CSE 544, Spring 2020: Probability & Statistics for Data Science

News:
02/02: A1 is now up on BB, due 2/12 in class.
01/15: Piazza sign-up link.
01/15: Welcome to CSE 544! Our first class will be on 1/27.

CSE 544: Probability & Statistics for Data Science
Spring 2020


When: Mon Wed, 2:30pm - 3:50pm
Where: Engineering 143
Instructor: Anshul Gandhi
Instructor Office Hours: Tues, Thurs, 3-4pm
             347, New CS building
Course TA and Graders: Supreeth Narasimhaswamy, Sayontan Ghosh
TA Office Hours: Fri, 12-1pm
          109, New CS building

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, a semester-end mini project, and in-class quizzes. For more details, see the section on grading below.

Syllabus & Schedule

Date Topic Readings Notes
Jan 27 (Mon)
[Lec 01]
Course introduction, class logistics
Jan 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 - 1.5
    MHB 3.1 - 3.4
    Feb 03 (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
    Feb 05 (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
    Python scripts:
    draw_Bernoulli, draw_Binomial, draw_Geometric
    Feb 10 (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_Uniform, draw_Exponential, draw_Normal
    Feb 12 (Wed)
    [Lec 06]
    Random variables - 3: Joint distributions & conditioning
  • Joint probability distribution
  • Linearity and product of expectation
  • Conditional expectation
  • AoS 2.5 - 2.8
    MHB 3.10 - 3.13, 3.15
    assignment 2 out
    assignment 1 due
    Feb 17 (Mon)
    [Lec 07]
    Probability Inequalities
  • Weak Law of Large Numbers
  • Central Limit Theorem
  • AoS 5.3, 5.4
    MHB 3.14.2, 5.2
    Feb 19 (Wed)
    [Lec 08]
    Markov chains
  • Stochastic processes
  • Setting up Markov chains
  • Balance equations
  • AoS 23.1 - 23.3
    MHB 8.1 - 8.7
    Feb 24 (Mon)
    [Lec 09]
    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. Required data: q2.dat, weather.dat
    assignment 2 due
    Feb 26 (Wed)
    [Lec 10]
    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 (Mon)
    [Lec 11]
    Confidence intervals
  • Percentiles, quantiles
  • Normal-based confidence intervals
  • DKW inequality
  • AoS 6.3.2, 7.1
    Mar 04 (Wed)
    [Lec 12]
    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 assignment 3 due
    Mar 09 (Mon)
    [Lec 13]
    Parametric inference - 2
  • Properties of MME
  • Basics of MLE
  • Maximum Likelihood Estimator (MLE)
  • Properties of MLE
  • AoS 9.3, 9.4, 9.6
    Mar 11 (Wed) Mid-term 1 This will be in-class, closed notes, closed book.
    Mar 16 (Mon) Spring Break No class. Stay safe and healthy.
    Mar 18 (Wed) Spring Break No class. Stay safe and healthy.
    Mar 23 (Mon) Extended Spring Break No class. Stay safe and healthy.
    Mar 25 (Wed) Extended Spring Break No class. Stay safe and healthy.
    Mar 30 (Mon)
    [Lec 14]
    Hypothesis testing - 1
  • Basics of hypothesis testing
  • Wald test
  • AoS 10 - 10.1
    DSD 5.3.1
    assignment 4 out
    Required data: acceleration, model, mpg, q6_X.dat, q6_Y.dat
    Apr 01 (Wed)
    [Lec 15]
    Hypothesis testing - 2
  • Type I and Type II errors
  • Wald test
  • AoS 10 - 10.1
    DSD 5.3.1
    Apr 06 (Mon)
    [Lec 16]
    Hypothesis testing - 3
  • Z-test
  • t-test
  • AoS 10.10.2
    DSD 5.3.2
    Apr 08 (Wed)
    [Lec 17]
    Hypothesis testing - 4
  • Kolmogorov-Smirnov test (KS test)
  • p-values
  • AoS 15.4, 10.2
    DSD 5.3.3, 5.5
    assignment 5 out
    assignment 4 due on Friday (4/10) 2:30pm via google forms
    Apr 13 (Mon)
    [Lec 18]
    Hypothesis testing - 5
  • p-values
  • Permutation test
  • AoS 10.2, 10.5
    DSD 5.5
    Apr 15 (Wed)
    [Lec 19]
    Hypothesis testing - 6
  • Pearson correlation coefficient
  • Chi-square test for independence
  • AoS 3.3, 10.3 - 10.4
    DSD 2.3
    Apr 20 (Mon)
    [Lec 20]
    Bayesian inference - 1
  • Bayesian reasoning
  • Bayesian inference
  • AoS 11.1 - 11.2, 11.6
    DSD 5.6
    assignment 6 out
    Required data: q2_sigma3.dat, q2_sigma100.dat, q4.dat, q5.csv
    assignment 5 due by 2:30pm via google forms
    Apr 22 (Wed)
    [Lec 21]
    Bayesian inference - 2
  • Priors
  • Conjugate priors
  • AoS 11.1 - 11.2, 11.6
    DSD 5.6
    Apr 27 (Mon)
    [Lec 22]
    Regression - 1
  • Basics of Regression
  • Simple Linear Regression
  • AoS 13.1, 13.3 - 13.4
    DSD 9.1
    Apr 29 (Wed)
    [Lec 23]
    Regression - 2
  • Multiple Linear Regression
  • AoS 13.5
    DSD 9.1
    assignment 6 due by 2:30pm via google forms
    May 04 (Mon)
    [Lec 24]
    Time Series Analysis
  • EWMA Time Series modeling
  • AR Time Series modeling

  • Resources

    Grading (tentative)

    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.
     Please report any errors to the Instructor.