CS 6140: Machine Learning Spring 2016

Transcription

1 CS 6140: Machine Learning Spring 2016 Instructor: Lu Wang College of Computer and Informa?on Science Northeastern University Webpage:

2 Time and Loca?on Time: Thursdays from 6:00 pm 9:00 pm Loca)on: Behrakis Health Sciences Cntr 325

3 Course Webpage hrp:// courses/cs6140_sp2016.html

4 Prerequisites Programming Being able to write code in some programming languages (e.g. Python, Java, C/C++) proficiently Courses Algorithms Probability and sta?s?cs Linear algebra Some knowledge in machine learning Background Check

5 Textbook and References Main Textbook Kevin Murphy, "Machine Learning - a Probabilis?c Perspec?ve", MIT Press, Other textbooks Christopher M. Bishop, "PaRern Recogni?on and Machine Learning", Springer, Tom Mitchell, "Machine Learning", McGraw Hill, Machine learning lectures

6 Content of the Course Regression: linear regression, logis?c regression Dimensionality Reduc)on: Principal Component Analysis (PCA), Independent Component Analysis (ICA), Linear Discriminant Analysis Probabilis)c Models: Naive Bayes, maximum likelihood es?ma?on, bayesian inference Sta)s)cal Learning Theory: VC dimension Kernels: Support Vector Machines (SVMs), kernel tricks, duality Sequen)al Models and Structural Models: Hidden Markov Model (HMM), Condi?onal Random Fields (CRFs) Clustering: spectral clustering, hierarchical clustering Latent Variable Models: K-means, mixture models, expecta?on-maximiza?on (EM) algorithms, Latent Dirichlet Alloca?on (LDA), representa?on learning Deep Learning: feedforward neural network, restricted Boltzmann machine, autoencoders, recurrent neural network, convolu?onal neural network and others, including advanced topics for machine learning in natural language processing and text analysis

7 The Goal Not only what, but also why!

8 Grading Assignments 3 assignments, 10% for each Exam 1 exam, 30% March, 31, 2016 Project 1 project, 35% Par?cipa?on 5% Classes Piazza

9 Exam Open book March 31, 2016

10 Course Project Op?on 1: A machine learning relevant research project Op?on 2: Yelp Challenge 2-3 students as a team

11 Research Project Machine learning relevant Natural language processing Computer vision Robo?cs Bioinforma?cs Health informa?cs Novelty

12 Yelp Challenge

13 Yelp Challenge

14 Yelp Challenge

15 Course Project Grading We want to see novel and interes?ng projects! The problem needs to be well-defined, novel, useful, and prac?cal machine learning techniques Reasonable results and observa?ons

16 Course Project Grading Three reports Proposal (5%) Progress, with code (10%) Final, with code (10%) One presenta?on In class (10%)

17 Submission and Late Policy Each assignment or report, both electronic copy and hard copy, is due at the beginning of class on the corresponding due date. Electronic version On blackboard Hard copy In class

18 Submission and Late Policy Assignment or report turned in late will be charged 10 points (out of 100 points) off for each late day (i.e. 24 hours). Each student has a budget of 5 days throughout the semester before a late penalty is applied.

19 How to find us? Course webpage: hrp:// cs6140_sp2016.html Office hours Lu Wang: Thursdays from 4:30pm to 5:30pm, or by appointment, 448 WVH Gabriel Bakiewicz (TA), Mondays and Tuesdays from 4:00pm to 5:00pm, 362 WVH Piazza hrp://piazza.com/northeastern/spring2016/cs6140 All course relevant ques?ons go here

20 What is Machine Learning? A set of methods that can automa?cally detect parerns in data, and then use the uncovered parerns to predict future data, or to perform other kinds of decisions making under certainty.

21 Real World Applica?ons

22 Real World Applica?ons

23 Real World Applica?ons

24 Real World Applica?ons

25 Real World Applica?ons

26 Real World Applica?ons

27 Real World Applica?ons

28 Real World Applica?ons

29 Real World Applica?ons

30 Rela?ons with Other Areas Natural Language Processing Computer Vision Robo?cs A lot of other areas

31 Today s Outline Basic concepts in machine learning K-nearest neighbors Linear regression Ridge regression

32 Supervised vs. Unsupervised Learning Supervised learning Training set Training sample Gold-standard label - Classifica)on, if categorical - Regression, if numerical

33 Supervised Learning

34 Supervised Learning

35 Supervised Learning Goal: Generalizable to new input samples Overfiung vs. underfiung we use probabilis?c models Typical setup: Training set, test set, development set Features Evalua?on

36 Supervised Learning

37 Supervised Learning

38 Supervised Learning

39 Supervised Learning

40 Supervised Learning Regression Predic?ng stock price Predic?ng temperature Predic?ng revenue

41 Supervised vs. Unsupervised Learning Unsupervised Learning More about knowledge discovery

42 Unsupervised Learning Dimension reduc?on Principal component analysis

43 Unsupervised Learning Clustering (e.g. graph mining) RolX: Role Extrac.on and Mining in Large Networks, by Henderson et al, 2011

44 Unsupervised Learning Topic modeling

45 Parametric vs. Non-parametric model Fixed number of parameters? If yes, parametric model Number of parameters grow with the amount of training data? If yes, non-parametric model Computa?onal tractability

46 A non-parametric classifier: K-nearest neighbors (KNN) Basic idea: memorize all the training samples The more you have in training data, the more the model has to remember Nearest neighbor: Tes?ng phase: find closet sample, and return corresponding label

47 A non-parametric classifier: K-nearest neighbors (KNN) Basic idea: memorize all the training samples The more you have in training data, the more the model has to remember K-Nearest neighbor: Tes?ng phase: find the K nearest neighbors, and return the majority vote of their labels

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49 About K K=1: just piecewise constant labeling K=N: global majority vote (class)

50 About K

51 Problems of knn Can be slow when training data is big Searching for the neighbors takes?me Needs lots of memory to store training data Needs to tune k and distance func?on Not a probability distribu?on

52 Problems of knn Distance func?on Euclidean distance

53 Problems of knn Distance func?on Mahalanobis distance: weights on components

54 Probabilis?c knn We prefer a probabilis?c output because some?mes we may get an uncertain result 99 samples as yes, 101 samples as no à? Probabilis?c knn:

55 Probabilis?c knn 3-class synthe?c training data

56 Smoothing Class 1: 3, class 2: 0, class 3: 1 Original probability: P(y=1)=3/4, p(y=2)=0/4, p(y=3)=1/4 Add-1 smoothing: Class 1: 3+1, class 2: 0+1, class 3: 1+1 P(y=1)=4/7, p(y=2)=1/7, p(y=3)=2/7

57 Sowmax Class 1: 3, class 2: 0, class 3: 1 Original probability: P(y=1)=3/4, p(y=2)=0/4, p(y=3)=1/4 Redistribute probability mass into different classes Define a sowmax as

58 A parametric classifier: linear regression Assump?on: the response is a linear func?on of the inputs Inner product between input sample X and weight vector W Residual error: difference between predic?on and true label

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60 A parametric classifier: linear regression Inner product between input sample X and weight vector W Residual error: difference between predic?on and true label Assume residual error has a normal distribu?on

61 A parametric classifier: linear regression We can further assume Basic func?on expansion

62 A parametric classifier: linear regression

63 Learning with Maximum Likelihood Es?ma?on (MLE) Maximum Likelihood Es?ma?on (MLE)

64 Learning with Maximum Likelihood Log-likelihood Es?ma?on (MLE) Maximize log-likelihood is equivalent to minimize nega?ve log-likelihood (NLL)

65 Learning with Maximum Likelihood Es?ma?on (MLE) With our normal distribu?on assump?on Residual sum of squares (RSS) à We want to minimize it!

66 Deriva?on of MLE for Linear Regression Rewrite our objec?ve func?on as

67 Deriva?on of MLE for Linear Regression Rewrite our objec?ve func?on as Get the deriva?ve (or gradient)

68 Deriva?on of MLE for Linear Regression Rewrite our objec?ve func?on as Get the deriva?ve (or gradient) Set our deriva?ve to 0 Ordinary least squares solu)on

69 Geometric Interpreta?on Remember we have Therefore the projected value of y is à This corresponds to an orthogonal project of y onto the column space of X

70 Geometric Interpreta?on

71 Overfiung

72 Overfiung

73 A Prior on the Weight Zero-mean Gaussian prior

74 A Prior on the Weight Zero-mean Gaussian prior New objec?ve func?on

75 A Prior on the Weight Zero-mean Gaussian prior New objec?ve func?on

76 We want to minimize Ridge Regression

77 Ridge Regression We want to minimize New es?ma?on for the weight

78 Ridge Regression We want to minimize L2 regulariza)on New es?ma?on for the weight

79 What we learned Basic concepts in machine learning K-nearest neighbors non-parametric Linear regression parametric Ridge regression parametric

80 Homework Reading Murphy ch1, ch2, and ch7 Sign up at Piazza hrp://piazza.com/northeastern/spring2016/cs6140 Start thinking about course project and find a team! Project proposal due Jan 28th