Homework #1 solution
A. Agarwal, A. Bouchard, J. Neeman and M. Traskin
September 15, 2009
1. (Directed Graphical models and conditional probabilities)
Let us introduce the following random variables.
X1 age variable, represents the age of a person in yea
CS281A, STAT241A Homework #3 solution
A. Agarwal and J. Neeman
October 25, 2009
Problem 1
Let us dene a vector cfw_zi,1 , . . . , zi,k for each i = 1 . . . n. The idea is that zi,j = 1 i yi = j . Hence we can
formulate the problem equivalently in terms o
CS281A/Stat241A Homework Assignment 1 (due September 15, 2009)
1. (Directed graphical models and conditional probabilities)
A standard test for prostate cancer, the prostate specic antigen (PSA) test, has a sensitivity of around
95% and a specicity of aro
Homework #4 solution
STAT C241A/CS C281A, Fall 2009
1
Prepared by: A. Agarwal, A. Bouchard, J. Neeman and M. Traskin
1. (HMMs with mixtures of Poissons)
(a) For time steps t cfw_1, . . . , T , let Qt be the Markov state sequence, Pt , the corresponding mi
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CS281A/Stat241A Homework Assignment 4 (due 5pm, October 28, 2009)
1. (HMMs with mixtures of Poissons) Suppose we wish to model trac in a network using an HMM.
Consider an HMM with discrete states qt (from a set of size m) and non-negative discrete observa
CS281A/Stat241A Homework Assignment 3 (due 5pm October 14, 2009)
1. (Logistic regression)
Suppose that we wish to model an unordered discrete response variable Y (such as the outcome
of a potential customers visit to a website), conditioned on a vector X
CS281A/Stat241A Homework Assignment 2 (due 5pm September 30, 2009)
1. (Polynomial representation)
Consider an undirected graphical model with potentials C (xC ) dened for each C in the set C of
maximal cliques. Suppose that the random variables X1 , . . .
i ` d S X VSX SX PS `dSX S X S x!XggygfxgWYYfYpy!acfw_kWY#X w 8Yga X P ihS d V X S S X y d R P PS P P Sy PS S X S P X X Vd g!GRuhask!up!y`a3k!a!gagafcyga!RW!p!xpgy S V d y P SX R X Sd y R Sd S P h e H y dS Pd BXHpkgEaYXY!usakxX!kaX w k!g9 x #tEkWg X S X y
Homework #2 solution
A. Agarwal and J. Neeman
STAT C241A/CS C281A , Fall 2009
1
Prepared by: A. Agarwal, A. Bouchard, J. Neeman and M. Traskin
1. Polynomial Representation
(a) We start from the basic representation of a probability distribution that facto
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Problem Set 2
Fall 2012
Issued: Tues. Sep. 4, 2012 Due: Thurs. Sep. 13, 2012
Reading: Chapters 6 and 8
Problem
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Solution to Problem Set 3
Fall 2012
Issued: Tues. Sep. 18, 2012 Due: Tues. Oct 2, 2012
Reading: Chapters 2, 3
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Problem Set 2
Fall 2012
Issued: Tues. Sep. 4, 2012 Due: Thurs. Sep. 13, 2012
Reading: Chapters 6 and 8
Problem
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Solution to Problem Set 5
Fall 2012
Issued: Tues. Oct. 16, 2012
Due: Tues. Oct. 30, 2012
Reading: Chapters 9,
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Problem Set 5
Fall 2012
Issued: Tues. Oct. 16, 2012
Due: Tues. Oct. 30, 2012
Reading: Chapters 9, 10, 11, 12
P
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Solutions to Problem Set 1
Fall 2012
Issued: Tuesday, August 28, 2012 Due: Tuesday, September 4, 2012
Reading:
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Problem Set 7
Fall 2012
Issued: Tues. Nov. 13, 2012
Due: Thurs. Nov. 29, 2012
Reading: Sampling chapter. Notes
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Solution to Problem Set 7
Fall 2012
Issued: Tues. Nov. 13, 2012
Due: Thurs. Nov. 29, 2012
Reading: Sampling ch
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Problem Set 4
Fall 2012
Issued: Tues. Oct. 2, 2012
Due: Tues. Oct. 16, 2012
Reading: Chapters 4, 17
Problem 4.
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Problem Set 6
Fall 2012
Issued: Tues. Oct. 30, 2012
Due: Tues. Nov. 13, 2012
Reading: Chapters 14, 15, 26; Sam
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Solution to Problem Set 4
Fall 2012
Issued: Tues. Oct. 2, 2012
Due: Tues. Oct. 16, 2012
Reading: Chapters 4, 1
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CS281A/Stat241A Homework Assignment 5 (due Monday November 16, 2009)
1. (Kalman lter) The data in le hw5-1.data on the course web site contains noisy measurements of
the location of a particle moving in the plane, subject to gravity, random forces, and dr
CS281A/Stat241A: Statistical Learning Theory
Elimination, Moralization and Sum-Product Algorithm (09/14/04)
Lecturer: Michael I. Jordan
1
Scribes: Parvez Ahammad and Ying Zhang
Elimination for Undirected Graphical Models
For an arbitrary undirected graphi
Homework #4 solution
STAT C241A/CS C281A, Fall 2009
1
Prepared by: A. Agarwal, A. Bouchard, J. Neeman and M. Traskin
1. (a) See Figure 1 for the plot of the particles true location xt .
(b) See Figure 2 for the plot of the observations yt on top of the pa
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UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Problem Set 1
Fall 2012
Issued: Tuesday, August 28, 2012 Due: Tuesday, September 4, 2012
Reading: This homewor
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Problem Set 3
Fall 2012
Issued: Tues. Sep. 18, 2012 Due: Tues. Oct 2, 2012
Reading: Chapters 2, 3 and 4
Proble
UC Berkeley
Department of Electrical Engineering and Computer Science
Department of Statistics
EECS 281A / STAT 241A Statistical Learning Theory
Solution to Problem Set 6
Fall 2012
Issued: Tues. Oct. 30, 2012
Due: Tues. Nov. 13, 2012
Reading: Chapters 14,