Course Info

This undergraduate-level special topics course covers probability and statistics topics required for data scientists to analyze and interpret data. The course will involve theoretical topics and some programming assignments. The course is targeted primarily for junior and senior undergraduate students who are comfortable with concepts relating to probability and are comfortable with basic programming. Undergraduates from Computer Science, Applied Mathematics and Statistics, and Electrical and Computer Engineering would be well suited for taking this class. Topics covered include Probability Theory, Random Variables, Stochastic Processes, Statistical Inference, Hypothesis Testing, Regression, Classification, and Clustering. 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 tentatively be based on assignments, exams, and class participation. For more details, refer to the section on grading below.

Syllabus & Schedule

Date	Topic	Readings	Notes
Aug 29 (Tue) [Lec 01]	Course introduction, class logistics
Aug 31 (Thu) [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 05 (Tue)	Labor Day		No class
Sep 07 (Thu) [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 12 (Tue) [Lec 04]	Random variables - 1: Overview Discrete and Continuous RVs Mean, Moments, Variance pmf, pdf, cdf	AoS 2.1 - 2.3 MHB 3.7 - 3.9
Sep 14 (Thu) [Lec 05]	Random variables - 2: Discrete RVs Bernoulli(p) Binomial(n, p) Geometric(p) Indicator RV	AoS 2.4 MHB 3.7 - 3.9, 3.14.1	Python scripts: draw_Bernoulli, draw_Binomial, draw_Geometric, sample_Bernoulli, sample_Binomial, sample_Geometric
Sep 19 (Tue) [Lec 06]	Random variables - 3: Continuous RVs Uniform(a, b) Exponential(λ) Normal(μ, σ2), and its several properties	AoS 2.7 MHB 3.14.1, 3.10, 3.13	assignment 1 due assignment 2 out Python scripts: draw_Uniform, draw_Exponential, draw_Normal, sample_Uniform, sample_Exponential, sample_Normal
Sep 21 (Thu)	Instructor traveling		No class
Sep 26 (Tue) [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
Sep 28 (Thu) [Lec 08]	Probability inequalities - 1 Markov's Inequality Chebyshev's inequality	AoS 4.1 - 4.2, 23.1 - 23.3 MHB 3.14.2, 8.1 - 8.7
Oct 03 (Tue) [Lec 09]	Probability inequalities - 2 Weak Law of Large Numbers Central Limit Theorem A2 solutions	AoS 4.1 - 4.2, 23.1 - 23.3 MHB 3.14.2, 8.1 - 8.7	assignment 2 due
Oct 05 (Thu) [Lec 10]	Mid-term 1 review
Oct 10 (Tue)	Mid-term 1
Oct 12 (Thu) [Lec 11]	Non-parametric inference - 1 Basics of inference Simple examples	AoS 6.1 - 6.2
Oct 17 (Tue) [Lec 12]	Non-parametric inference - 2 Empirical PMF Sample mean bias, se, MSE	AoS 6.3.1
Oct 19 (Thu) [Lec 13]	Non-parametric inference - 3 Empirical Distribution Function (or eCDF) Statistical Functionals Plug-in estimator	AoS 7.1 - 7.2	assignment 3 out Required weather.dat dataset for A3. Python script used in class: eCDF
Oct 24 (Tue) [Lec 14]	Confidence intervals Percentiles, quantiles Normal-based confidence intervals DKW inequality	AoS 6.3.2, 7.1
Oct 26 (Thu) [Lec 15]	Parametric inference - 1 Basics of parametric inference Method of Moments Estimator (MME)	AoS 6.3.1 - 6.3.2, 9.1 - 9.2
Oct 31 (Tue) [Lec 16]	Parametric inference - 2 Method of Moments Estimator (MME) Properties of MME	AoS 9.1 - 9.2	assignment 3 due assignment 4 out Required q4.dat dataset for A4.
Nov 02 (Thu) [Lec 17]	Parametric inference - 3 Likelihood Maximum Likelihood Estimator (MLE) Properties of MLE	AoS 9.3 - 9.4, 9.6
Nov 07 (Tue) [Lec 18]	Hypothesis testing - 1 Basics of hypothesis testing The Wald test	AoS 10 - 10.1, 10.10.2 DSD 5.3.1 - 5.3.2
Nov 09 (Thu) [Lec 19]	Hypothesis testing - 2 The Wald test t-test Kolmogorov-Smirnov test (KS test)	AoS 15.4 DSD 5.3.3	assignment 4 due assignment 5 out Required q3_X.dat, q3_Y.dat, and gamma.dat datasets for A5.
Nov 14 (Tue) [Lec 20]	Hypothesis testing - 3 p-values Permutation test	AoS 10.2, 10.5 DSD 5.5
Nov 16 (Thu) [Lec 21]	Bayesian inference Bayesian reasoning Bayesian inference	AoS 11.1 - 11.2 DSD 5.6
Nov 21 (Tue) [Lec 22]	Regression - 1 Basics of Regression Simple Linear Regression A5 solutions	AoS 13.1, 13.3 - 13.4	assignment 5 due assignment 6 out, due Dec 11, to Caitao Zhan. Required q2.dat dataset for A6.
Nov 23 (Thu)	Thanksgiving Break		No class.
Nov 28 (Tue) [Lec 23]	Mid-term 2 review
Nov 30 (Thu)	Mid-term 2
Dec 05 (Tue) [Lec 24]	Regression - 2 Multiple Linear Regression	AoS 13.5
Dec 07 (Thu)	Instructor traveling

Resources

• Recommended 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

Grading (tentative)

• Assignments: 48%
• Roughly 6 assignments during the semester. Expect 5-6 questions per assignment, including some programming questions (after mid-term 1).
• Assignments are due in class, at the beginning of the lecture. No late submissions allowed. Hard-copies only, please.


• Exams: 42%
• Two in-class exams.
• Mid-term 1: 17%.
• Mid-term 2: 25%.
• Roughly as difficult as the assignments.


• Class interaction: 10%
• The basic idea is to get you to talk in the class and contribute to discussions.
• By the end of the semester, if I can recognize you based on your contributions to the class discussion, you should get a good score on this.
• Very helpful for bumping your grade if you are on the border.


• 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. The instructor is obligated to uphold these policies.
  No exceptions will be made for any student and no special circumstances will be entertained.

Academic Integrity

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity. Please note that any incident of academic dishonesty will immediately result in an F grade for the student.

Critical Incident Management

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.

Disability Support Services

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential. http://studentaffairs.stonybrook.edu/dss.