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 data analysis project. For more details, see the section on grading below.

Online Instruction and Learning

The course will be online, including lectures, office hourse, and exams, as mentioned below. There is no hybrid component.

• Lectures will be synchronous (live), via zoom. The zoom link can be found for enrolled students on Blackboard under the Zoom Meeting tab on the left.
  Please do not distribute the zoom link and please do not cause any disruption on the zoom lectures. Any such incidents will be reported to the Office of Judicial Affairs.
  
• All lectures will be automatically recorded by the Blackboard zoom account and will be available on the Zoom Meeting tab on Blackboard (usually a couple hours after the lecture).
• All lecture slides and code used in the class will be made available on this website (under the syllabus section) after class.


• Office hours will be via zoom. Information on this will be provided early in the semester once office hours are finalized.


• All offline communication will be via piazza; please sign up. You are responsible for monitoring piazza to ensure you do not miss important class announcements.


• Exams will be held remotely in an online manner via Blackboard.
• Assignments will be released via Blackboard (under the Assignments tab) and will need to be submitted online via the link that Blackboard provides.
• Assignment, exam, and project grades will be uploaded on Blackboard by the TAs along with summary comments on the grading scheme. Any regrading issues must be directed to the TAs.

Please email the instructor if you have any problems with remote instruction, such as a poor network connection, unaccommodating environment, or time zone issues.

Syllabus & Schedule

Date	Topic	Readings	Notes
Jan 24 (Mon) [Lec 01]	Course introduction, class logistics
Jan 26 (Wed) [Lec 02]	Probability review - 1 Basics: sample space, outcomes, probability Events: mutually exclusive, independent Calculating probability: sets, counting, tree diagram	AoS 1.1 - 1.5 MHB 3.1 - 3.4
Jan 31 (Mon) [Lec 03]	Probability review - 2 Conditional probability Law of total probability Bayes' theorem	AoS 1.6, 1.7 MHB 3.3 - 3.6	assignment 1 out, due Feb 9
Feb 02 (Wed) [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 - 2.3, 3.1 - 3.4 MHB 3.7 - 3.9
Feb 07 (Mon) [Lec 05]	Random variables - 2: Continuous RVs Uniform(a, b) Exponential(λ) Normal(μ, σ2), and its several properties	AoS 2.4, 3.1 - 3.4 MHB 3.7 - 3.9, 3.14.1	Python scripts: draw_Bernoulli, draw_Binomial, draw_Geometric, draw_Uniform, draw_Exponential, draw_Normal
Feb 09 (Wed) [Lec 06]	Random variables - 3: Joint distributions & conditioning Joint probability distribution Linearity of expectation	AoS 2.5 - 2.8 MHB 3.10 - 3.13, 3.15	assignment 2 out, due Feb 23 assignment 1 due
Feb 14 (Mon) [Lec 07]	Random variables - 4: Joint distributions & conditioning Independent random variables Product of expectation Conditional expectation	AoS 2.5 - 2.8 MHB 3.10 - 3.13, 3.15
Feb 16 (Wed) [Lec 08]	Probability Inequalities Weak Law of Large Numbers Central Limit Theorem	AoS 5.3, 5.4 MHB 3.14.2, 5.2
Feb 21 (Mon) [Lec 09]	Markov chains Stochastic processes Setting up Markov chains Balance equations	AoS 23.1 - 23.3 MHB 8.1 - 8.7
Feb 23 (Wed) [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	assignment 3 out, due March 4 Required data: a3_q2.csv, a3_q4.csv, a3_q8.csv assignment 2 due
Feb 28 (Mon) [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	Python scripts: sample_Bernoulli, sample_Binomial, sample_Geometric, sample_Uniform, sample_Exponential, sample_Normal, draw_eCDF
Mar 02 (Wed) [Lec 12]	Confidence intervals Percentiles, quantiles Normal-based confidence intervals DKW inequality	AoS 6.3.2, 7.1
Mar 07 (Mon) [Lec 13]	Parametric inference - 1 Consistency, Asymptotic Normality Basics of parametric inference Method of Moments Estimator (MME)	AoS 6.3.1 - 6.3.2, 9.1 - 9.2
Mar 09 (Wed)	Mid-term 1		Via Blackboard
Mar 14 (Mon)	No class		Spring Break
Mar 16 (Wed)	No class		Spring Break
Mar 21 (Mon) [Lec 14]	Parametric inference - 2 Properties of MME Basics of MLE Maximum Likelihood Estimator (MLE) Properties of MLE	AoS 9.3, 9.4, 9.6	assignment 4 out Required data: acceleration, model, mpg, q8_a.csv, q8_b_X.csv, q8_b_Y.csv
Mar 23 (Wed) [Lec 15]	Hypothesis testing - 1 Basics of hypothesis testing Wald test	AoS 10 - 10.1 DSD 5.3.1
Mar 28 (Mon) [Lec 16]	Hypothesis testing - 2 Type I and Type II errors Wald test	AoS 10 - 10.1 DSD 5.3.1
Mar 30 (Wed) [Lec 17]	Hypothesis testing - 3 Z-test t-test	AoS 10.10.2 DSD 5.3.2
Apr 04 (Mon) [Lec 18]	Hypothesis testing - 4 Kolmogorov-Smirnov test (KS test) p-values	AoS 15.4, 10.2 DSD 5.3.3, 5.5	assignment 5 out Required data: a5_q6 assignment 4 due
Apr 06 (Wed) [Lec 19]	Hypothesis testing - 5 p-values Permutation test	AoS 10.2, 10.5 DSD 5.5
Apr 11 (Mon) [Lec 20]	Hypothesis testing - 6 Pearson correlation coefficient Chi-square test for independence	AoS 3.3, 10.3 - 10.4 DSD 2.3
Apr 13 (Wed) [Lec 21]	Bayesian inference - 1 Bayesian reasoning Bayesian inference	AoS 11.1 - 11.2, 11.6 DSD 5.6
Apr 18 (Mon) [Lec 22]	Bayesian inference - 2 Priors Conjugate priors	AoS 11.1 - 11.2, 11.6 DSD 5.6	assignment 6 out Required data: q2.dat, q4.csv, q5.csv, q6.csv assignment 5 due
Apr 20 (Wed) [Lec 23]	Regression - 1 Basics of Regression Simple Linear Regression	AoS 13.1, 13.3 - 13.4 DSD 9.1
Apr 25 (Mon) [Lec 24]	Regression - 2 Multiple Linear Regression	AoS 13.5 DSD 9.1
Apr 27 (Wed) [Lec 25]	Time Series Analysis EWMA Time Series modeling AR Time Series modeling
May 02 (Mon) [Lec 26]	M2 review, Project discussion
May 04 (Wed)	Mid-term 2		Via Blackboard
May 17 (Tues)	Project due	By 8pm (per final exam schedule)	Via Blackboard

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

Grading (tentative)

• Assignments: 45%
• 6 assignments during the semester. Expect 5-8 questions per assignment, including some programming questions.
• Collaboration is allowed (max group size 4). You are free to form your own groups, and group membership can change between assignments.
• Submit one softcopy (e.g., PDF or doc) solution per group, typed or handwritten, but should be legible. Should include all required plots and work. Include group member names and ID numbers on the first page.
• Assignments are due via Blackboard, at the beginning of the lecture (8:15pm). No late submissions allowed.
• One person per group (not all) should submit the softcopy on Blackboard under the designated assigment number.


• Exams: 45%
• Two online (via Blackboard), open-book, timed exams.
• Mid-term 1: 20%.
• Mid-term 2: 25%.
• Easier than the assignments but the questions will be on the same lines.
• Sample mid-terms will be available the week before for practice.


• Mini group project: 10%
• One semester-end project to be done in groups. The project work is expected to begin in the last month of the course.
• Further details on the project will be provided in class around mid-March.


• In-class mini-quizzes: 0%
• Blackboard-based in-class quizzes, roughly one per week.
• Only for self-evaluation, will not be graded.
• Will help with exam practice.

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.

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.

Student Accessibility Support Services

If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, 128 ECC Building, (631) 632-6748, or at sasc@stonybrook.edu. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. https://www.stonybrook.edu/sasc.