CSE 544, Fall 2018: Probability & Statistics for Data Science

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CSE 544: Probability & Statistics for Data Science
Fall 2018

When: Mon Wed, 4:00pm - 5:20pm
Where: Javits 111
Instructor: Anshul Gandhi
Instructor Office Hours: Mon 5:30-6:30pm; Thur 4-5pm
347, New CS building
Course TA and Graders: Abhinav Jain, Swethasri Kavuri, Parth Limbachiya, Ankit Sabharwal, Gagan Somashekar, Amogha Suresh

### Course Info

This grad-level course covers probability and statistics topics required for data scientists to analyze and interpret data. The course is also part of the Data Science and Engineering Specialization. The course is targeted primarily at PhD and Masters students in the Computer Science Department. Topics covered include Probability Theory, Random Variables, Stochastic Processes, Statistical Inference, Hypothesis Testing, Regression, and Time Series Analysis. For more details, refer to the syllabus below.

The class is expected to be interactive and students are encouraged to participate in class discussions.

Grading will be on a curve, and will be based on assignments, exams, and a semester-end mini project. For more details, see the section on grading below.

### Syllabus & Schedule

Aug 27 (Mon)
[Lec 01]
Course introduction, class logistics
Aug 29 (Wed)
[Lec 02]
Probability review - 1
• Basics: sample space, outcomes, probability
• Events: mutually exclusive, independent
• Calculating probability: sets, counting, tree diagram
• AoS 1.1 - 1.6
MHB 3.1 - 3.5
Sep 03 (Mon) Labor Day observed No class
Sep 05 (Wed)
[Lec 03]
Probability review - 2
• Conditional probability
• Law of total probability
• Bayes' theorem
• AoS 1.7
MHB 3.6, 3.10 - 3.11
assignment 1 out
Sep 10 (Mon)
[Lec 04]
Random variables - 1: Overview and Discrete RVs
• Discrete and Continuous RVs
• Mean, Moments, Variance
• pmf, pdf, cdf
• Discrete RVs: Bernoulli, Binomial, Geometric, Indicator
• AoS 2.1 - 2.4
MHB 3.7 - 3.9, 3.14.1
Sep 12 (Wed)
[Lec 05]
Random variables - 2: Continuous RVs
• Uniform(a, b)
• Exponential(λ)
• AoS 2.7
MHB 3.14.1, 3.10, 3.13
Python scripts:
draw_Bernoulli, draw_Binomial, draw_Geometric
Sep 17 (Mon)
[Lec 06]
Random variables - 3: The Normal distribution
• Normal(μ, σ2), and its several properties
• AoS 2.7
MHB 3.14.1, 3.10, 3.13
Python scripts:
draw_Uniform, draw_Exponential, draw_Normal
Sep 19 (Wed)
[Lec 07]
Random variables - 4: Joint distributions & conditioning
• Joint probability distribution
• Linearity (and product) of expectation
• Conditional expectation
• Sum of a random number of RVs
• AoS 2.8
MHB 3.11 - 3.12, 3.15
assignment 2 out
assignment 1 due
Sep 24 (Mon)
[Lec 08]
Probability inequalities
• Markov's Inequality
• Chebyshev's inequality
• Weak Law of Large Numbers
• Central Limit Theorem
• AoS 4.1 - 4.2, 23.1 - 23.3
MHB 3.14.2, 8.1 - 8.7
Sep 26 (Wed)
[Lec 09]
Markov chains
• Stochastic processes
• Setting up Markov chains
• Balance equations
• AoS 4.1 - 4.2, 23.1 - 23.3
MHB 3.14.2, 8.1 - 8.7
Oct 01 (Mon)
[Lec 10]
Non-parametric inference - 1
• Basics of inference
• Simple examples
• Empirical PMF
• Sample mean
• bias, se, MSE
• AoS 6.1 - 6.2, 6.3.1 Python scripts:
sample_Bernoulli, sample_Binomial, sample_Geometric,
sample_Uniform, sample_Exponential, sample_Normal
Oct 03 (Wed)
[Lec 11]
Non-parametric inference - 2
• Empirical Distribution Function (or eCDF)
• Kernel Density Estimation (KDE)
• Statistical Functionals
• Plug-in estimator
• AoS 7.1 - 7.2 assignment 2 due
Oct 08 (Mon) Fall break No class
Oct 10 (Wed) Mid-term 1 This will be in-class, closed notes, closed book.
Oct 15 (Mon)
[Lec 12]
Confidence intervals
• Percentiles, quantiles
• Normal-based confidence intervals
• DKW inequality
• AoS 6.3.2, 7.1 assignment 3 out
Required data q8.dat
Oct 17 (Wed)
[Lec 13]
Parametric inference - 1
• Consistency, Asymptotic Normality
• Basics of parametric inference
• Method of Moments Estimator (MME)
• AoS 6.3.1 - 6.3.2
Oct 22 (Mon)
[Lec 14]
Parametric inference - 2
• Properties of MME
• Basics of MLE
• Maximum Likelihood Estimator (MLE)
• Properties of MLE
• AoS 9.1 - 9.4, 9.6
Oct 24 (Wed) Instructor traveling No class
Oct 29 (Mon)
[Lec 15]
Hypothesis testing - 1
• Basics of hypothesis testing
• The Wald test
• AoS 10 - 10.1
DSD 5.3.1
assignment 4 out
Required data: q5_sigma3.dat, q5_sigma100.dat, q7_X.dat, q7_Y.dat
Oct 31 (Wed)
[Lec 16]
Hypothesis testing - 2
• t-test
• Kolmogorov-Smirnov test (KS test)
• AoS 10.10.2, 15.4
DSD 5.3.2
assignment 3 due
Nov 05 (Mon)
[Lec 17]
Hypothesis testing - 3
• p-values
• Permutation test
• AoS 10.2, 10.5
DSD 5.3.3, 5.5
Nov 07 (Wed)
[Lec 18]
Bayesian inference
• Bayesian reasoning
• Bayesian inference
• Priors
• Conjugate priors
• AoS 11.1 - 11.2, 11.6
DSD 5.6
Nov 12 (Mon)
[Lec 19]
Regression - 1
• Basics of Regression
• Simple Linear Regression
• AoS 13.1, 13.3 - 13.4
DSD 9.1
assignment 4 due
assignment 5 out
Required data A5_q2.dat, A5_q5.dat, A5_q6.dat.
Nov 14 (Wed)
[Lec 20]
Regression - 2, Mini-project discussion
• Multiple Linear Regression
• AoS 13.5
DSD 9.1
assignment 6 out
due Dec 7th, 1pm (to Amogha, NCS 336)
Nov 19 (Mon) Mid-term 2 This will be in-class, closed notes, closed book.
Nov 21 (Wed) Thanksgiving break No class
Nov 26 (Mon)
[Lec 21]
Time Series Analysis
• EWMA Time Series modeling
• AR Time Series modeling
• Nov 28 (Wed)
[Lec 22]
Mini-project discussion (finalize hypothesis) assignment 5 due

### Resources

• Required text: (AoS) "All of Statistics : A Concise Course in Statistical Inference" by Larry Wasserman (Springer publication).
• Students are strongly suggested to purchase a copy of this book.
• Recommended text: (MHB) "Performance Modeling and Design of Computer Systems: Queueing Theory in Action" by Mor Harchol-Balter (Cambridge University Press)
• Suggested for probability review and stochastic processes.
• There is copy placed on reserve in the library. The instructor also has a few personal copies that you can borrow.
• Recommended text: (DSD) "The Data Science Design Manual" by (our very own) Steven Skiena (Springer publication).
• Suggested for data science topics in the second half of the course.

• Others:
• S.M. Ross, Introduction to Probability Models, Academic Press
• S.M. Ross, Stochastic Processes, Wiley

• Assignments: 50%
• 5 assignments during the semester. Expect 6-8 questions per assignment, including some programming questions (after mid-term 1).
• Collaboration is allowed (max group size 5). Submit one solution per group.
• Assignments are due in class, at the beginning of the lecture. No late submissions allowed. Hard-copies only, please.

• Exams: 40%
• Two in-class exams.
• Mid-term 1: 15%.
• Mid-term 2: 25%.
• Easier than the assignments but the questions will be on the same lines.

• Mini group project: 10%
• One semester-end project to be done in groups. The project work is expected to begin around mid-term 2.
• Further details on the project will be provided in class around November.

• Important:
• Academic dishonesty will immediately result in an F and the student will be referred to the Academic Judiciary. See below section on Academic Integrity.
• Grading will be on a curve.
• Assignment of grades by the instructor will be final; no regrading requests will be entertained.
• There is a University policy on grading, as well as a set of grading guidelines agreed upon by the CS faculty.
No exceptions will be made for any student and no special circumstances will be entertained.