Benefits of Business Mobility
Enhance mobility
Provides immediate data access
Increases location and monitoring capability
Improves work flow
Provides mobile business opportunities
Provides alternative to wiring
IS 312 : Lecture 5
1
Challenges of Business
Massachusetts Institute of Technology
6.867 Machine Learning Fall 2006
Problem Set 1 Solutions
Section A (background questions)
1. Lets begin with a little math. Let us denote by Pn the probability that n people with
randomly chosen birthdays (chosen unif
Lecture 23
Computational geometry
Supplemental reading in CLRS: Chapter 33 except 33.3
There are many important problems in which the relationships we wish to analyze have geometric
structure. For example, computational geometry plays an important role in
Lecture 22
Derandomization
Supplemental reading in CLRS: None
Here are three facts about randomness:
Randomness can speed up algorithms (e.g., sublinear-time approximations)
Under reasonable assumptions, we know that the speed-up cant be too large. Adva
Massachusetts Institute of Technology
6.867 Machine Learning Fall 2006
Problem Set : Solutions
1. (a) (5 points) From the lecture notes (Eqn 14, Lecture 5), the optimal parameter values for linear
regression given the matrix of training examples X and the
Lecture 19
Compression and Huffman Coding
Supplemental reading in CLRS: Section 16.3
19.1
Compression
As you probably know at this point in your career, compression is a tool used to facilitate storing
large data sets. There are two different sorts of goa
Lecture 21
Clustering
Supplemental reading in CLRS: None
Clustering is the process of grouping objects based on similarity as quantied by a metric. Each
object should be similar to the other objects in its cluster, and somewhat different from the objects
Design and Analysis of Algorithms
Massachusetts Institute of Technology
Profs. Dana Moshkovitz and Bruce Tidor
Final Exam
Mean: 121.3; Median: 122; Standard deviation: 30.8
May 23, 2012
6.046J/18.410J
Final Exam
6.046J/18.410J Final Exam
Name
2
Problem 1.
Lecture 17
Complexity and NP-completeness
Supplemental reading in CLRS: Chapter 34
As an engineer or computer scientist, it is important not only to be able to solve problems, but also to
know which problems one can expect to solve efciently. In this lect
Problem 2
2.1. (3 points) Let F be a set of classiers whose VC-dimension is 5. Suppose we have
four training examples and labels, cfw_(x1 , y1 ), . . . , (x4 , y4 ), and select a classier f
from F by minimizing classication error on the training set. In t
Theory of Parallel Hardware
Massachusetts Institute of Technology
Charles Leiserson, Michael Bender, Bradley Kuszmaul
April 12, 2004
6.896
Handout 14
Solution Set 6
Due: In class on Wednesday, March 31. Starred problems are optional.
Problem 6-1. A compar
Design and Analysis of Algorithms
Massachusetts Institute of Technology
Profs. Dana Moshkovitz and Bruce Tidor
6.046J/18.410J
Practice Quiz 2 for Spring 2012
Practice Quiz 2 for Spring 2012
These problems are four of the ve problems from the take-home exa
6.867 Machine learning
Mid-term exam
October 15, 2003
2 points) Your name and MIT ID:
SOLUTIONS
Problem 1
Suppose we are trying to solve an active learning problem, where the possible inputs you
can select form a discrete set. Specically, we have a set of
Lecture 18
Polynomial-Time
pproximations
Supplemental reading in CLRS: Chapter 35 except 35.4
If you try to design algorithms in the real world, it is inevitable that you will come across NP-hard
problems. So what should you do?
1. Maybe the problem you w
Today
Proof of Converse Coding Theorem
Intuition: For message m, let Sm cfw_0, 1n
be the set of received words that decode to
m. (Sm = D1(m).
More on Shannons theory
Proof of converse.
Few words on generality.
Contrast with Hamming theory.
Average s
Theory of Parallel Hardware
Massachusetts Institute of Technology
Charles Leiserson, Michael Bender, Bradley Kuszmaul
April 23, 2004
6.896
Handout 16
Solution Set 7
Due: In class on Wednesday, April 7. Starred problems are optional.
Problem 7-1. Show that
Q1. Bankers Algorithm
(a) [10 points] Briey describe two drawbacks of the Bankers algorithm for deadlock
avoidance.
1. Users need to estimate their maximum need; ifthese estimates are too high, the algorithm
can be very conservative about granting request
Lecture 20
Sublinear-Time
lgorithms
Supplemental reading in CLRS: None
If we settle for approximations, we can sometimes get much more efcient algorithms. In Lecture 18,
we saw polynomial-time approximations to a few NP-hard problems. In what follows, we