Instance-Based Learning: Nearest neighbor and kernel regression and classificiation
|
|
- Joy Ford
- 5 years ago
- Views:
Transcription
1 Instance-Based Learning: Nearest neighbor and kernel regression and classificiation Emily Fox University of Washington February 3, 2017 Simplest approach: Nearest neighbor regression 1
2 Fit locally to each data point Predicted value = closest y i y 1 nearest neighbor (1-NN) regression price ($) Here, this is the closest datapoint 3 sq.ft. x 1-NN regression more formally Dataset of (,$) pairs: (x 1,y 1 ), (x 2,y 2 ),,(x N,y N ) Query point: x q 1. Find closest x i in dataset 2. Predict y price ($) Here, this is the closest datapoint 4 sq.ft. x 2
3 Visualizing 1-NN in multiple dimensions Voronoi tesselation (or diagram): - Divide space into N regions, each containing 1 datapoint - Defined such that any x in region is closest to region s datapoint Don t explicitly form! 5 Distance metrics: Defining notion of closest In 1D, just Euclidean distance: distance(x j,x q ) = x j -x q In multiple dimensions: - can define many interesting distance functions - most straightforwardly, might want to weight different dimensions differently 6 3
4 Weighting housing inputs Some inputs are more relevant than others # bedrooms # bathrooms sq.ft. living sq.ft. lot floors year built year renovated waterfront 7 Scaled Euclidean distance Formally, this is achieved via distance(x j, x q ) = a 1 (x j [1]-x q [1]) a d (x j [d]-x q [d]) 2 weight on each input (defining relative importance) Other example distance metrics: - Mahalanobis, rank-based, correlation-based, cosine similarity, Manhattan, Hamming, 8 4
5 Different distance metrics lead to different predictive surfaces Euclidean distance Manhattan distance 9 Can 1-NN be used for classification? Yes!! Just predict class of neighbor 10 5
6 1-NN algorithm Performing 1-NN search Query house: Dataset: Specify: Distance metric Output: Most similar house 6
7 1-NN algorithm closest house Initialize Dist2NN =, = Ø For i=1,2,,n Compute: δ = distance(, ) If δ < Dist2NN set = i set Dist2NN = δ Return most similar house i q query house closest house to query house 1-NN in practice 1.4 Nearest Neighbors Kernel (K = 1) Fit looks good for data dense in x and low noise
8 Sensitive to regions with little data 1.4 Nearest Neighbors Kernel (K = 1) Not great at interpolating over large regions Also sensitive to noise in data Fits can look quite wild Overfitting? 16 8
9 k-nearest neighbors Get more comps More reliable estimate if you base estimate off of a larger set of comparable homes $ = 850k $ =??? $ = 749k $ = 833k $ = 901k 18 9
10 k-nn regression more formally Dataset of (,$) pairs: (x 1,y 1 ), (x 2,y 2 ),,(x N,y N ) Query point: x q 1. Find k closest x i in dataset 2. Predict 19 Performing k-nn search Query house: Dataset: Specify: Distance metric Output: Most similar houses 10
11 k-nn algorithm Initialize Dist2kNN = sort(δ 1,,δ k ) = sort(,, ) 1 k For i=k+1,,n Compute: δ = distance( i, q ) If δ < Dist2kNN[k] find j such that δ > Dist2kNN[j-1] but δ < Dist2kNN[j] remove furthest house and shift queue: [j+1:k] = [j:k-1] Dist2kNN[j+1:k] = Dist2kNN[j:k-1] set Dist2kNN[j] = δ and [j] = Return k most similar houses sort first k houses by distance to query house list of sorted distances query house list of sorted houses i closest houses to query house k-nn in practice Much more reasonable fit in the presence of noise Boundary & sparse region issues 22 11
12 k-nn in practice Discontinuities! Neighbor either in or out 23 Issues with discontinuities Overall predictive accuracy might be okay, but For example, in housing application: - If you are a buyer or seller, this matters - Can be a jump in estimated value of house going just from 2640 sq.ft. to 2641 sq.ft. - Don t really believe this type of fit 24 12
13 Weighted k-nearest neighbors Weighted k-nn Weigh more similar houses more than those less similar in list of k-nn Predict: weights on NN q = c qnn1 y NN1 + c qnn2 y NN2 + c qnn3 y NN3 + + c qnnk y NNk c qnnj 26 13
14 How to define weights? Want weight c qnnj to be small when distance(x NNj,x q ) large and c qnnj to be large when distance(x NNj,x q ) small 27 Kernel weights for d=1 Define: c qnnj = Kernel λ ( x NNj -x q ) simple isotropic case Gaussian kernel: Kernel λ ( x i -x q ) = exp(-(x i -x q ) 2 /λ) Note: never exactly 0! 28 -λ 0 λ 14
15 Kernel weights for d Define: c qnnj = Kernel λ (distance(x NNj,x q )) 29 -λ 0 λ Kernel regression 15
16 Weighted k-nn Weigh more similar houses more than those less similar in list of k-nn Predict: weights on NN q = c qnn1 y NN1 + c qnn2 y NN2 + c qnn3 y NN3 + + c qnnk y NNk c qnnj 31 Kernel regression Instead of just weighting NN, weight all points Predict: weight on each datapoint Nadaraya-Watson kernel weighted average q = c qi y i c qi = Kernel λ (distance(x i,x q )) * y i Kernel λ (distance(x i,x q )) 32 16
17 Kernel regression in practice Kernel has bounded support Only subset of data needed to compute local fit 33 Choice of bandwidth λ Often, choice of kernel matters much less than choice of λ λ = 0.04 λ = 0.2 λ = 0.4 Boxcar kernel 34 17
18 Choosing λ (or k in k-nn) How to choose? Same story as always Cross Validation 35 Formalizing the idea of local fits 18
19 Contrasting with global average A globally constant fit weights all points equally equal weight on each datapoint q = 1 y i N = c y i c 37 Contrasting with global average Kernel regression leads to locally constant fit - slowly add in some points and let others gradually die off q = Kernel λ (distance(x i,x q )) * y i Kernel λ (distance(x i,x q )) 38 19
20 Local linear regression So far, fitting constant function locally at each point locally weighted averages Can instead fit a line or polynomial locally at each point locally weighted linear regression 39 Local regression rules of thumb - Local linear fit reduces bias at boundaries with minimum increase in variance - Local quadratic fit doesn t help at boundaries and increases variance, but does help capture curvature in the interior - With sufficient data, local polynomials of odd degree dominate those of even degree Recommended default choice: local linear regression 40 20
21 Discussion on k-nn and kernel regression Nonparametric approaches k-nn and kernel regression are examples of nonparametric regression General goals of nonparametrics: - Flexibility - Make few assumptions about f(x) - Complexity can grow with the number of observations N Lots of other choices: - Splines, trees, locally weighted structured regression models 42 21
22 Limiting behavior of NN: Noiseless setting (ε i =0) In the limit of getting an infinite amount of noiseless data, the MSE of 1-NN fit goes to 0 43 Limiting behavior of NN: Noiseless setting (ε i =0) In the limit of getting an infinite amount of noiseless data, the MSE of 1-NN fit goes to 0 1-NN fit Quadratic fit Not true for parametric models! 44 22
23 Error vs. amount of data Error 45 # data points in training set Limiting behavior of NN: Noisy data setting In the limit of getting an infinite amount of data, the MSE of NN fit goes to 0 if k grows, too 1-NN fit 200-NN fit Quadratic fit 46 23
24 NN and kernel methods for large d or small N NN and kernel methods work well when the data cover the space, but - the more dimensions d you have, the more points N you need to cover the space - need N = O(exp(d)) data points for good performance This is where parametric models become useful 47 Complexity of NN search Naïve approach: Brute force search - Given a query point x q - Scan through each point x 1,x 2,, x N - O(N) distance computations per 1-NN query! - O(Nlogk) per k-nn query! What if N is huge??? (and many queries) KD-trees! Locality-sensitive hashing, etc
25 k-nn for classification Spam filtering example Not spam Spam Input: x Output: y 50 Text of , sender, IP, 25
26 Using k-nn for classification Space of labeled s (not spam vs. spam), organized by similarity of text query not spam vs. spam: decide via majority vote of k-nn 51 Using k-nn for classification Space of labeled s (not spam vs. spam), organized by similarity of text query not spam vs. spam: decide via majority vote of k-nn 52 26
27 Summary for nearest neighbor and kernel regression What you can do now Motivate the use of nearest neighbor (NN) regression Define distance metrics in 1D and multiple dimensions Perform NN and k-nn regression Analyze computational costs of these algorithms Discuss sensitivity of NN to lack of data, dimensionality, and noise Perform weighted k-nn and define weights using a kernel Define and implement kernel regression Describe the effect of varying the kernel bandwidth λ or # of nearest neighbors k Select λ or k using cross validation Compare and contrast kernel regression with a global average fit Define what makes an approach nonparametric and why NN and kernel regression are considered nonparametric methods Analyze the limiting behavior of NN regression Use NN for classification 54 27
28 Recap of topics so far Emily Fox University of Washington February 3, 2017 What you have learned thus far Point estimation Regression Training, test, validation, generalization error Overfitting Bias-variance tradeoff Regularized regression = ridge, LASSO Cross validation Logistic regression Decision trees Boosting Instance-based learning 56 28
29 The ML pipeline Inputs Features Task Model Algorithm x Sq.ft. #bedrooms #bathrooms text of review loan application h j (x) x[j] x[j] p tf-idf Regression x or h j (x) R Classification x or h j (x) {0,1,...,k} (We ve focused on {-1,+1}) Linear models w T h(x) Decision trees Ensembles NN Optimize a lost function Gradient = 0 Gradient ascent/descent Stochastic gradient ascent/descent Coordinate ascent/descent Boosting/AdaBoost Evaluation and model selection: Training, validation or cross-validation, test error 57 Concepts: bias-variance tradeoff, overfitting Your Midterm Exam Content: Everything up to today Only 50mins, so arrive early and settle down quickly Cheat sheet: - Single 8 ½ x 11 handwritten sheet, front and back No: - Computer, phone, other materials, The exam: - Covers key concepts and ideas, work on understanding the big picture, and differences between methods 58 29
Instance-Based Learning: Nearest neighbor and kernel regression and classificiation
Instance-Based Learning: Nearest neighbor and kernel regression and classificiation Emily Fox University of Washington February 3, 2017 Simplest approach: Nearest neighbor regression 1 Fit locally to each
More informationGoing nonparametric: Nearest neighbor methods for regression and classification
Going nonparametric: Nearest neighbor methods for regression and classification STAT/CSE 46: Machine Learning Emily Fox University of Washington May 3, 208 Locality sensitive hashing for approximate NN
More informationGoing nonparametric: Nearest neighbor methods for regression and classification
Going nonparametric: Nearest neighbor methods for regression and classification STAT/CSE 46: Machine Learning Emily Fox University of Washington May 8, 28 Locality sensitive hashing for approximate NN
More informationProblem 1: Complexity of Update Rules for Logistic Regression
Case Study 1: Estimating Click Probabilities Tackling an Unknown Number of Features with Sketching Machine Learning for Big Data CSE547/STAT548, University of Washington Emily Fox January 16 th, 2014 1
More informationNearest Neighbor with KD Trees
Case Study 2: Document Retrieval Finding Similar Documents Using Nearest Neighbors Machine Learning/Statistics for Big Data CSE599C1/STAT592, University of Washington Emily Fox January 22 nd, 2013 1 Nearest
More informationNearest Neighbor with KD Trees
Case Study 2: Document Retrieval Finding Similar Documents Using Nearest Neighbors Machine Learning/Statistics for Big Data CSE599C1/STAT592, University of Washington Emily Fox January 22 nd, 2013 1 Nearest
More informationInstance-based Learning
Instance-based Learning Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University February 19 th, 2007 2005-2007 Carlos Guestrin 1 Why not just use Linear Regression? 2005-2007 Carlos Guestrin
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 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 24 2019 Logistics HW 1 is due on Friday 01/25 Project proposal: due Feb 21 1 page description
More informationSupervised Learning: Nearest Neighbors
CS 2750: Machine Learning Supervised Learning: Nearest Neighbors Prof. Adriana Kovashka University of Pittsburgh February 1, 2016 Today: Supervised Learning Part I Basic formulation of the simplest classifier:
More informationTask Description: Finding Similar Documents. Document Retrieval. Case Study 2: Document Retrieval
Case Study 2: Document Retrieval Task Description: Finding Similar Documents Machine Learning for Big Data CSE547/STAT548, University of Washington Sham Kakade April 11, 2017 Sham Kakade 2017 1 Document
More informationNotes and Announcements
Notes and Announcements Midterm exam: Oct 20, Wednesday, In Class Late Homeworks Turn in hardcopies to Michelle. DO NOT ask Michelle for extensions. Note down the date and time of submission. If submitting
More informationCSC 411: Lecture 05: Nearest Neighbors
CSC 411: Lecture 05: Nearest Neighbors Raquel Urtasun & Rich Zemel University of Toronto Sep 28, 2015 Urtasun & Zemel (UofT) CSC 411: 05-Nearest Neighbors Sep 28, 2015 1 / 13 Today Non-parametric models
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 informationLocality- Sensitive Hashing Random Projections for NN Search
Case Study 2: Document Retrieval Locality- Sensitive Hashing Random Projections for NN Search Machine Learning for Big Data CSE547/STAT548, University of Washington Sham Kakade April 18, 2017 Sham Kakade
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 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 informationCS178: Machine Learning and Data Mining. Complexity & Nearest Neighbor Methods
+ CS78: Machine Learning and Data Mining Complexity & Nearest Neighbor Methods Prof. Erik Sudderth Some materials courtesy Alex Ihler & Sameer Singh Machine Learning Complexity and Overfitting Nearest
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 informationCOMPUTATIONAL INTELLIGENCE SEW (INTRODUCTION TO MACHINE LEARNING) SS18. Lecture 6: k-nn Cross-validation Regularization
COMPUTATIONAL INTELLIGENCE SEW (INTRODUCTION TO MACHINE LEARNING) SS18 Lecture 6: k-nn Cross-validation Regularization LEARNING METHODS Lazy vs eager learning Eager learning generalizes training data before
More informationInstance-based Learning CE-717: Machine Learning Sharif University of Technology. M. Soleymani Fall 2015
Instance-based Learning CE-717: Machine Learning Sharif University of Technology M. Soleymani Fall 2015 Outline Non-parametric approach Unsupervised: Non-parametric density estimation Parzen Windows K-Nearest
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 informationText classification II CE-324: Modern Information Retrieval Sharif University of Technology
Text classification II CE-324: Modern Information Retrieval Sharif University of Technology M. Soleymani Fall 2015 Some slides have been adapted from: Profs. Manning, Nayak & Raghavan (CS-276, Stanford)
More informationCS246: Mining Massive Datasets Jure Leskovec, Stanford University
CS246: Mining Massive Datasets Jure Leskovec, Stanford University http://cs246.stanford.edu [Kumar et al. 99] 2/13/2013 Jure Leskovec, Stanford CS246: Mining Massive Datasets, http://cs246.stanford.edu
More informationMachine Learning Lecture 3
Machine Learning Lecture 3 Probability Density Estimation II 19.10.2017 Bastian Leibe RWTH Aachen http://www.vision.rwth-aachen.de leibe@vision.rwth-aachen.de Announcements Exam dates We re in the process
More informationClassification and K-Nearest Neighbors
Classification and K-Nearest Neighbors Administrivia o Reminder: Homework 1 is due by 5pm Friday on Moodle o Reading Quiz associated with today s lecture. Due before class Wednesday. NOTETAKER 2 Regression
More informationSupport Vector Machines + Classification for IR
Support Vector Machines + Classification for IR Pierre Lison University of Oslo, Dep. of Informatics INF3800: Søketeknologi April 30, 2014 Outline of the lecture Recap of last week Support Vector Machines
More informationNearest Neighbor Classification. Machine Learning Fall 2017
Nearest Neighbor Classification Machine Learning Fall 2017 1 This lecture K-nearest neighbor classification The basic algorithm Different distance measures Some practical aspects Voronoi Diagrams and Decision
More informationThe Boundary Graph Supervised Learning Algorithm for Regression and Classification
The Boundary Graph Supervised Learning Algorithm for Regression and Classification! Jonathan Yedidia! Disney Research!! Outline Motivation Illustration using a toy classification problem Some simple refinements
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 informationRecap: Gaussian (or Normal) Distribution. Recap: Minimizing the Expected Loss. Topics of This Lecture. Recap: Maximum Likelihood Approach
Truth Course Outline Machine Learning Lecture 3 Fundamentals (2 weeks) Bayes Decision Theory Probability Density Estimation Probability Density Estimation II 2.04.205 Discriminative Approaches (5 weeks)
More informationNeural Networks. Single-layer neural network. CSE 446: Machine Learning Emily Fox University of Washington March 10, /10/2017
3/0/207 Neural Networks Emily Fox University of Washington March 0, 207 Slides adapted from Ali Farhadi (via Carlos Guestrin and Luke Zettlemoyer) Single-layer neural network 3/0/207 Perceptron as a neural
More informationUVA CS 6316/4501 Fall 2016 Machine Learning. Lecture 15: K-nearest-neighbor Classifier / Bias-Variance Tradeoff. Dr. Yanjun Qi. University of Virginia
UVA CS 6316/4501 Fall 2016 Machine Learning Lecture 15: K-nearest-neighbor Classifier / Bias-Variance Tradeoff Dr. Yanjun Qi University of Virginia Department of Computer Science 11/9/16 1 Rough Plan HW5
More informationK-Nearest Neighbour (Continued) Dr. Xiaowei Huang
K-Nearest Neighbour (Continued) Dr. Xiaowei Huang https://cgi.csc.liv.ac.uk/~xiaowei/ A few things: No lectures on Week 7 (i.e., the week starting from Monday 5 th November), and Week 11 (i.e., the week
More informationNearest Neighbor Predictors
Nearest Neighbor Predictors September 2, 2018 Perhaps the simplest machine learning prediction method, from a conceptual point of view, and perhaps also the most unusual, is the nearest-neighbor method,
More informationMachine Learning: k-nearest Neighbors. Lecture 08. Razvan C. Bunescu School of Electrical Engineering and Computer Science
Machine Learning: k-nearest Neighbors Lecture 08 Razvan C. Bunescu School of Electrical Engineering and Computer Science bunescu@ohio.edu Nonparametric Methods: k-nearest Neighbors Input: A training dataset
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 informationFeature Extractors. CS 188: Artificial Intelligence Fall Some (Vague) Biology. The Binary Perceptron. Binary Decision Rule.
CS 188: Artificial Intelligence Fall 2008 Lecture 24: Perceptrons II 11/24/2008 Dan Klein UC Berkeley Feature Extractors A feature extractor maps inputs to feature vectors Dear Sir. First, I must solicit
More informationInstance-based Learning
Instance-based Learning Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University October 15 th, 2007 2005-2007 Carlos Guestrin 1 1-Nearest Neighbor Four things make a memory based learner:
More informationCISC 4631 Data Mining
CISC 4631 Data Mining Lecture 03: Nearest Neighbor Learning Theses slides are based on the slides by Tan, Steinbach and Kumar (textbook authors) Prof. R. Mooney (UT Austin) Prof E. Keogh (UCR), Prof. F.
More informationSupervised Learning: K-Nearest Neighbors and Decision Trees
Supervised Learning: K-Nearest Neighbors and Decision Trees Piyush Rai CS5350/6350: Machine Learning August 25, 2011 (CS5350/6350) K-NN and DT August 25, 2011 1 / 20 Supervised Learning Given training
More informationCS6375: Machine Learning Gautam Kunapuli. Mid-Term Review
Gautam Kunapuli Machine Learning Data is identically and independently distributed Goal is to learn a function that maps to Data is generated using an unknown function Learn a hypothesis that minimizes
More informationLinear Regression and K-Nearest Neighbors 3/28/18
Linear Regression and K-Nearest Neighbors 3/28/18 Linear Regression Hypothesis Space Supervised learning For every input in the data set, we know the output Regression Outputs are continuous A number,
More informationK-Nearest Neighbors. Jia-Bin Huang. Virginia Tech Spring 2019 ECE-5424G / CS-5824
K-Nearest Neighbors Jia-Bin Huang ECE-5424G / CS-5824 Virginia Tech Spring 2019 Administrative Check out review materials Probability Linear algebra Python and NumPy Start your HW 0 On your Local machine:
More informationMachine Learning Lecture 3
Many slides adapted from B. Schiele Machine Learning Lecture 3 Probability Density Estimation II 26.04.2016 Bastian Leibe RWTH Aachen http://www.vision.rwth-aachen.de leibe@vision.rwth-aachen.de Course
More informationMachine Learning Lecture 3
Course Outline Machine Learning Lecture 3 Fundamentals (2 weeks) Bayes Decision Theory Probability Density Estimation Probability Density Estimation II 26.04.206 Discriminative Approaches (5 weeks) Linear
More informationk-nearest Neighbors + Model Selection
10-601 Introduction to Machine Learning Machine Learning Department School of Computer Science Carnegie Mellon University k-nearest Neighbors + Model Selection Matt Gormley Lecture 5 Jan. 30, 2019 1 Reminders
More informationMIT 801. Machine Learning I. [Presented by Anna Bosman] 16 February 2018
MIT 801 [Presented by Anna Bosman] 16 February 2018 Machine Learning What is machine learning? Artificial Intelligence? Yes as we know it. What is intelligence? The ability to acquire and apply knowledge
More information7. Nearest neighbors. Learning objectives. Foundations of Machine Learning École Centrale Paris Fall 2015
Foundations of Machine Learning École Centrale Paris Fall 2015 7. Nearest neighbors Chloé-Agathe Azencott Centre for Computational Biology, Mines ParisTech chloe agathe.azencott@mines paristech.fr Learning
More informationDistribution-free Predictive Approaches
Distribution-free Predictive Approaches The methods discussed in the previous sections are essentially model-based. Model-free approaches such as tree-based classification also exist and are popular for
More information7. Nearest neighbors. Learning objectives. Centre for Computational Biology, Mines ParisTech
Foundations of Machine Learning CentraleSupélec Paris Fall 2016 7. Nearest neighbors Chloé-Agathe Azencot Centre for Computational Biology, Mines ParisTech chloe-agathe.azencott@mines-paristech.fr Learning
More informationMS1b Statistical Data Mining Part 3: Supervised Learning Nonparametric Methods
MS1b Statistical Data Mining Part 3: Supervised Learning Nonparametric Methods Yee Whye Teh Department of Statistics Oxford http://www.stats.ox.ac.uk/~teh/datamining.html Outline Supervised Learning: Nonparametric
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 informationGeometric data structures:
Geometric data structures: Machine Learning for Big Data CSE547/STAT548, University of Washington Sham Kakade Sham Kakade 2017 1 Announcements: HW3 posted Today: Review: LSH for Euclidean distance Other
More informationCS 340 Lec. 4: K-Nearest Neighbors
CS 340 Lec. 4: K-Nearest Neighbors AD January 2011 AD () CS 340 Lec. 4: K-Nearest Neighbors January 2011 1 / 23 K-Nearest Neighbors Introduction Choice of Metric Overfitting and Underfitting Selection
More informationChapter 5 Efficient Memory Information Retrieval
Chapter 5 Efficient Memory Information Retrieval In this chapter, we will talk about two topics: (1) What is a kd-tree? (2) How can we use kdtrees to speed up the memory-based learning algorithms? Since
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 informationUVA CS 4501: Machine Learning. Lecture 10: K-nearest-neighbor Classifier / Bias-Variance Tradeoff. Dr. Yanjun Qi. University of Virginia
UVA CS 4501: Machine Learning Lecture 10: K-nearest-neighbor Classifier / Bias-Variance Tradeoff Dr. Yanjun Qi University of Virginia Department of Computer Science 1 Where are we? è Five major secfons
More informationData Mining. Lecture 03: Nearest Neighbor Learning
Data Mining Lecture 03: Nearest Neighbor Learning Theses slides are based on the slides by Tan, Steinbach and Kumar (textbook authors) Prof. R. Mooney (UT Austin) Prof E. Keogh (UCR), Prof. F. Provost
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 informationCS 5614: (Big) Data Management Systems. B. Aditya Prakash Lecture #19: Machine Learning 1
CS 5614: (Big) Data Management Systems B. Aditya Prakash Lecture #19: Machine Learning 1 Supervised Learning Would like to do predicbon: esbmate a func3on f(x) so that y = f(x) Where y can be: Real number:
More informationAnnouncements. CS 188: Artificial Intelligence Spring Generative vs. Discriminative. Classification: Feature Vectors. Project 4: due Friday.
CS 188: Artificial Intelligence Spring 2011 Lecture 21: Perceptrons 4/13/2010 Announcements Project 4: due Friday. Final Contest: up and running! Project 5 out! Pieter Abbeel UC Berkeley Many slides adapted
More informationNonparametric Regression
Nonparametric Regression John Fox Department of Sociology McMaster University 1280 Main Street West Hamilton, Ontario Canada L8S 4M4 jfox@mcmaster.ca February 2004 Abstract Nonparametric regression analysis
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 informationClassification: Feature Vectors
Classification: Feature Vectors Hello, Do you want free printr cartriges? Why pay more when you can get them ABSOLUTELY FREE! Just # free YOUR_NAME MISSPELLED FROM_FRIEND... : : : : 2 0 2 0 PIXEL 7,12
More informationSlides for Data Mining by I. H. Witten and E. Frank
Slides for Data Mining by I. H. Witten and E. Frank 7 Engineering the input and output Attribute selection Scheme-independent, scheme-specific Attribute discretization Unsupervised, supervised, error-
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 informationVECTOR SPACE CLASSIFICATION
VECTOR SPACE CLASSIFICATION Christopher D. Manning, Prabhakar Raghavan and Hinrich Schütze, Introduction to Information Retrieval, Cambridge University Press. Chapter 14 Wei Wei wwei@idi.ntnu.no Lecture
More informationBias-Variance Analysis of Ensemble Learning
Bias-Variance Analysis of Ensemble Learning Thomas G. Dietterich Department of Computer Science Oregon State University Corvallis, Oregon 97331 http://www.cs.orst.edu/~tgd Outline Bias-Variance Decomposition
More informationLarge-Scale Lasso and Elastic-Net Regularized Generalized Linear Models
Large-Scale Lasso and Elastic-Net Regularized Generalized Linear Models DB Tsai Steven Hillion Outline Introduction Linear / Nonlinear Classification Feature Engineering - Polynomial Expansion Big-data
More informationSUPERVISED LEARNING METHODS. Stanley Liang, PhD Candidate, Lassonde School of Engineering, York University Helix Science Engagement Programs 2018
SUPERVISED LEARNING METHODS Stanley Liang, PhD Candidate, Lassonde School of Engineering, York University Helix Science Engagement Programs 2018 2 CHOICE OF ML You cannot know which algorithm will work
More informationPreface to the Second Edition. Preface to the First Edition. 1 Introduction 1
Preface to the Second Edition Preface to the First Edition vii xi 1 Introduction 1 2 Overview of Supervised Learning 9 2.1 Introduction... 9 2.2 Variable Types and Terminology... 9 2.3 Two Simple Approaches
More informationCSC411/2515 Tutorial: K-NN and Decision Tree
CSC411/2515 Tutorial: K-NN and Decision Tree Mengye Ren csc{411,2515}ta@cs.toronto.edu September 25, 2016 Cross-validation K-nearest-neighbours Decision Trees Review: Motivation for Validation Framework:
More informationLecture 24: Image Retrieval: Part II. Visual Computing Systems CMU , Fall 2013
Lecture 24: Image Retrieval: Part II Visual Computing Systems Review: K-D tree Spatial partitioning hierarchy K = dimensionality of space (below: K = 2) 3 2 1 3 3 4 2 Counts of points in leaf nodes Nearest
More informationA popular method for moving beyond linearity. 2. Basis expansion and regularization 1. Examples of transformations. Piecewise-polynomials and splines
A popular method for moving beyond linearity 2. Basis expansion and regularization 1 Idea: Augment the vector inputs x with additional variables which are transformation of x use linear models in this
More informationNon-Bayesian Classifiers Part I: k-nearest Neighbor Classifier and Distance Functions
Non-Bayesian Classifiers Part I: k-nearest Neighbor Classifier and Distance Functions Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr CS 551, Fall 2017 CS 551,
More informationKernels and Clustering
Kernels and Clustering Robert Platt Northeastern University All slides in this file are adapted from CS188 UC Berkeley Case-Based Learning Non-Separable Data Case-Based Reasoning Classification from similarity
More informationAnnouncements. CS 188: Artificial Intelligence Spring Classification: Feature Vectors. Classification: Weights. Learning: Binary Perceptron
CS 188: Artificial Intelligence Spring 2010 Lecture 24: Perceptrons and More! 4/20/2010 Announcements W7 due Thursday [that s your last written for the semester!] Project 5 out Thursday Contest running
More informationMachine Learning. Nonparametric methods for Classification. Eric Xing , Fall Lecture 2, September 12, 2016
Machine Learning 10-701, Fall 2016 Nonparametric methods for Classification Eric Xing Lecture 2, September 12, 2016 Reading: 1 Classification Representing data: Hypothesis (classifier) 2 Clustering 3 Supervised
More informationNonparametric and Semiparametric Econometrics Lecture Notes for Econ 221. Yixiao Sun Department of Economics, University of California, San Diego
Nonparametric and Semiparametric Econometrics Lecture Notes for Econ 221 Yixiao Sun Department of Economics, University of California, San Diego Winter 2007 Contents Preface ix 1 Kernel Smoothing: Density
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 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 20 2018 Review Solution for multiple linear regression can be computed in closed form
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 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 informationAnnouncements:$Rough$Plan$$
UVACS6316 Fall2015Graduate: MachineLearning Lecture16:K@nearest@neighbor Classifier/Bias@VarianceTradeoff 10/27/15 Dr.YanjunQi UniversityofVirginia Departmentof ComputerScience 1 Announcements:RoughPlan
More informationCPSC 340: Machine Learning and Data Mining. Multi-Class Classification Fall 2017
CPSC 340: Machine Learning and Data Mining Multi-Class Classification Fall 2017 Assignment 3: Admin Check update thread on Piazza for correct definition of trainndx. This could make your cross-validation
More information3 Nonlinear Regression
3 Linear models are often insufficient to capture the real-world phenomena. That is, the relation between the inputs and the outputs we want to be able to predict are not linear. As a consequence, nonlinear
More informationData Mining Classification: Alternative Techniques. Lecture Notes for Chapter 4. Instance-Based Learning. Introduction to Data Mining, 2 nd Edition
Data Mining Classification: Alternative Techniques Lecture Notes for Chapter 4 Instance-Based Learning Introduction to Data Mining, 2 nd Edition by Tan, Steinbach, Karpatne, Kumar Instance Based Classifiers
More informationK Nearest Neighbor Wrap Up K- Means Clustering. Slides adapted from Prof. Carpuat
K Nearest Neighbor Wrap Up K- Means Clustering Slides adapted from Prof. Carpuat K Nearest Neighbor classification Classification is based on Test instance with Training Data K: number of neighbors that
More informationClustering. Mihaela van der Schaar. January 27, Department of Engineering Science University of Oxford
Department of Engineering Science University of Oxford January 27, 2017 Many datasets consist of multiple heterogeneous subsets. Cluster analysis: Given an unlabelled data, want algorithms that automatically
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 informationCPSC 340: Machine Learning and Data Mining. Kernel Trick Fall 2017
CPSC 340: Machine Learning and Data Mining Kernel Trick Fall 2017 Admin Assignment 3: Due Friday. Midterm: Can view your exam during instructor office hours or after class this week. Digression: the other
More informationNeural Network Optimization and Tuning / Spring 2018 / Recitation 3
Neural Network Optimization and Tuning 11-785 / Spring 2018 / Recitation 3 1 Logistics You will work through a Jupyter notebook that contains sample and starter code with explanations and comments throughout.
More informationInstance-Based Learning.
Instance-Based Learning www.biostat.wisc.edu/~dpage/cs760/ Goals for the lecture you should understand the following concepts k-nn classification k-nn regression edited nearest neighbor k-d trees for nearest
More informationLecture 16: High-dimensional regression, non-linear regression
Lecture 16: High-dimensional regression, non-linear regression Reading: Sections 6.4, 7.1 STATS 202: Data mining and analysis November 3, 2017 1 / 17 High-dimensional regression Most of the methods we
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 informationUninformed Search Methods. Informed Search Methods. Midterm Exam 3/13/18. Thursday, March 15, 7:30 9:30 p.m. room 125 Ag Hall
Midterm Exam Thursday, March 15, 7:30 9:30 p.m. room 125 Ag Hall Covers topics through Decision Trees and Random Forests (does not include constraint satisfaction) Closed book 8.5 x 11 sheet with notes
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 informationPerceptron Introduction to Machine Learning. Matt Gormley Lecture 5 Jan. 31, 2018
10-601 Introduction to Machine Learning Machine Learning Department School of Computer Science Carnegie Mellon University Perceptron Matt Gormley Lecture 5 Jan. 31, 2018 1 Q&A Q: We pick the best hyperparameters
More informationApplying Supervised Learning
Applying Supervised Learning When to Consider Supervised Learning A supervised learning algorithm takes a known set of input data (the training set) and known responses to the data (output), and trains
More information