DS Machine Learning and Data Mining I. Alina Oprea Associate Professor, CCIS Northeastern University
|
|
- Flora Thomas
- 5 years ago
- Views:
Transcription
1 DS 4400 Machine Learning and Data Mining I Alina Oprea Associate Professor, CCIS Northeastern University September
2 Review Solution for multiple linear regression can be computed in closed form Matrix inversion is computationally intense In practice several techniques can help generate more robust models Outlier removal Feature scaling Gradient descent is an efficient algorithm for optimization and training LR The most widely used algorithm in ML! 2
3 Multiple Linear Regression Dataset: x (i) R d, y i R Hypothesis h θ x = θ T x MSE = 1 σ n n i=1 θ T x (i) y (i) 2 loss / cost 3
4 Gradient Descent Outline Derivation for simple and multiple Linear Regression Issues with Gradient Descent Comparison with closed-form solution Regularization Ridge and Lasso regression Lab example 4
5 How to optimize J(θ)? Move in the direction of steepest descent 5
6 Gradient Descent Gradient = slope of line tangent to curve at the same point 6
7 Gradient Descent What happens when θ reaches a local minimum? The slope is 0, and gradient descent converges! 7
8 Gradient Descent As you approach the minimum, the slope gets smaller, and GD will take smaller steps It converges to local minimum (which is global minimum for convex functions)! 8
9 GD Converges to Local Minimum Solution: start from multiple random locations 9
10 GD for Simple Linear Regression J θ = 1 σ n n i=1 θ 0 + θ 1 x (i) y (i) 2 J(θ) θ 0 J(θ) θ 1 = 2 σ n i=1 n (θ 0 + θ 1 x (i) y (i) ) = 2 σ n i=1 n (θ 0 + θ 1 x i y (i) ) x (i) Update of each parameter component depends on all training data 10
11 GD for Multiple Linear Regression 2 n 2 n 1 n 1 n 11
12 GD for Linear Regression 2 n Can also bound number of iterations 12
13 GD Example 13
14 GD Example 14
15 GD Example 15
16 GD Example 16
17 GD Example 17
18 GD Example 18
19 GD Example 19
20 GD Example 20
21 GD Example 21
22 Choosing learning rate 22
23 Feature Scaling 23
24 Gradient Descent vs Closed Form Gradient Descent Closed form 24
25 Issues with Gradient Descent Might get stuck in local optimum and not converge to global optimum Restart from multiple initial points Only works with differentiable loss functions Small or large gradients Feature scaling helps Tune learning rate Can use line search for determining optimal learning rate 25
26 Gradient Descent Outline Derivation for simple and multiple Linear Regression Issues with Gradient Descent Comparison with closed-form solution Regularization Ridge and Lasso regression Lab example 26
27 Generalization in ML Simple model Complex model Goal is to generalize well on new testing data Risk of overfitting to training data MSE close to 0, but performs poorly on test data 27
28 Bias-Variance Tradeoff Under-fitting Over-fitting Bias = Difference between estimated and true models Variance = Model difference on different training sets MSE is proportional to Bias + Variance 28
29 Regularization Reduce model complexity Reduce model variance 29
30 Ridge regression 1 2 λ λ 2 If λ = 0, we train linear regression If λ is large, the coefficients will shrink close to 0 30
31 Bias-Variance Tradeoff MSE Optimal Ridge regression Bias Variance Linear regression Reduced model complexity Ridge performs better when linear regression has high variance Example: d (dimension) is close to n (training set size) 31
32 Coefficient shrinkage Predict credit card balance 32
33 GD for Ridge Regression 1 2 α α αλθ j θ j θ j (1 αλ) α h θ x (i) y (i) x j (i) 33
34 GD for Ridge Regression 1 2 α α αλθ j θ j θ j (1 αλ) α h θ x (i) y (i) x j (i) 34
35 Lasso regression n d J θ = h θ x i y (i) 2 + λ θ j i=1 j=1 Squared Residuals Regularization L1 norm for regularization No closed form solution Algorithms based on quadratic programming or other optimization techniques 35
36 Ridge Alternative Formulations L2 Regularization min θ n σ i=1 h θ x i y i 2 subject to d σj=1 θ j 2 ε Lasso L1 regularization min θ σn i=1 h θ x i y (i) 2 subject to σd j=1 θ j ε 36
37 Lasso vs Ridge Ridge shrinks all coefficients Lasso sets some coefficients at 0 (sparse solution) Perform feature selection θ 1 መθ θ 1 መθ Optimum Optimum θ 0 θ 0 Lasso Ridge 37
38 Lasso vs Ridge 38
39 Lab example 39
40 Ridge regression Data processing (omit N/A) Fit ridge regression Coefficient values Coefficient norm 40
41 Ridge regression Fit ridge regression Coefficient values Coefficient norm λ controls parameter size 41
42 Lasso regression Fit Lasso regression 13 coefficients set at zero Coefficient norm 42
43 Acknowledgements Slides made using resources from: Andrew Ng Eric Eaton David Sontag Thanks!
DS Machine Learning and Data Mining I. Alina Oprea Associate Professor, CCIS Northeastern University
DS 4400 Machine Learning and Data Mining I Alina Oprea Associate Professor, CCIS Northeastern University January 24 2019 Logistics HW 1 is due on Friday 01/25 Project proposal: due Feb 21 1 page description
More informationDS Machine Learning and Data Mining I. Alina Oprea Associate Professor, CCIS Northeastern University
DS 4400 Machine Learning and Data Mining I Alina Oprea Associate Professor, CCIS Northeastern University January 22 2019 Outline Practical issues in Linear Regression Outliers Categorical variables Lab
More informationDS Machine Learning and Data Mining I. Alina Oprea Associate Professor, CCIS Northeastern University
DS 4400 Machine Learning and Data Mining I Alina Oprea Associate Professor, CCIS Northeastern University September 18 2018 Logistics HW 1 is on Piazza and Gradescope Deadline: Friday, Sept. 28, 2018 Office
More informationLinear Regression & Gradient Descent
Linear Regression & Gradient Descent These slides were assembled by Byron Boots, with grateful acknowledgement to Eric Eaton and the many others who made their course materials freely available online.
More informationLecture 13: Model selection and regularization
Lecture 13: Model selection and regularization Reading: Sections 6.1-6.2.1 STATS 202: Data mining and analysis October 23, 2017 1 / 17 What do we know so far In linear regression, adding predictors always
More informationOptimization Plugin for RapidMiner. Venkatesh Umaashankar Sangkyun Lee. Technical Report 04/2012. technische universität dortmund
Optimization Plugin for RapidMiner Technical Report Venkatesh Umaashankar Sangkyun Lee 04/2012 technische universität dortmund Part of the work on this technical report has been supported by Deutsche Forschungsgemeinschaft
More informationCSE Data Mining Concepts and Techniques STATISTICAL METHODS (REGRESSION) Professor- Anita Wasilewska. Team 13
CSE 634 - Data Mining Concepts and Techniques STATISTICAL METHODS Professor- Anita Wasilewska (REGRESSION) Team 13 Contents Linear Regression Logistic Regression Bias and Variance in Regression Model Fit
More informationCPSC 340: Machine Learning and Data Mining. More Regularization Fall 2017
CPSC 340: Machine Learning and Data Mining More Regularization Fall 2017 Assignment 3: Admin Out soon, due Friday of next week. Midterm: You can view your exam during instructor office hours or after class
More informationNetwork Traffic Measurements and Analysis
DEIB - Politecnico di Milano Fall, 2017 Sources Hastie, Tibshirani, Friedman: The Elements of Statistical Learning James, Witten, Hastie, Tibshirani: An Introduction to Statistical Learning Andrew Ng:
More informationFMA901F: Machine Learning Lecture 3: Linear Models for Regression. Cristian Sminchisescu
FMA901F: Machine Learning Lecture 3: Linear Models for Regression Cristian Sminchisescu Machine Learning: Frequentist vs. Bayesian In the frequentist setting, we seek a fixed parameter (vector), with value(s)
More informationRobust Regression. Robust Data Mining Techniques By Boonyakorn Jantaranuson
Robust Regression Robust Data Mining Techniques By Boonyakorn Jantaranuson Outline Introduction OLS and important terminology Least Median of Squares (LMedS) M-estimator Penalized least squares What is
More informationOptimization. Industrial AI Lab.
Optimization Industrial AI Lab. Optimization An important tool in 1) Engineering problem solving and 2) Decision science People optimize Nature optimizes 2 Optimization People optimize (source: http://nautil.us/blog/to-save-drowning-people-ask-yourself-what-would-light-do)
More information6 Model selection and kernels
6. Bias-Variance Dilemma Esercizio 6. While you fit a Linear Model to your data set. You are thinking about changing the Linear Model to a Quadratic one (i.e., a Linear Model with quadratic features φ(x)
More informationLinear Regression QuadraJc Regression Year
Linear Regression Regression Given: n Data X = x (1),...,x (n)o where x (i) 2 R d n Corresponding labels y = y (1),...,y (n)o where y (i) 2 R September Arc+c Sea Ice Extent (1,000,000 sq km) 9 8 7 6 5
More informationCPSC 340: Machine Learning and Data Mining. Robust Regression Fall 2015
CPSC 340: Machine Learning and Data Mining Robust Regression Fall 2015 Admin Can you see Assignment 1 grades on UBC connect? Auditors, don t worry about it. You should already be working on Assignment
More informationCSE446: Linear Regression. Spring 2017
CSE446: Linear Regression Spring 2017 Ali Farhadi Slides adapted from Carlos Guestrin and Luke Zettlemoyer Prediction of continuous variables Billionaire says: Wait, that s not what I meant! You say: Chill
More informationMachine Learning / Jan 27, 2010
Revisiting Logistic Regression & Naïve Bayes Aarti Singh Machine Learning 10-701/15-781 Jan 27, 2010 Generative and Discriminative Classifiers Training classifiers involves learning a mapping f: X -> Y,
More informationCS535 Big Data Fall 2017 Colorado State University 10/10/2017 Sangmi Lee Pallickara Week 8- A.
CS535 Big Data - Fall 2017 Week 8-A-1 CS535 BIG DATA FAQs Term project proposal New deadline: Tomorrow PA1 demo PART 1. BATCH COMPUTING MODELS FOR BIG DATA ANALYTICS 5. ADVANCED DATA ANALYTICS WITH APACHE
More informationREGRESSION ANALYSIS : LINEAR BY MAUAJAMA FIRDAUS & TULIKA SAHA
REGRESSION ANALYSIS : LINEAR BY MAUAJAMA FIRDAUS & TULIKA SAHA MACHINE LEARNING It is the science of getting computer to learn without being explicitly programmed. Machine learning is an area of artificial
More informationMachine Learning and Computational Statistics, Spring 2016 Homework 1: Ridge Regression and SGD
Machine Learning and Computational Statistics, Spring 2016 Homework 1: Ridge Regression and SGD Due: Friday, February 5, 2015, at 6pm (Submit via NYU Classes) Instructions: Your answers to the questions
More informationGradient Descent Optimization Algorithms for Deep Learning Batch gradient descent Stochastic gradient descent Mini-batch gradient descent
Gradient Descent Optimization Algorithms for Deep Learning Batch gradient descent Stochastic gradient descent Mini-batch gradient descent Slide credit: http://sebastianruder.com/optimizing-gradient-descent/index.html#batchgradientdescent
More informationLasso Regression: Regularization for feature selection
Lasso Regression: Regularization for feature selection CSE 416: Machine Learning Emily Fox University of Washington April 12, 2018 Symptom of overfitting 2 Often, overfitting associated with very large
More informationProximal operator and methods
Proximal operator and methods Master 2 Data Science, Univ. Paris Saclay Robert M. Gower Optimization Sum of Terms A Datum Function Finite Sum Training Problem The Training Problem Convergence GD I Theorem
More informationGradient LASSO algoithm
Gradient LASSO algoithm Yongdai Kim Seoul National University, Korea jointly with Yuwon Kim University of Minnesota, USA and Jinseog Kim Statistical Research Center for Complex Systems, Korea Contents
More informationCSC 4510 Machine Learning
4: Regression (con.nued) CSC 4510 Machine Learning Dr. Mary Angela Papalaskari Department of CompuBng Sciences Villanova University Course website: www.csc.villanova.edu/~map/4510/ The slides in this presentabon
More informationCPSC 340: Machine Learning and Data Mining. Regularization Fall 2016
CPSC 340: Machine Learning and Data Mining Regularization Fall 2016 Assignment 2: Admin 2 late days to hand it in Friday, 3 for Monday. Assignment 3 is out. Due next Wednesday (so we can release solutions
More informationGradient Descent. Wed Sept 20th, James McInenrey Adapted from slides by Francisco J. R. Ruiz
Gradient Descent Wed Sept 20th, 2017 James McInenrey Adapted from slides by Francisco J. R. Ruiz Housekeeping A few clarifications of and adjustments to the course schedule: No more breaks at the midpoint
More informationEE 511 Linear Regression
EE 511 Linear Regression Instructor: Hanna Hajishirzi hannaneh@washington.edu Slides adapted from Ali Farhadi, Mari Ostendorf, Pedro Domingos, Carlos Guestrin, and Luke Zettelmoyer, Announcements Hw1 due
More informationOverfitting. Machine Learning CSE546 Carlos Guestrin University of Washington. October 2, Bias-Variance Tradeoff
Overfitting Machine Learning CSE546 Carlos Guestrin University of Washington October 2, 2013 1 Bias-Variance Tradeoff Choice of hypothesis class introduces learning bias More complex class less bias More
More informationA Brief Look at Optimization
A Brief Look at Optimization CSC 412/2506 Tutorial David Madras January 18, 2018 Slides adapted from last year s version Overview Introduction Classes of optimization problems Linear programming Steepest
More informationMachine Learning Basics: Stochastic Gradient Descent. Sargur N. Srihari
Machine Learning Basics: Stochastic Gradient Descent Sargur N. srihari@cedar.buffalo.edu 1 Topics 1. Learning Algorithms 2. Capacity, Overfitting and Underfitting 3. Hyperparameters and Validation Sets
More informationMachine Learning and Computational Statistics, Spring 2015 Homework 1: Ridge Regression and SGD
Machine Learning and Computational Statistics, Spring 2015 Homework 1: Ridge Regression and SGD Due: Friday, February 6, 2015, at 4pm (Submit via NYU Classes) Instructions: Your answers to the questions
More informationThe exam is closed book, closed notes except your one-page cheat sheet.
CS 189 Fall 2015 Introduction to Machine Learning Final Please do not turn over the page before you are instructed to do so. You have 2 hours and 50 minutes. Please write your initials on the top-right
More informationCOMPUTATIONAL INTELLIGENCE (INTRODUCTION TO MACHINE LEARNING) SS18. Lecture 2: Linear Regression Gradient Descent Non-linear basis functions
COMPUTATIONAL INTELLIGENCE (INTRODUCTION TO MACHINE LEARNING) SS18 Lecture 2: Linear Regression Gradient Descent Non-linear basis functions LINEAR REGRESSION MOTIVATION Why Linear Regression? Simplest
More informationEnsemble Methods: Bagging
Ensemble Methods: Bagging Instructor: Jessica Wu Harvey Mudd College The instructor gratefully acknowledges Eric Eaton (UPenn), Jenna Wiens (UMich), Tommi Jaakola (MIT), David Kauchak (Pomona), David Sontag
More informationOptimization. 1. Optimization. by Prof. Seungchul Lee Industrial AI Lab POSTECH. Table of Contents
Optimization by Prof. Seungchul Lee Industrial AI Lab http://isystems.unist.ac.kr/ POSTECH Table of Contents I. 1. Optimization II. 2. Solving Optimization Problems III. 3. How do we Find x f(x) = 0 IV.
More informationNeural Networks. Robot Image Credit: Viktoriya Sukhanova 123RF.com
Neural Networks These slides were assembled by Eric Eaton, with grateful acknowledgement of the many others who made their course materials freely available online. Feel free to reuse or adapt these slides
More informationMachine Learning Lecture-1
Machine Learning Lecture-1 Programming Club Indian Institute of Technology Kanpur pclubiitk@gmail.com February 25, 2016 Programming Club (IIT Kanpur) ML-1 February 25, 2016 1 / 18 Acknowledgement This
More informationChapter 6: Linear Model Selection and Regularization
Chapter 6: Linear Model Selection and Regularization As p (the number of predictors) comes close to or exceeds n (the sample size) standard linear regression is faced with problems. The variance of the
More informationLECTURE 12: LINEAR MODEL SELECTION PT. 3. October 23, 2017 SDS 293: Machine Learning
LECTURE 12: LINEAR MODEL SELECTION PT. 3 October 23, 2017 SDS 293: Machine Learning Announcements 1/2 Presentation of the CS Major & Minors TODAY @ lunch Ford 240 FREE FOOD! Announcements 2/2 CS Internship
More informationCS489/698: Intro to ML
CS489/698: Intro to ML Lecture 14: Training of Deep NNs Instructor: Sun Sun 1 Outline Activation functions Regularization Gradient-based optimization 2 Examples of activation functions 3 5/28/18 Sun Sun
More informationCombine the PA Algorithm with a Proximal Classifier
Combine the Passive and Aggressive Algorithm with a Proximal Classifier Yuh-Jye Lee Joint work with Y.-C. Tseng Dept. of Computer Science & Information Engineering TaiwanTech. Dept. of Statistics@NCKU
More informationLecture on Modeling Tools for Clustering & Regression
Lecture on Modeling Tools for Clustering & Regression CS 590.21 Analysis and Modeling of Brain Networks Department of Computer Science University of Crete Data Clustering Overview Organizing data into
More informationCollaborative Sparsity and Compressive MRI
Modeling and Computation Seminar February 14, 2013 Table of Contents 1 T2 Estimation 2 Undersampling in MRI 3 Compressed Sensing 4 Model-Based Approach 5 From L1 to L0 6 Spatially Adaptive Sparsity MRI
More informationUnderstanding Andrew Ng s Machine Learning Course Notes and codes (Matlab version)
Understanding Andrew Ng s Machine Learning Course Notes and codes (Matlab version) Note: All source materials and diagrams are taken from the Coursera s lectures created by Dr Andrew Ng. Everything I have
More informationExperimental Data and Training
Modeling and Control of Dynamic Systems Experimental Data and Training Mihkel Pajusalu Alo Peets Tartu, 2008 1 Overview Experimental data Designing input signal Preparing data for modeling Training Criterion
More informationChapter 7: Numerical Prediction
Ludwig-Maximilians-Universität München Institut für Informatik Lehr- und Forschungseinheit für Datenbanksysteme Knowledge Discovery in Databases SS 2016 Chapter 7: Numerical Prediction Lecture: Prof. Dr.
More informationMachine Learning Basics. Sargur N. Srihari
Machine Learning Basics Sargur N. srihari@cedar.buffalo.edu 1 Overview Deep learning is a specific type of ML Necessary to have a solid understanding of the basic principles of ML 2 Topics Stochastic Gradient
More informationPerformance Estimation and Regularization. Kasthuri Kannan, PhD. Machine Learning, Spring 2018
Performance Estimation and Regularization Kasthuri Kannan, PhD. Machine Learning, Spring 2018 Bias- Variance Tradeoff Fundamental to machine learning approaches Bias- Variance Tradeoff Error due to Bias:
More informationDivide and Conquer Kernel Ridge Regression
Divide and Conquer Kernel Ridge Regression Yuchen Zhang John Duchi Martin Wainwright University of California, Berkeley COLT 2013 Yuchen Zhang (UC Berkeley) Divide and Conquer KRR COLT 2013 1 / 15 Problem
More informationLinear models. Subhransu Maji. CMPSCI 689: Machine Learning. 24 February February 2015
Linear models Subhransu Maji CMPSCI 689: Machine Learning 24 February 2015 26 February 2015 Overvie Linear models Perceptron: model and learning algorithm combined as one Is there a better ay to learn
More informationCSE446: Linear Regression. Spring 2017
CSE446: Linear Regression Spring 2017 Ali Farhadi Slides adapted from Carlos Guestrin and Luke Zettlemoyer Prediction of continuous variables Billionaire says: Wait, that s not what I meant! You say: Chill
More informationConvexization in Markov Chain Monte Carlo
in Markov Chain Monte Carlo 1 IBM T. J. Watson Yorktown Heights, NY 2 Department of Aerospace Engineering Technion, Israel August 23, 2011 Problem Statement MCMC processes in general are governed by non
More informationAn MM Algorithm for Multicategory Vertex Discriminant Analysis
An MM Algorithm for Multicategory Vertex Discriminant Analysis Tong Tong Wu Department of Epidemiology and Biostatistics University of Maryland, College Park May 22, 2008 Joint work with Professor Kenneth
More informationLinear Methods for Regression and Shrinkage Methods
Linear Methods for Regression and Shrinkage Methods Reference: The Elements of Statistical Learning, by T. Hastie, R. Tibshirani, J. Friedman, Springer 1 Linear Regression Models Least Squares Input vectors
More informationLearning via Optimization
Lecture 7 1 Outline 1. Optimization Convexity 2. Linear regression in depth Locally weighted linear regression 3. Brief dips Logistic Regression [Stochastic] gradient ascent/descent Support Vector Machines
More informationEE613 Machine Learning for Engineers LINEAR REGRESSION. Sylvain Calinon Robot Learning & Interaction Group Idiap Research Institute Nov.
EE613 Machine Learning for Engineers LINEAR REGRESSION Sylvain Calinon Robot Learning & Interaction Group Idiap Research Institute Nov. 4, 2015 1 Outline Multivariate ordinary least squares Singular value
More informationSVM in Oracle Database 10g: Removing the Barriers to Widespread Adoption of Support Vector Machines
SVM in Oracle Database 10g: Removing the Barriers to Widespread Adoption of Support Vector Machines Boriana Milenova, Joseph Yarmus, Marcos Campos Data Mining Technologies Oracle Overview Support Vector
More informationCPSC 340: Machine Learning and Data Mining. Logistic Regression Fall 2016
CPSC 340: Machine Learning and Data Mining Logistic Regression Fall 2016 Admin Assignment 1: Marks visible on UBC Connect. Assignment 2: Solution posted after class. Assignment 3: Due Wednesday (at any
More informationCOMPUTATIONAL INTELLIGENCE (CS) (INTRODUCTION TO MACHINE LEARNING) SS16. Lecture 2: Linear Regression Gradient Descent Non-linear basis functions
COMPUTATIONAL INTELLIGENCE (CS) (INTRODUCTION TO MACHINE LEARNING) SS16 Lecture 2: Linear Regression Gradient Descent Non-linear basis functions LINEAR REGRESSION MOTIVATION Why Linear Regression? Regression
More information10703 Deep Reinforcement Learning and Control
10703 Deep Reinforcement Learning and Control Russ Salakhutdinov Machine Learning Department rsalakhu@cs.cmu.edu Policy Gradient I Used Materials Disclaimer: Much of the material and slides for this lecture
More informationMachine Learning: Think Big and Parallel
Day 1 Inderjit S. Dhillon Dept of Computer Science UT Austin CS395T: Topics in Multicore Programming Oct 1, 2013 Outline Scikit-learn: Machine Learning in Python Supervised Learning day1 Regression: Least
More informationComparison of Optimization Methods for L1-regularized Logistic Regression
Comparison of Optimization Methods for L1-regularized Logistic Regression Aleksandar Jovanovich Department of Computer Science and Information Systems Youngstown State University Youngstown, OH 44555 aleksjovanovich@gmail.com
More informationYelp Recommendation System
Yelp Recommendation System Jason Ting, Swaroop Indra Ramaswamy Institute for Computational and Mathematical Engineering Abstract We apply principles and techniques of recommendation systems to develop
More information3 Types of Gradient Descent Algorithms for Small & Large Data Sets
3 Types of Gradient Descent Algorithms for Small & Large Data Sets Introduction Gradient Descent Algorithm (GD) is an iterative algorithm to find a Global Minimum of an objective function (cost function)
More informationCPSC 340: Machine Learning and Data Mining. More Linear Classifiers Fall 2017
CPSC 340: Machine Learning and Data Mining More Linear Classifiers Fall 2017 Admin Assignment 3: Due Friday of next week. Midterm: Can view your exam during instructor office hours next week, or after
More informationMachine Learning. Topic 4: Linear Regression Models
Machine Learning Topic 4: Linear Regression Models (contains ideas and a few images from wikipedia and books by Alpaydin, Duda/Hart/ Stork, and Bishop. Updated Fall 205) Regression Learning Task There
More informationLecture 27, April 24, Reading: See class website. Nonparametric regression and kernel smoothing. Structured sparse additive models (GroupSpAM)
School of Computer Science Probabilistic Graphical Models Structured Sparse Additive Models Junming Yin and Eric Xing Lecture 7, April 4, 013 Reading: See class website 1 Outline Nonparametric regression
More informationMachine Learning using Matlab. Lecture 3 Logistic regression and regularization
Machine Learning using Matlab Lecture 3 Logistic regression and regularization Presentation Date (correction) 10.07.2017 11.07.2017 17.07.2017 18.07.2017 24.07.2017 25.07.2017 Project proposals 13 submissions,
More information2. Linear Regression and Gradient Descent
Pattern Recognition And Machine Learning - EPFL - Fall 2015 Emtiyaz Khan, Timur Bagautdinov, Carlos Becker, Ilija Bogunovic & Ksenia Konyushkova 2. Linear Regression and Gradient Descent 2.1 Goals The
More informationModel Complexity and Generalization
HT2015: SC4 Statistical Data Mining and Machine Learning Dino Sejdinovic Department of Statistics Oxford http://www.stats.ox.ac.uk/~sejdinov/sdmml.html Generalization Learning Curves Underfit Generalization
More informationPerceptron as a graph
Neural Networks Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University October 10 th, 2007 2005-2007 Carlos Guestrin 1 Perceptron as a graph 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0-6 -4-2
More informationHyperparameters and Validation Sets. Sargur N. Srihari
Hyperparameters and Validation Sets Sargur N. srihari@cedar.buffalo.edu 1 Topics in Machine Learning Basics 1. Learning Algorithms 2. Capacity, Overfitting and Underfitting 3. Hyperparameters and Validation
More informationCS294-1 Assignment 2 Report
CS294-1 Assignment 2 Report Keling Chen and Huasha Zhao February 24, 2012 1 Introduction The goal of this homework is to predict a users numeric rating for a book from the text of the user s review. The
More informationLasso. November 14, 2017
Lasso November 14, 2017 Contents 1 Case Study: Least Absolute Shrinkage and Selection Operator (LASSO) 1 1.1 The Lasso Estimator.................................... 1 1.2 Computation of the Lasso Solution............................
More informationCPSC 340: Machine Learning and Data Mining. Principal Component Analysis Fall 2016
CPSC 340: Machine Learning and Data Mining Principal Component Analysis Fall 2016 A2/Midterm: Admin Grades/solutions will be posted after class. Assignment 4: Posted, due November 14. Extra office hours:
More informationRegularization Methods. Business Analytics Practice Winter Term 2015/16 Stefan Feuerriegel
Regularization Methods Business Analytics Practice Winter Term 2015/16 Stefan Feuerriegel Today s Lecture Objectives 1 Avoiding overfitting and improving model interpretability with the help of regularization
More informationIntroduction to optimization methods and line search
Introduction to optimization methods and line search Jussi Hakanen Post-doctoral researcher jussi.hakanen@jyu.fi How to find optimal solutions? Trial and error widely used in practice, not efficient and
More informationCSE 446 Bias-Variance & Naïve Bayes
CSE 446 Bias-Variance & Naïve Bayes Administrative Homework 1 due next week on Friday Good to finish early Homework 2 is out on Monday Check the course calendar Start early (midterm is right before Homework
More informationHMC CS 158, Fall 2017 Problem Set 3 Programming: Regularized Polynomial Regression
HMC CS 158, Fall 2017 Problem Set 3 Programming: Regularized Polynomial Regression Goals: To open up the black-box of scikit-learn and implement regression models. To investigate how adding polynomial
More informationLeveling Up as a Data Scientist. ds/2014/10/level-up-ds.jpg
Model Optimization Leveling Up as a Data Scientist http://shorelinechurch.org/wp-content/uploa ds/2014/10/level-up-ds.jpg Bias and Variance Error = (expected loss of accuracy) 2 + flexibility of model
More informationComputational Intelligence (CS) SS15 Homework 1 Linear Regression and Logistic Regression
Computational Intelligence (CS) SS15 Homework 1 Linear Regression and Logistic Regression Anand Subramoney Points to achieve: 17 pts Extra points: 5* pts Info hour: 28.04.2015 14:00-15:00, HS i12 (ICK1130H)
More informationCSC 411: Lecture 02: Linear Regression
CSC 411: Lecture 02: Linear Regression Raquel Urtasun & Rich Zemel University of Toronto Sep 16, 2015 Urtasun & Zemel (UofT) CSC 411: 02-Regression Sep 16, 2015 1 / 16 Today Linear regression problem continuous
More informationThe Alternating Direction Method of Multipliers
The Alternating Direction Method of Multipliers With Adaptive Step Size Selection Peter Sutor, Jr. Project Advisor: Professor Tom Goldstein October 8, 2015 1 / 30 Introduction Presentation Outline 1 Convex
More informationMachine Learning. Chao Lan
Machine Learning Chao Lan Machine Learning Prediction Models Regression Model - linear regression (least square, ridge regression, Lasso) Classification Model - naive Bayes, logistic regression, Gaussian
More informationEE613 Machine Learning for Engineers LINEAR REGRESSION. Sylvain Calinon Robot Learning & Interaction Group Idiap Research Institute Nov.
EE613 Machine Learning for Engineers LINEAR REGRESSION Sylvain Calinon Robot Learning & Interaction Group Idiap Research Institute Nov. 9, 2017 1 Outline Multivariate ordinary least squares Matlab code:
More informationOptimization for Machine Learning
with a focus on proximal gradient descent algorithm Department of Computer Science and Engineering Outline 1 History & Trends 2 Proximal Gradient Descent 3 Three Applications A Brief History A. Convex
More informationDeep Neural Networks Optimization
Deep Neural Networks Optimization Creative Commons (cc) by Akritasa http://arxiv.org/pdf/1406.2572.pdf Slides from Geoffrey Hinton CSC411/2515: Machine Learning and Data Mining, Winter 2018 Michael Guerzhoy
More informationGradient Descent - Problem of Hiking Down a Mountain
Gradient Descent - Problem of Hiking Down a Mountain Udacity Have you ever climbed a mountain? I am sure you had to hike down at some point? Hiking down is a great exercise and it is going to help us understand
More informationLecture 26: Missing data
Lecture 26: Missing data Reading: ESL 9.6 STATS 202: Data mining and analysis December 1, 2017 1 / 10 Missing data is everywhere Survey data: nonresponse. 2 / 10 Missing data is everywhere Survey data:
More informationMachine Learning in Python. Rohith Mohan GradQuant Spring 2018
Machine Learning in Python Rohith Mohan GradQuant Spring 2018 What is Machine Learning? https://twitter.com/myusuf3/status/995425049170489344 Traditional Programming Data Computer Program Output Getting
More informationECS289: Scalable Machine Learning
ECS289: Scalable Machine Learning Cho-Jui Hsieh UC Davis Sept 22, 2016 Course Information Website: http://www.stat.ucdavis.edu/~chohsieh/teaching/ ECS289G_Fall2016/main.html My office: Mathematical Sciences
More informationELEG Compressive Sensing and Sparse Signal Representations
ELEG 867 - Compressive Sensing and Sparse Signal Representations Gonzalo R. Arce Depart. of Electrical and Computer Engineering University of Delaware Fall 211 Compressive Sensing G. Arce Fall, 211 1 /
More informationA Multilevel Acceleration for l 1 -regularized Logistic Regression
A Multilevel Acceleration for l 1 -regularized Logistic Regression Javier S. Turek Intel Labs 2111 NE 25th Ave. Hillsboro, OR 97124 javier.turek@intel.com Eran Treister Earth and Ocean Sciences University
More informationThe exam is closed book, closed notes except your one-page (two-sided) cheat sheet.
CS 189 Spring 2015 Introduction to Machine Learning Final You have 2 hours 50 minutes for the exam. The exam is closed book, closed notes except your one-page (two-sided) cheat sheet. No calculators or
More informationMachine Learning Techniques for Detecting Hierarchical Interactions in GLM s for Insurance Premiums
Machine Learning Techniques for Detecting Hierarchical Interactions in GLM s for Insurance Premiums José Garrido Department of Mathematics and Statistics Concordia University, Montreal EAJ 2016 Lyon, September
More informationCS 229 Midterm Review
CS 229 Midterm Review Course Staff Fall 2018 11/2/2018 Outline Today: SVMs Kernels Tree Ensembles EM Algorithm / Mixture Models [ Focus on building intuition, less so on solving specific problems. Ask
More informationCase Study 1: Estimating Click Probabilities
Case Study 1: Estimating Click Probabilities SGD cont d AdaGrad Machine Learning for Big Data CSE547/STAT548, University of Washington Sham Kakade March 31, 2015 1 Support/Resources Office Hours Yao Lu:
More informationNonparametric Methods Recap
Nonparametric Methods Recap Aarti Singh Machine Learning 10-701/15-781 Oct 4, 2010 Nonparametric Methods Kernel Density estimate (also Histogram) Weighted frequency Classification - K-NN Classifier Majority
More informationNon-linear models. Basis expansion. Overfitting. Regularization.
Non-linear models. Basis epansion. Overfitting. Regularization. Petr Pošík Czech Technical Universit in Prague Facult of Electrical Engineering Dept. of Cbernetics Non-linear models Basis epansion.....................................................................................................
More information