Bayesian networks
Lecture 11
David Sontag
New York University
Outline for today
Modeling sequen&al data (e.g., =me series,
speech processing) using hidden Markov
models (HMMs)
Bayesian networks
Independence prope

Machine Learning and
Computational Statistics
(DS-GA-1003 and CSCI-GA.2567)
David Sontag
New York University
Slides adapted from Luke Zettlemoyer, Vibhav Gogate, Pedro
Domingos, and Carlos Guestrin
Logistics
Class webpage:
http:/cs.nyu.edu/~dsontag/cour

Introduc)on to Bayesian methods
Lecture 10
David Sontag
New York University
Slides adapted from Luke Zettlemoyer, Carlos Guestrin, Dan Klein,
and Vibhav Gogate
Bayesian learning
Bayesian learning uses probability to model
data a

Supervised learning methods
Lecture 5
David Sontag
New York University
Slides adapted from Vibhav Gogate, Carlos Guestrin,
Luke Zettlemoyer, and Andrew Moore
Plan for next few weeks
Midterm review
Guest lecture:
Yann LeCun on

Learning Parameters of Bayesian networks
Lecture 12
David Sontag
New York University
Bayesian networks
Reference: Chapter 3
Bayesian networks
A Bayesian network is specied by a directed acyclic graph
G=(V,E) with:
A Bayes

Machine Learning and Computational Statistics
David Sontag
New York University
Lecture 13, April 29, 2014
David Sontag (NYU)
Machine Learning and Computational Stats
Lecture 13, April 29, 2014
1 / 15
Expectation maximization
Algorithm is as follows:
1 Wri

Unsupervised learning
Lecture 13
David Sontag
New York University
Slides adapted from Carlos Guestrin, Dan Klein, Luke Ze@lemoyer,
Dan Weld, Vibhav Gogate, and Andrew Moore
Gaussian Mixture Models
P(Y): There are k

Learning theory
Lecture 4
David Sontag
New York University
Slides adapted from Carlos Guestrin & Luke Zettlemoyer
Whats next
We gave several machine learning algorithms:
Perceptron
Linear support vector machine (SVM)
SVM

Clustering
Lecture 8
David Sontag
New York University
Slides adapted from Luke Zettlemoyer, Vibhav Gogate,
Carlos Guestrin, Andrew Moore, Dan Klein
Clustering
Clustering:
Unsupervised learning
Requires data, but no labels
Detect patterns e.

Dimensionality Reduc1on
Lecture 9
David Sontag
New York University
Slides adapted from Carlos Guestrin and Luke Zettlemoyer
Class notes
PS5 will be released by Friday, due Monday
4/14
Feedback on project proposals will be

SVMs and Kernel Methods
Lecture 3
David Sontag
New York University
Slides adapted from Luke Zettlemoyer, Vibhav Gogate,
and Carlos Guestrin
Todays lecture
Dual form of soft-margin SVM
Feature mappings & kernels
Convexity, Mercers theorem
(Time permitting)

Support vector machines (SVMs)
Lecture 2
David Sontag
New York University
Slides adapted from Luke Zettlemoyer, Vibhav Gogate,
and Carlos Guestrin
Geometry of linear separators
(see blackboard)
A plane can be specified as the set of all points given by:
V