Machine Learning and Deep Learning! Vincent Lepetit!

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1 Machine Learning and Deep Learning!! Vincent Lepetit! 1!

2 What is Machine Learning?! 2!

3 Hand-Written Digit Recognition! 2 9 3!

4 Hand-Written Digit Recognition! Formalization! 0 1 x A Images are 28x28 pixels.! f : x 2 R 784! {0, 1, 2,, 9}? Classification problem! 4!

5 Hand-Written Digit Recognition! Training Set! 5!

6 Face Detection! 6!

7 Face Detection! Formalization! 7!

8 Face Detection! Formalization! 8!

9 Face Detection! Formalization! f : x 2 R m n! {face, non-face}? Classification problem! 9!

10 Face Detection! Training Set! Faces: near frontal, varying age, race, gender, lighting;!! Non-faces: images containing anything else.! 10!

11 Spam Detection! 11!

12 Spam Detection! Formalization! f : x! {spam, non-spam} Classification problem! 12!

13 Spam Detection! Formalization! f : x! {spam, non-spam} x = 0 #viagra #pills. 1 C A 13!

14 Stock Price Prediction!?! 14!

15 Stock Price Prediction! Formalization!?! f : x 2 R T! stock price 2 R x Regression problem! 15!

16 Machine Translation! 16!

17 Recommendation Systems! 17!

18 Machine Learning! Supervised Learning! Unsupervised Learning! 18!

19 Machine Learning! Supervised Learning! Unsupervised Learning! 19!

20 Machine Learning! Supervised Learning! {(, face), (, face), (, face),, (, non-face), (, non-face), (, non-face),... } à face or non-face?! 20!

21 Machine Learning! Unsupervised Learning! 21!

22 Machine Learning! Unsupervised Learning! 22!

23 Artificial Intelligence/Machine Learning/Deep Learning! Artificial Intelligence! Expert Systems! A*! Machine Learning! Support Vector Machines! min-max! Machine Learning:! Algorithms that can improve their performance with training data.! Boosting! Deep Learning! Random Forests! 23!

24 Recommended Book! Pattern Recognition and Machine Learning.! Christopher Bishop, Springer, 2006.!! 24!

25 Schedule! 1 Jan 24: Introduction to Machine Learning! 2 Jan 31: Support Vector Machines! Feb 7: No lecture! 3 Feb 14: Support Vector Machines - TP! 4 Feb 28: Boosting! 5 Mar 7: Boosting - TP! 6 Mar 14: Random Forest! 7 Mar 21: Random Forest - TP! 8 Mar 28: Introduction to Deep Learning! 9 Apr 4: Deep Learning - optimisation! 10 Apr 11: Deep Learning - TP1! 11 Apr 25: Deep Learning - object detection! 12 May 2: Deep Learning - TP2, object detection! 13 May 16: GANs and deep reinforcement learning!! 25!

26 A First Example! 26!

27 Binary Classification! SALMON or SEA BASS?! 27!

28 Using Brightness! some algorithm! brightness Training set! brightness 28!

29 Using Length! some algorithm! length length Training set! brightness 29!

30 Using Brightness and Length! some algorithms! x = brightness length length brightness 30!

31 Using Brightness and Length! some algorithms! x = brightness length length Training set! brightness 31!

32 Nearest-Neighbor Classifier! Algorithm:! Given a new x to be classified, find the nearest neighbor in the training set;! Classify the point according to the label of this nearest neighbor.! length?! brightness 32!

33 Nearest-Neighbor Classifier! Voronoï diagram of the training set! Classification boundary! 33!

34 K-Nearest-Neighbor Classifier! Algorithm:! Given a new x to be classified, find its k nearest neighbors in the training set;! Classify the point according to the majority of labels of its nearest neighbors.! length?! brightness 34!

35 Training Set and Test Set! Training set! Test set! 35!

36 Training Set and Test Set! Training set! Test set! The real aim of supervised learning is to do well on test data that is not known during learning.!! Measure classification error as! 1 T X (x,y)2t [f(x) 6= y] 36!

37 Classification Error, k = 1! 1 T X (x,y)2t [f(x) 6= y] Training set! error =?! Test set! 37!

38 Classification Error, k = 1! 1 T X (x,y)2t [f(x) 6= y] Training set! Test set! error = 0.0! error = 0.15! 38!

39 Classification Error, k = 3! 1 T X (x,y)2t [f(x) 6= y] Training set! Test set! error = ! error = ! 39!

40 Classification Error, k = 7! 1 T X (x,y)2t [f(x) 6= y] Training set! Test set! error = ! error = ! 40!

41 Classification Error, k = 21! 1 T X (x,y)2t [f(x) 6= y] Training set! Test set! error = ! error = ! 41!

42 Generalization! The real aim of supervised learning is to do well on test data that is not known during learning.!! Choosing the values for the meta-parameters (only k here) that minimize the classification error on the training set is not necessarily the best policy!!! How to choose these parameters?!!! 42!

43 Meta-Parameters and Validation Set: Cross-Validation! Split training set into 'real training set' and validation set, and!! choose k that minimizes the classification error on the validation set.!!! 43!

44 Example: hand written digit recognition! test sample! nearest neighbors! 44!

45 Hand Written Digit Recognition! We need a way to measure the distance between 2 samples. For example:! dist(a, B) = s X (A(i, j) B(i, j)) 2 i,j 45!

46 k-nearest Neighbor: Summary! Simple but effective classification method:! On MNIST, 60k training samples, 10k test samples à 5% classification error.!! Also applies to multi-class problems.!! Only one single meta-parameter (k), easily tuned by cross-validation.!!!! 46!

47 k-nearest Neighbor: Disadvantages! What does nearest mean? Need for a distance measure.!! Computational cost: Must store and search through the training set.! Some data structures and algorithms can alleviate this problem.! 47!

48 The Curse of Dimensionality! For an estimator to be effective, you need the distance between neighboring points to be less than some value d, which depends on the problem. In one dimension, this requires on average n \sim 1/d points. In the context of the above k-nn example, if the data is described by just one feature with values ranging from 0 to 1 and with n training observations, then new data will be no further away than 1/n. Therefore, the nearest neighbor decision rule will be efficient as soon as 1/n is small compared to the scale of between-class feature variations.!! If the number of features is p, you now require n \sim 1/d^p points. Let s say that we require 10 points in one dimension: now 10^p points are required in p dimensions to pave the [0, 1] space. As p becomes large, the number of training points required for a good estimator grows exponentially.!! For example, if each point is just a single number (8 bytes), then an effective k- NN estimator in a paltry p \sim 20 dimensions would require more training data than the current estimated size of the entire internet (±1000 Exabytes or so).!! 48!

49 Naïve Bayesian Classifier! 49!

50 But first, a reminder on probabilities! 50!

51 Example!?! Hypothesis h B Hypothesis h W 51!

52 Prior!?! Hypothesis h B Hypothesis h W Prior:! P (H = h B )=0.5 P (H = h W )=0.5 H : random variable! 52!

53 Measures! Measure: Drawing a marble and looking at its color.!! Random variable C i, color of the i-th drawn marble.! 53!

54 Exploiting a Measure! Hypothesis h B Hypothesis h W Posterior:! P (H = h W C 0 =White)?! 54!

55 Using the Bayesian Theorem! Hypothesis h B Hypothesis h W Likelihood! P (H = h W C 0 =White)= P (C 0 =White H = h W )P (H = h W ) P (C 0 =White) 55!

56 P (C 0 =White) Hypothesis h B Hypothesis h W P (C 0 =White)= P (C 0 =White H = h W )P (H = h W )+ P (C 0 =White H = h B )P (H = h B ) 56!

57 P (C 0 =White) Hypothesis h B Hypothesis h W P (C 0 =White)= P (C 0 =White H = h W )P (H = h W )+ P (C 0 =White H = h B )P (H = h B ) (In fact, we do not need to estimate! P (C 0 =White) to decide which hypothesis is correct.)! 57!

58 Exploiting two Measures! Hypothesis h B Hypothesis h W Posterior:! P (H = h W C 0 =White,C 1 =Blue)?! 58!

59 Exploiting two Measures! P (H = h W C 0 =White,C 1 =Blue) W 0 1 = P (C 0=White,C 1 =Blue H=h W )P (H=h W ) P (C 0 =White,C 1 =Blue) W 0 P (C 0 =White,C 1 =Blue H=h W )P?! 59!

60 Naïve Bayesian! Assuming that C 0 and C 1 are independent:! P (C 0 =White,C 1 =Blue H = h W ) = P (C 0 =White H = h W )P (C 1 =Blue H = h W ) 60!

61 Deciding (after 1 measure)! If! P (H = h W C 0 =White)>P(H = h B C 0 =White)! we can decide that h W is the correct hypothesis.! P (H = h W C 0 =White)= P (C 0 =White H = h W )P (H = h W ) P (C 0 =White) P (H = h B C 0 =White)= P (C 0 =White H = h B )P (H = h B ) P (C 0 =White) P (C 0 =White) We do not need to compute! to do the comparison.! 61!

62 Naïve Bayesian Classifier for! Spam Filtering! 62!

63 If P (H = spam...) >P(H = not spam...), label as spam. What can we use as measures?!! One possibility: presence or absence of some words.!! Such measures, which are used for classification, are called 'features'.! 63!

64 !!! If P (H = spam W 0 = 1) >P(H = not spam W 0 = 1), label as spam. W 0 = 0 : Word W 0 is not found in the ;! W 0 = 1 : Word W 0 is found in the .! For the comparison, we only need to compare! P (W 0 =1 H = spam)p (H = spam) and P (W 0 =1 H = not spam)p (H = not spam).!! How do we know! P (W 0 =1 H = not spam) P (W 0 =1 H = spam)p P (H = spam) P (H = not spam) 64!

65 Training Set! First step: collecting a dataset of s, labeled as 'spam' or 'not-spam'.!! Second step: counting the number of spams and nonspams some words appear.!! Example: For a dataset of 432 spams and 2170 non-spams:! word! Appearances in spams! Appearances in non-spams! 0! Exercise! 6! 39! 1! Fun! 59! 9! 2! Viagra! 39! 19! Exercise: An contains the words 'Exercise', 'Fun', but not 'Viagra'. Given this dataset, would you classify it as spam or not spam?! 65!

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