ENGN 2520 / CSCI 1950-F Homework 2
Due Friday February 15 by 4pm
Problem 1
In this problem we consider binary classication under a non-uniform loss function.
Let X be a nite input space and Y = cfw_0,
CSCI 1950-F Homework 3:
Handwritten Digit Classication
Brown University, Spring 2012
Homework due at 12:00pm on February 23, 2012
In this problem set, we consider the problem of handwritten digit reco
CSCI 1950-F Homework 6: Regularization & Sparsity
Brown University, Spring 2012
Homework due at 12:00pm on April 5, 2012
Question 1:
This problem compares various approaches to regularization and feat
ENGN 2520 / CSCI 1950-F Homework 3
Solution Key
Problem 1
Part A
We can plug the denition of logistic regression into the denition of the error function:
E(w) = log p(Dy | Dx , w)
n
p(yi | xi , w)
= l
Homework 7: Gaussian Processes & Neural Networks
CSCI 1420 & ENGN 2520, Brown University
Homework due at 11:59pm on November 7, 2013
Question 1:
The rst question explores binary Gaussian process class
Homework 3: Handwritten Digit Classication
CSCI1420 & ENGN2520, Brown University
Homework due at 11:59pm on October 3, 2013
In this problem set, we consider the problem of handwritten digit recognitio
ENGN 2520 / CSCI 1950-F Homework 3
Due Friday March 1 by 4pm
Problem 1
Consider binary classication (Y = cfw_0, 1) with logistic regression. In logistic regression we
assume p(y = 1|x) = (wT (x) for a
CSCI 1950-F Homework 10: HMMs & Topic Models
Brown University, Spring 2012
EXTRA CREDIT: Homework due at 12:00pm on May 10, 2012
Question 1:
We begin by learning hidden Markov models (HMMs) which desc
CSCI 1950-F Homework 1:
Naive Bayes Spam Classication
Brown University, Spring 2012
Homework due at 12:00pm on February 10, 2012
Hello, I am a prince in desperate need of a personal favor. Ive been re
ENGN 2520 / CSCI 1950-F Homework 7
Due Monday April 29 by 4pm
In this homework you will implement the EM algorithm for tting mixtures of Gaussians.
As described in class EM is an iterative method with
ENGN 2520 / CSCI 1950-F Homework 6
Due Tuesday April 16 by 4pm
Students may discuss and work on homework problems in groups. However, each student
must write down their solutions independently.
All of
ENGN 2520 / CSCI 1950-F Homework 1
Solution Key
Problem 1
The quantity p(apple) represents the marginal probability of selecting an apple, so we can simply sum over
all of the boxes:
p(apple | box)p(b
ENGN 2520 / CSCI 1950-F Homework 5
Due Friday March 15 by 4pm
Problem 1
Let S = cfw_s1 , . . . , sK be the set of states of a Markov chain. Let be the initial state distribution and M be the transiti
ENGN 2520 / CSCI 1950-F Homework 4
In this assignment you will implement a multiclass SVM to recognize handwritten digits.
You will use the data from Homework 2 that is available on the course website
ENGN 2520 / CSCI 1950-F Homework 2
Solution Key
Problem 1
To make an optimal decision rule for all x, for a given x we can choose the action that minimizes its individual
loss. If we choose c(x) = 0:
CSCI 1950-F Homework 9:
EM for Factor Analysis & Regression
Brown University, Spring 2012
Homework due at 12:00pm on May 3, 2012
Question 1:
The MovieLens dataset (http:/movielens.org) contains rating
CSCI 1950-F Homework 8:
K-Means Clustering & Bernoulli Mixture Models
Brown University, Spring 2012
Homework due at 12:00pm on April 26, 2012
Question 1:
In this question, we use the K-means algorithm
Homework 9: Hidden Markov Models
CSCI 1420 & ENGN 2520, Brown University
Homework due at 11:59pm on November 21, 2013
Question 1:
We rst examine a simple hidden Markov model (HMM). We observe a sequen
Homework 8: K-Means Clustering & Bernoulli Mixtures
CSCI 1420 & ENGN 2520, Brown University
Homework due at 11:59pm on November 14, 2013
Question 1:
We rst use the K-means algorithm to cluster handwri
Homework 5: Logistic Regression
CSCI1420 & ENGN2520, Brown University
Homework due at 11:59pm on October 17, 2013
Question 1:
This problem investigates logistic regression classiers. Let y cfw_1, . .
Homework 6: Regularization & Sparsity
CSCI 1420 & ENGN 2520, Brown University
Homework due at 11:59pm on October 31, 2013
Question 1:
This problem compares various approaches to regularization and fea
Homework 1: Naive Bayes Spam Classication
CSCI1420 & ENGN2520, Brown University; revised Sept. 15, 2013
Homework due at 11:59pm on September 19, 2013
Question 1:
Hello, I am a prince in desperate need
Homework 2: ML & Bayesian Estimation
CSCI1420 & ENGN2520, Brown University
Homework due at 11:59pm on September 26, 2013
Question 1:
We begin by considering examples, produced by a sophisticated simul
Homework 4: Linear Regression
CSC1420 & ENGN2520, Brown University
Homework due at 11:59pm on October 10, 2013
In the rst two problems, we study dierent approaches to linear regression using a onedime
ENGN 2520 / CSCI 1950-F Homework 1
Due Friday February 8 by 4pm
Problem 1
Suppose we have three boxes r (red), b (blue), and g (green). Box r contains 3 apples, 4
oranges, and 3 limes, box b contains
CSCI 1950-F Homework 2: ML & Bayesian Estimation
Brown University, Spring 2012
Homework due at 12:00pm on February 16, 2012
We begin by considering examples, produced by a sophisticated simulator, of
CSCI 1950-F Homework 4: Linear Regression
Brown University, Spring 2012
Homework due at 12:00pm on March 1, 2012
In this problem set, we study dierent approaches to linear regression using a onedimens
CSCI 1950-F Homework 5: Logistic Regression
Brown University, Spring 2012
Homework due at 12:00pm on March 12, 2012
Question 1:
In this question, we consider a continuous estimation problem in which t
CSCI 1950-F Homework 7:
Gaussian Processes & Laplace Approximations
Brown University, Spring 2012
Homework due at 12:00pm on April 12, 2012
Question 1:
The rst question explores binary Gaussian proces
Homework 10: EM for Factor Analysis & Regression
CSCI 1420 & ENGN 2520, Brown University
Homework due at 11:59pm on December 5, 2013
Question 1:
The MovieLens dataset (http:/movielens.org) contains ra