Problem 1
Chapter 4, Exercise 4 (p. 168).
When the number of features p is large, there tends to be a deterioration in the performance of KNN
and other local approaches that perform prediction using only observations that are near the test
observation for
Problem 1
Complete Exercise 2 from section 2.4 of the textbook (p. 52).
2. Explain whether each scenario is a classification or regression problem, and indicate whether
we are most interested in inference or prediction. Finally, provide n and p.
(a) We co
Problem1
Chapter6,Exercise3(p.260).
(a) As we increase s from 0, the training RSS will:
i. Increase initially, and then eventually start decreasing in an inverted U shape.
ii. Decrease initially, and then eventually start increasing in a U shape.
iii. Ste
Stats 202 Midterm Note
Lecture 1
Types of Data
- Qualitative: descriptive, categorical, 2 subtypes
Discrete finite, countable, integer value, does not change
o # cups coffee you drank today
- Quantitative: numerical
Ordinal meaningful rank, ordered
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Stat 200: Assignment No. 1
Due Monday, January 23
Read: Chapter 7, Sections 1-4 and Chapter 4, Section 6.
Work the following Exercises on pages 239-254
4, 7, 22, 23, 24, 26, 28, 29, 37, 41, 48, 51.
1
Stat 200: Assignment No. 5
Due Wednesday, March 15
Read Chapter 13 Sections 2, 5, and 6. Read Chapter 14, Sections 1 and 2, and pages
564-565 in Section 3.
In Chapter 13, work problems 1 and 18. In Chapter 14 work problems 2, 6 (You may
assume there is no
Stat 200: Assignment No. 4
Due Friday, March 3
Read Sections 9.7-9.10. Work problems 54 and 57 on page 373.
Read Chapter 11, except 11.2.4, and also Chapter 6.
Work the following Exercises on pages 459-476:
13 (Remark: The sign test uses as test statistic
Stat 200: Assignment No. 2
Due Wednesday, February 1
Read: Chapter 8, omitting Sections 8.6.1 and 8.8.2.
Work the following Exercises on pages 312-328:
3, 5a,b,c, 13, 19, 21 a,b, 26, 30, 41, 66.
(A) For the data given on the third row of Table 2 in the pa
STATS 310B: Theory of Probability II
Winter 2016/17
Lecture 6: January 26
Lecturer: Sourav Chatterjee
6.1
Scribes: Kenneth Tay
Uniform Integrability
Definition 6.1 A sequence of random variables cfw_Xn is uniformly integrable if:
1. E|Xn |< for all n, an
STATS 310B: Theory of Probability II
Winter 2016/17
Lecture 8: February 2
Lecturer: Sourav Chatterjee
8.1
Scribes: Kenneth Tay
The Secretary Problem
This is an application of stochastic optimization for finite horizon which we discussed last lecture.
8.1.
STATS 310B: Theory of Probability II
Winter 2016/17
Lecture 16: March 2
Lecturer: Sourav Chatterjee
Scribes: Kenneth Tay
16.1
Time Homogeneous Markov Chains on Countable State Spaces
16.1.1
Accessibility, Communication, Irreducibility
Let X0 , X1 , . . .
STATS 310B: Theory of Probability II
Winter 2016/17
Lecture 10: February 8
Lecturer: Sourav Chatterjee
10.1
Scribes: Kenneth Tay
Martingale Strong Law of Large Numbers
We first prove 2 technical lemmas in analysis:
Lemma 10.1 If an is a sequence of positi
STATS 310B: Theory of Probability II
Winter 2016/17
Lecture 9: February 6
Lecturer: Sourav Chatterjee
9.1
Scribes: Kenneth Tay
Martingales with Bounded Increments
Lemmas we proved from last time:
Lemma 9.1 If cfw_Zn , Fn is any martingale and is a stoppi
Stat 310B: Problem Set 6
Due Thursday, March 9
1. Let d 1 and = cfw_0, 1E , where E is the set of edges of Zd . Let be
endowed with the product -algebra. Let p (0, 1) and let be the
infinite product of Bernoulli(p) measures on . That is, is the law
of a c
Stat 310B: Problem Set 4
Due Tuesday, February 14
1. Consider the following variant of the secretary problem: Let N be a
positive integer, and let X1 , . . . , XN be i.i.d. random variables with
cumulative distribution function F . For each n, let Fn be t
Stat 310B: Problem Set 5
Due Tuesday, February 21
1. Let Y1 , Y2 , . . . be independent, identically distributed random variPk
ables with a finite mean value, and put Sk =
1 Yi . Let Mn =
Pn 1
+
max0kn Sk . Show that E(Mn ) =
1 k E(Sk ). Hint: Split the
e
Stat 310B: Problem Set 3
Due Tuesday, February 7
1. Let cfw_Xn , Fn n1 be a martingale, and assume that supn E|Xn | < .
Show that Xn can be written as the difference of two non-negative
martingales and hence in proving the martingale convergence theorm
th
Stat 310B: Problem Set 2
Due in class on Tuesday, January 31
1. Let Xn be a martingale with X0 = 0 and E(Xn2 ) < 1. Show that
P ( max Xm )
1mn
E(Xn2 )
.
E(Xn2 ) + 2
Hint: Use the fact that (Xn + c)2 is a submartingale and optimize
over c.
2. Let Sn be a
Go
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2014 2015 2016
2
captures
19 Sep
14 - 18
Feb 15
You may discuss homework problems with other students, but you have to prepare the written
assignments yourself. La
Problem Set 3
Due at gradescope, Tuesday November 8, 2016
Problems 5 and 6 are team work (usual rules apply) and problems 1 to 4
are individual.
1. Weisberg 4th edition, 2.12.
2. These observations are from a time series. Answer a, b below ignoring
that.
CS224n is in this interstice
cartoon from xkcd.com
Natural Language Processing
CS224N/Ling284
Christopher Manning
Lecture 1
Lecture Plan
1. Human Language and Natural Language Processing: Their
nature and goals (10 mins)
2. Why is langu
CS 161: Recitation 1 (Fall 2016) Solutions
Note: These are sketches for solutions to the problems planned for the recitation sections. Some of these
solutions may be incomplete or not entirely formal, but they should be detailed enough to allow you to com
CS 161: Homework 2 Solutions
Question 1
a. Let us first consider only horizontal lines. Although there are an infinite number of candidate horizontal
lines, we notice that if we consider only the top and bottom tangent lines (lets call them boundary
lines
CS 161: Homework 1 Solutions
Question 1
1. Consider the mapping between subsets of cfw_1, 2, ., and -bit binary strings where the element is
included in the subset if and only if the corresponding bit string has a 1 in the th position. This
mapping is bo
CS 161: Recitation 1 (Fall 2016)
Question 1
1. Order the following functions so that 1 = (2 ), 2 = (3 ), . . . , 6 = (7 ):
2
log 2
2 log
1/4
(log )4
4
100
2100
2. Each row in the following table describes the running time of two different algorithms tha
CS 161: Recitation 3 (Fall 2016) Solutions
Note: These are sketches for solutions to the problems planned for the recitation sections. Some of these
solutions may be incomplete or not entirely formal, but they should be detailed enough to allow you to com
CS 161: Recitation 2 (Fall 2016) Solutions
Note: These are sketches for solutions to the problems planned for the recitation sections. Some of these
solutions may be incomplete or not entirely formal, but they should be detailed enough to allow you to com
CS 161: Recitation 2 (Fall 2016)
Question 1
Given two arrays and of size and a number , determine whether there is a pair of indices (, ) such
that [] + [] = .
Question 2
Suppose you have sorted arrays, each with elements, and you want to combine them int