Machine Learning
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1 Machine Learning Tom M. Mitchell Machine Learning Department Carnegie Mellon University April 5, 2011 Today: Latent Dirichlet Allocation topic models Social network analysis based on latent probabilistic models Kernel regression Readings: Kernels: Bishop Ch. 6.1 optional: Bishop Ch 6.2, 6.3 Kernel Methods for Pattern Analysis, Shawe-Taylor & Cristianini, Chapter 2 Supervised Dimensionality Reduction 1
2 Supervised Dimensionality Reduction Neural nets: learn hidden layer representation, designed to optimize network prediction accuracy PCA: unsupervised, minimize reconstruction error but sometimes people use PCA to re-represent original data before classification (to reduce dimension, to reduce overfitting) Fisher Linear Discriminant like PCA, learns a linear projection of the data but supervised: it uses labels to choose projection Fisher Linear Discriminant A method for projecting data into lower dimension to hopefully improve classification We ll consider 2-class case Project data onto vector that connects class means? 2
3 Fisher Linear Discriminant Project data onto one dimension, to help classification Define class means: Could choose w according to: Instead, Fisher Linear Discriminant chooses: Summary: Fisher Linear Discriminant Choose n-1 dimension projection for n-class classification problem Use within-class covariances to determine the projection Minimizes a different error function (the projected withinclass variances) 3
4 4 STORY STORIES TELL CHARACTER CHARACTERS AUTHOR READ TOLD SETTING TALES PLOT TELLING SHORT FICTION ACTION TRUE EVENTS TELLS TALE NOVEL MIND WORLD DREAM DREAMS THOUGHT IMAGINATION MOMENT THOUGHTS OWN REAL LIFE IMAGINE SENSE CONSCIOUSNESS STRANGE FEELING WHOLE BEING MIGHT HOPE WATER FISH SEA SWIM SWIMMING POOL LIKE SHELL SHARK TANK SHELLS SHARKS DIVING DOLPHINS SWAM LONG SEAL DIVE DOLPHIN UNDERWATER DISEASE BACTERIA DISEASES GERMS FEVER CAUSE CAUSED SPREAD VIRUSES INFECTION VIRUS MICROORGANISMS PERSON INFECTIOUS COMMON CAUSING SMALLPOX BODY INFECTIONS CERTAIN Example topics induced from a large collection of text MAGNETIC MAGNET WIRE NEEDLE CURRENT COIL POLES IRON COMPASS LINES CORE ELECTRIC DIRECTION FORCE MAGNETS BE MAGNETISM POLE INDUCED SCIENCE STUDY SCIENTISTS SCIENTIFIC KNOWLEDGE WORK RESEARCH CHEMISTRY TECHNOLOGY MANY MATHEMATICS BIOLOGY PHYSICS LABORATORY STUDIES WORLD SCIENTIST STUDYING SCIENCES BALL GAME TEAM FOOTBALL BASEBALL PLAYERS PLAY PLAYER BASKETBALL COACH PLAYED PLAYING HIT TENNIS TEAMS GAMES SPORTS BAT TERRY JOB WORK JOBS CAREER EXPERIENCE EMPLOYMENT OPPORTUNITIES WORKING TRAINING SKILLS CAREERS POSITIONS FIND POSITION OCCUPATIONS REQUIRE OPPORTUNITY EARN ABLE [Tennenbaum et al] What about Probabilistic Approaches? Supervised? Unsupervised?
5 5 STORY STORIES TELL CHARACTER CHARACTERS AUTHOR READ TOLD SETTING TALES PLOT TELLING SHORT FICTION ACTION TRUE EVENTS TELLS TALE NOVEL MIND WORLD DREAM DREAMS THOUGHT IMAGINATION MOMENT THOUGHTS OWN REAL LIFE IMAGINE SENSE CONSCIOUSNESS STRANGE FEELING WHOLE BEING MIGHT HOPE WATER FISH SEA SWIM SWIMMING POOL LIKE SHELL SHARK TANK SHELLS SHARKS DIVING DOLPHINS SWAM LONG SEAL DIVE DOLPHIN UNDERWATER DISEASE BACTERIA DISEASES GERMS FEVER CAUSE CAUSED SPREAD VIRUSES INFECTION VIRUS MICROORGANISMS PERSON INFECTIOUS COMMON CAUSING SMALLPOX BODY INFECTIONS CERTAIN Example topics induced from a large collection of text MAGNETIC MAGNET WIRE NEEDLE CURRENT COIL POLES IRON COMPASS LINES CORE ELECTRIC DIRECTION FORCE MAGNETS BE MAGNETISM POLE INDUCED SCIENCE STUDY SCIENTISTS SCIENTIFIC KNOWLEDGE WORK RESEARCH CHEMISTRY TECHNOLOGY MANY MATHEMATICS BIOLOGY PHYSICS LABORATORY STUDIES WORLD SCIENTIST STUDYING SCIENCES BALL GAME TEAM FOOTBALL BASEBALL PLAYERS PLAY PLAYER BASKETBALL COACH PLAYED PLAYING HIT TENNIS TEAMS GAMES SPORTS BAT TERRY JOB WORK JOBS CAREER EXPERIENCE EMPLOYMENT OPPORTUNITIES WORKING TRAINING SKILLS CAREERS POSITIONS FIND POSITION OCCUPATIONS REQUIRE OPPORTUNITY EARN ABLE [Tennenbaum et al] Plate Notation
![Latent Dirichlet Allocation Model Also extended to case where number of topics is not known in advance (hierarchical Dirichlet processes [Blei et al, 2004]) Clustering words into topics with Latent](/docs-images/77/75213468/images/6-0.jpg "Dirichlet Allocation [Blei, Ng, Jordan 2003] Probabilistic model for document set: For each of the D documents: 1. Pick a θ d ~ P(θ α) to define P(z θ d ) 2.")
6 Latent Dirichlet Allocation Model Also extended to case where number of topics is not known in advance (hierarchical Dirichlet processes [Blei et al, 2004]) Clustering words into topics with Latent Dirichlet Allocation [Blei, Ng, Jordan 2003] Probabilistic model for document set: For each of the D documents: 1. Pick a θ d ~ P(θ α) to define P(z θ d ) 2. For each of the N d words w Pick topic z n ~ P(z θ d ) Pick word w n ~ P(w z n, φ) Training this model defines topics (i.e., φ which defines P(W Z)) 6
7 Example topics induced from a large collection of text DISEASE BACTERIA WATER FISH MIND WORLD STORY STORIES DISEASES SEA DREAM TELL Significance: GERMS SWIM DREAMS CHARACTER FEVER SWIMMING THOUGHT CHARACTERS CAUSE POOL IMAGINATION AUTHOR Learned CAUSED topics LIKE reveal MOMENT implicit READ SPREAD SHELL THOUGHTS TOLD semantic VIRUSES categories SHARK of OWN words SETTING INFECTION TANK REAL TALES within VIRUS the documents SHELLS LIFE PLOT MICROORGANISMS SHARKS IMAGINE TELLING PERSON DIVING SENSE SHORT In INFECTIOUS many cases, DOLPHINS we CONSCIOUSNESS can FICTION COMMON SWAM STRANGE ACTION represent CAUSING documents LONG FEELING with 10 2 TRUE SMALLPOX SEAL WHOLE EVENTS topics BODY instead DIVE of 10 5 words BEING TELLS INFECTIONS CERTAIN DOLPHIN UNDERWATER MIGHT HOPE TALE NOVEL Especially important for short documents (e.g., s). Topics overlap when words don t! MAGNETIC MAGNET WIRE NEEDLE CURRENT COIL POLES IRON COMPASS LINES CORE ELECTRIC DIRECTION FORCE MAGNETS BE MAGNETISM POLE INDUCED SCIENCE STUDY SCIENTISTS SCIENTIFIC KNOWLEDGE WORK RESEARCH CHEMISTRY TECHNOLOGY MANY MATHEMATICS BIOLOGY PHYSICS LABORATORY STUDIES WORLD SCIENTIST STUDYING SCIENCES BALL GAME TEAM FOOTBALL BASEBALL PLAYERS PLAY PLAYER BASKETBALL COACH PLAYED PLAYING HIT TENNIS TEAMS GAMES SPORTS BAT TERRY [Tennenbaum et al] JOB WORK JOBS CAREER EXPERIENCE EMPLOYMENT OPPORTUNITIES WORKING TRAINING SKILLS CAREERS POSITIONS FIND POSITION OCCUPATIONS REQUIRE OPPORTUNITY EARN ABLE Analyzing topic distributions in 7
8 Author-Recipient-Topic model for Latent Dirichlet Allocation (LDA) [Blei, Ng, Jordan, 2003] Author-Recipient Topic (ART) [McCallum, Corrada, Wang, 2005] Enron Corpus 250k messages 23k people Date: Wed, 11 Apr :56: (PDT) From: To: Subject: Enron/TransAltaContract dated Jan 1, 2001 Please see below. Katalin Kiss of TransAlta has requested an electronic copy of our final draft? Are you OK with this? If so, the only version I have is the original draft without revisions. DP Debra Perlingiere Enron North America Corp. Legal Department 1400 Smith Street, EB 3885 Houston, Texas dperlin@enron.com 8
9 Topics, and prominent sender/receivers discovered by ART [McCallum et al, 2005] Top words within topic : Top author-recipients exhibiting this topic Topics, and prominent sender/receivers discovered by ART Beck = Chief Operations Officer Dasovich = Government Relations Executive Shapiro = Vice Presidence of Regulatory Affairs Steffes = Vice President of Government Affairs 9
10 Discovering Role Similarity Traditional SNA ART connection strength (A,B) = Similarity in recipients they sent to Similarity in authored topics, conditioned on recipient Discovering Role Similarity Tracy Geaconne Dan McCarty Traditional SNA ART Similar (send to same individuals) Different (discuss different topics) Geaconne = Secretary McCarty = Vice President 10
11 Discovering Role Similarity Lynn Blair Kimberly Watson Traditional SNA ART Different (send to different individuals) Similar (discuss same topics) Blair = Gas pipeline logistics Watson = Pipeline facilities planning What you should know Unsupervised dimension reduction using all features Principle Components Analysis Minimize reconstruction error Singular Value Decomposition Efficient PCA Independent components analysis Canonical correlation analysis Probabilistic models with latent variables Supervised dimension reduction Fisher Linear Discriminant Project to n-1 dimensions to discriminate n classes Hidden layers of Neural Networks Most flexible, local minima issues LOTS of ways of combining discovery of latent features with classification tasks 11
12 Kernel Functions Kernel functions provide a way to manipulate data as though it were projected into a higher dimensional space, by operating on it in its original space This leads to efficient algorithms And is a key component of algorithms such as Support Vector Machines kernel PCA kernel CCA kernel regression Linear Regression Wish to learn f: X Y, where X=<X 1, X n >, Y real-valued Learn where 12
13 Linear Regression Wish to learn f: X Y, where X=<X 1, X n >, Y real-valued Learn where note l th row of X is l th training example x Tl Linear Regression Wish to learn f: X Y, where X=<X 1, X n >, Y real-valued Learn where solve by taking derivative wrt w, setting to zero so: 13
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