ECE 5424: Introduction to Machine Learning
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1 ECE 5424: Introduction to Machine Learning Topics: Supervised Learning Measuring performance Nearest Neighbor Distance Metrics Readings: Barber 14 (knn) Stefan Lee Virginia Tech
2 Administrative Course add period is over If not enrolled, please leave. Virginia law apparently. (C) Dhruv Batra 2
3 HW0 HW0 is graded Average: 81% Median: 85% Max: 100% Min: 35% The lower your score, the harder you should expect to work. (C) Dhruv Batra 3
4 Question 1: HW0 Sam is an odd and not-so-honest person who carries around a bag containing 3 fair coins (heads and tails) and 1 coin which has heads on both sides (which he uses to cheat his friends out of small amounts of cash). He selects a coin randomly from the bag and flips it 4 times and the coin comes up heads each time. He bets you $10 the next flip will be heads. What is the probability the next flip will be heads? Only 1 coin is drawn from the bag, this coin is flipped 4 times. What is the probability of the 5 th flip being heads? Want: P(H 4H) P(H 4 H) = P(H fair) P(fair 4H) + P(H unfair) P(unfair 4H) P(fair 4H) = P(4H fair) P(fair) / P(4H) (Bayes Rule) P(4H) = P(4H fair) P(fair) + P(4H unfair) P(unfair) (C) Dhruv Batra 4
5 Recap from last time (C) Dhruv Batra 5
6 (C) Dhruv Batra Slide Credit: Yaser Abu-Mostapha 6
7 Nearest Neighbor Demo (C) Dhruv Batra 7
8 Proportion as Confidence Gender Classification from body proportions Igor Janjic & Daniel Friedman, Juniors (C) Dhruv Batra 8
9 Plan for today Supervised/Inductive Learning (A bit more on) Loss functions Nearest Neighbor Common Distance Metrics Kernel Classification/Regression Curse of Dimensionality (C) Dhruv Batra 9
10 Loss/Error Functions How do we measure performance? Regression: L 2 error Classification: #misclassifications Weighted misclassification via a cost matrix For 2-class classification: True Positive, False Positive, True Negative, False Negative For k-class classification: Confusion Matrix ROC curves (C) Dhruv Batra 10
11 Nearest Neighbors (C) Dhruv Batra Image Credit: Wikipedia 11
12 Instance/Memory-based Learning Four things make a memory based learner: A distance metric How many nearby neighbors to look at? A weighting function (optional) How to fit with the local points? (C) Dhruv Batra Slide Credit: Carlos Guestrin 12
13 1-Nearest Neighbour Four things make a memory based learner: A distance metric Euclidean (and others) How many nearby neighbors to look at? 1 A weighting function (optional) unused How to fit with the local points? Just predict the same output as the nearest neighbour. (C) Dhruv Batra Slide Credit: Carlos Guestrin 13
14 k-nearest Neighbour Four things make a memory based learner: A distance metric Euclidean (and others) How many nearby neighbors to look at? k A weighting function (optional) unused How to fit with the local points? Just predict the average output among the nearest neighbors. (C) Dhruv Batra Slide Credit: Carlos Guestrin 14
15 1-NN for Regression Here, this is the closest datapoint y x (C) Dhruv Batra Figure Credit: Carlos Guestrin 15
16 Multivariate distance metrics Suppose the input vectors x 1, x 2, x N are two dimensional: x 1 = ( x 11, x 12 ), x 2 = ( x 21, x 22 ), x N = ( x N1, x N2 ). One can draw the nearest-neighbor regions in input space. Dist(x i,x j ) = (x i1 x j1 ) 2 + (x i2 x j2 ) 2 Dist(x i,x j ) =(x i1 x j1 ) 2 +(3x i2 3x j2 ) 2 The relative scalings in the distance metric affect region shapes Slide Credit: Carlos Guestrin
17 Euclidean distance metric Or equivalently, D(x, x 0 )= D(x, x 0 )= s X i 2 i (x i x 0 i )2 q (x i x 0 i )T A(x i x 0 i ) where A Slide Credit: Carlos Guestrin
18 Notable distance metrics (and their level sets) Scaled Euclidian (L 2 ) Mahalanobis (non-diagonal A) Slide Credit: Carlos Guestrin
19 Minkowski distance Image Credit: By Waldir (Based on File:MinkowskiCircles.svg) (C) Dhruv Batra [CC BY-SA 3.0 ( via Wikimedia Commons 19
20 Notable distance metrics (and their level sets) Scaled Euclidian (L 2 ) L 1 norm (absolute) Mahalanobis (non-diagonal A) Slide Credit: Carlos Guestrin L inf (max) norm
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