absolute or other distances to
solve problem
S |predictedi – actuali| : L1 vs L2
SSE leads to a parabolic error surface
which is good for gradient descent
Which line would least squares choose?
– There is always one “best” fit with SSE
(L2)
CS 472 - Regression 7
8. SSE and Linear Regression
SSE leads to a parabolic error
surface which is good for gradient
descent
Which line would least squares
choose?
– There is always one “best” fit
CS 472 - Regression 8
7
9. SSE and Linear Regression
SSE leads to a parabolic error
surface which is good for gradient
descent
Which line would least squares
choose?
– There is always one “best” fit
CS 472 - Regression 9
7
5
10. SSE and Linear Regression
SSE leads to a parabolic error
surface which is good for gradient
descent
Which line would least squares
choose?
– There is always one “best” fit
Note that the squared error causes
the model to be more highly
influenced by outliers
– Though best fit assuming Gaussian noise
error from true surface
CS 472 - Regression 10
3
3
7
5
11. SSE and Linear Regression Generalization
CS 472 - Regression 11
3
3
7
5
In generalization all x
values map to a y
value on the chosen
regression line
x – Input Value
y – Input Value
0 1 2 3
1
12. Linear Regression - Challenge Question
Assume we start with all weights as 1 (don’t use bias weight though
you usually always will – else forces the line through the origin)
Remember for regression we use an output node which is not
thresholded (just does a linear sum) and iteratively apply the delta rule
– thus the net is the output
What are the new weights after one iteration through the following
training set using the delta rule with a learning rate c = 1
How does it generalize for the novel input (-.3, 0)?
CS 472 - Regression 12
x1 x2 Target y
.5 -.2 1
1 0 -.4
Dwi = c(t -net)xi
After one epoch the weight vector is:
A. 1 .5
B. 1.35 .94
C. 1.35 .86
D. .4 .86
E. None of the above
13. Linear Regression - Challenge Question
Assume we start with all weights as 1
What are the new weights after one iteration through the
training set using the delta rule with a learning rate c = 1
How does it generalize for the novel input (-.3, 0)?
CS 472 - Regression 13
Dwi = c(t -net)xi
x1 x2 Target Net w1 w2
1 1
.5 -.2 1
1 0 -.4
w1 = 1 +
14. Linear Regression - Challenge Question
Assume we start with all weights as 1
What are the new weights after one iteration through the
training set using the delta rule with a learning rate c = 1
How does it generalize for the novel input (-.3, 0)?
– -.3*-.4 + 0*.86 = .12
CS 472 - Regression 14
Dwi = c(t -net)xi
x1 x2 Target Net w1 w2
1 1
.5 -.2 1 .3 1.35 .86
1 0 -.4 1.35 -.4 .86
w1 = 1 + 1(1 – .3).5 = 1.35
15. Linear Regression Homework
Assume we start with all weights as 0 (Include the bias!)
What are the new weights after one iteration through the
following training set using the delta rule with a learning
rate c = .2
How does it generalize for the novel input (1, .5)?
CS 472 - Regression 15
x1 x2 Target
.3 .8 .7
-.3 1.6 -.1
.9 0 1.3
Dwi = c(t -net)xi
16. Intelligibility (Interpretable ML, Transparent)
One advantage of linear regression models (and linear
classification) is the potential to look at the coefficients to give
insight into which input variables are most important in
predicting the output
The variables with the largest magnitude have the highest
correlation with the output
– A large positive coefficient implies that the output will increase when
this input is increased (positively correlated)
– A large negative coefficient implies that the output will decrease when
this input is increased (negatively correlated)
– A small or 0 coefficient suggests that the input is uncorrelated with the
output (at least at the 1st order)
Linear regression/classification can be used to find best
"indicators"
– Be careful not to confuse correlation with causality
– Linear cannot detect higher order correlations!! The power of more
complex machine learning models.
CS 472 - Regression 16
18. Delta rule natural for regression, not classification
First consider the one-dimensional case
The decision surface for the perceptron would be any (first) point that divides
instances
Delta rule will try to fit a line through the target values which minimizes SSE
and the decision point is where the line crosses .5 for 0/1 targets. Looking
down on data for perceptron view. Now flip it on its side for delta rule view.
Will converge to the one optimal line (and dividing point) for this objective
CS 472 - Regression 18
x
x
z
0
1
Dwi = c(t -net)xi
19. Delta Rule for Classification?
What would happen in this adjusted case for perceptron and delta rule and
where would the decision point (i.e. .5 crossing) be?
CS 472 - Regression 19
x
z
0
1
x
z
0
1
20. Delta Rule for Classification?
CS 472 - Regression 20
x
z
0
1
x
z
0
1
Leads to misclassifications even though the data is linearly separable
For Delta rule the objective function is to minimize the regression line SSE,
not maximize classification
21. Delta Rule for Classification?
What would happen if we were doing a regression fit with a sigmoid/logistic
curve rather than a line?
CS 472 - Regression 21
x
z
0
1
x
z
0
1
x
z
0
1
22. Delta Rule for Classification?
Sigmoid fits many decision cases quite well! This is basically what logistic
regression does.
CS 472 - Regression 22
x
z
0
1
x
z
0
1
x
z
0
1
23. 23
1
0
Observation: Consider the 2 input perceptron case without a bias weight. Note that
the output z is a function of 2 input variables for the 2 input case (x1, x2), and thus we
really have a 3-d decision surface (i.e. a plane accounting for the two input variables
and the 3rd dimension for the output), yet the decision boundary is still a line in the 2-
d input space when we represent the outputs with different colors, symbols, etc. The
Delta rule would fit a regression plane to these points with the decision line being that
line where the plane went through .5. What would logistic regression do?
q
q
<
=
³
å
å
=
=
i
n
i
i
i
n
i
i
w
x
z
w
x
1
1
if
0
if
1
CS 472 - Regression
25. Logistic Regression
One commonly used algorithm is Logistic Regression
Assumes that the dependent (output) variable is binary
which is often the case in medical and other studies. (Does
person have disease or not, survive or not, accepted or not,
etc.)
Like Quadric, Logistic Regression does a particular non-
linear transform on the data after which it just does linear
regression on the transformed data
Logistic regression fits the data with a sigmoidal/logistic
curve rather than a line and outputs an approximation of
the probability of the output given the input
CS 472 - Regression 25
26. Logistic Regression Example
Age (X axis, input variable) – Data is fictional
Heart Failure (Y axis, 1 or 0, output variable)
If use value of regression line as a probability approximation
– Extrapolates outside 0-1 and not as good empirically
Sigmoidal curve to the right gives empirically good probability
approximation and is bounded between 0 and 1
CS 472 - Regression 26
27. Logistic Regression Approach
Learning
1. Transform initial input probabilities into log odds (logit)
2. Do a standard linear regression using the logit values
– This effectively fits a logistic curve to the data, while still just
doing a linear regression with the transformed input (ala quadric
machine, etc.)
Generalization
1. Find the value for the new input on the logit line
2. Transform that logit value back into a probability
CS 472 - Regression 27
30. Logistic Regression Approach
Could use linear regression with the probability points, but
that would not extrapolate well
Logistic version is better but how do we get it?
Similar to Quadric we do a non-linear pre-process of the
input and then do linear regression on the transformed
values – do a linear regression on the log odds - Logit
CS 472 - Regression 30
0 10 20 30 40 50 60
prob.
Cured
0
1
0 10 20 30 40 50 60
prob.
Cured
0
1
32. Regression of Log Odds
CS 472 - Regression 32
Medication
Dosage
#
Cured
Total
Patients
Probability:
#
Cured/Total
Patients
Odds:
p/(1-p) =
# cured/
# not cured
Log
Odds:
ln(Odds)
20 1 5 .20 .25 -1.39
30 2 6 .33 .50 -0.69
40 4 6 .67 2.0 0.69
50 6 7 .86 6.0 1.79
0 10 20 30 40 50 60
+2
-2
0
• y = .11x – 3.8 - Logit regression equation
• Now we have a regression line for log odds (logit)
• To generalize, we use the log odds value for the new data point
• Then we transform that log odds point to a probability: p = elogit(x)/(1+elogit(x))
• For example assume we want p for dosage = 10
Logit(10) = .11(10) – 3.8 = -2.7
p(10) = e-2.7/(1+e-2.7) = .06 [note that we just work backwards from logit to p]
• These p values make up the sigmoidal regression curve (which we never have to
actually plot)
prob.
Cured
0
1
33. Logistic Regression Homework
No longer a required homework
You don’t actually have to come up with the weights for this one,
though you could do so quickly by using the closed form linear
regression approach
Sketch each step you would need to learn the weights for the following
data set using logistic regression
Sketch how you would generalize the probability of a heart attack
given a new input heart rate of 60
CS 472 - Regression 33
Heart Rate Heart Attack
50 Y
50 N
50 N
50 N
70 N
70 Y
90 Y
90 Y
90 N
90 Y
90 Y
34. Summary
Linear Regression and Logistic Regression are nice tools
for many simple situations
– But both force us to fit the data with one shape (line or sigmoid)
which will often underfit
Intelligible results
When problem includes more arbitrary non-linearity then
we need more powerful models which we will introduce
– Though non-linear data transformation can help in these cases
while still using a linear model for learning
These models are commonly used in data mining
applications and also as a "first attempt" at understanding
data trends, indicators, etc.
CS 472 - Regression 34
35. Non-Linear Regression
Note that linear regression is to regression what the
perceptron is to classification
– Simple, useful models which will often underfit
All of the more powerful classification models which we
will be discussing later in class can also be used for non-
linear regression, though we will mostly discuss them
using classification
– MLP with Backpropagation, Decision Trees, Nearest Neighbor,
etc.
They can learn functions with arbitrarily complex high
dimensional shapes
CS 472 - Regression 35