PROGRAMMING FOR DATA SCIENCE

PROGRAMMING FOR DS

Course Overview: 
This course introduces Python programming, covering data structures, control-flow, objects, and functions, along with libraries like re, requests, numpy, pandas, scikit-learn, scipy, and more. These skills are applied to real-world data science tasks, including AB testing, data manipulation, modeling, optimization, simulations, and data visualization.

Students will develop computational thinking abilities, including problem decomposition, pattern recognition, data representation, abstraction, and algorithm design, through practical exercises.

• TR 8:40 a.m.-9:55 a.m.
• Instructor: Benjamin K Goodrich
  Info
• 3 points

TIME SERIES ANALYSIS

Prerequisites: STAT GR5205 Least squares smoothing and prediction, linear systems, Fourier analysis, and spectral estimation. Impulse response and transfer function. Fourier series, the fast Fourier transform, autocorrelation function, and spectral density. Univariate Box-Jenkins modeling and forecasting. Emphasis on applications. Examples from the physical sciences, social sciences, and business. Computing is an integral part of the course.

• TR 2:40 p.m.-3:55 p.m.
• Instructor: Rongning Wu
  CULPA: 1 Info
• 3 points

Causal Inference

This course is an introduction to Causal Inference at the masters level. Students will be introduced to a broad range of causal inference methods including randomized
experiments, observational studies, instrumental variables, di?erence-in-di?erences, regression discontinuity design, and synthetic controls. In addition, the course will cover modern, controversial debates regarding the foundations and limitations of causal inference.

The primary learning goal of this course will be to familiarize students with a variety of the most popular causal inference methods: which causal e?ects they seek to estimate, basic assumptions required for identi?cation and estimation, and their practical implementation. To this end, the course will focus both on developing the pre-requisite statistical / methodological theory and as well as gaining hands-on experience through implementation exercises with real datasets. By the end of the course, students should have deep familiarity of various causal inference methods and—more importantly—be able to determine which method is most appropriate
for a given applied problem and to judge whether the pre-requisite identifying conditions are appropriate.

• W 2:40 p.m.-5:25 p.m.
• Instructor: Christopher Harshaw
  Info
• 3 points

ADVANCED MACHINE LEARNING

Prerequisites: STAT GR5241 This course covers some advanced topics in machine learning and has an emphasis on applications to real world data. A major part of this course is a course project which consists of an in-class presentation and a written project report.

• R 6:10 p.m.-8:55 p.m.
• W 6:20 p.m.-9:05 p.m.
• Instructor: Parijat Dube
  Info
• Instructor: Kamiar Rahnama Rad
  Info
• 3 points

Unsupervised Learning

Description.
Unsupervised Learning is a masters level course on foundations, methods, practice, and applications in machine learning from data without associated labels or outcomes.  This course will focus on dimension reduction and clustering techniques while also covering graphical models, missing data imputation, anomaly detection, generative models, and others. The course will also emphasize conceptual understanding and practical applications of unsupervised learning in data visualization, exploratory data analysis, data pre-processing, and data-driven discovery.   

 

Prerequisites.

STAT GR 5206 Statistical Computing and Intro to Data Science

STAT GR 5241 Statistical Machine Learning (strongly recommended)

STAT GR 5205 Linear Regression (recommended)

STAT GR 5203 Probability (recommended)

Students should also be familiar with linear algebra.

• TR 8:40 a.m.-9:55 a.m.
• Instructor: Yoonhaeng Hur
  Info
• 3 points

STATISTICAL METHODS IN FINANCE

Prerequisites: STAT GR5204 or the equivalent. STAT GR5205 is recommended. A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, smoothing techniques and estimation of yield curves statistical methods for financial time series, value at risk, term structure models and fixed income research, and estimation and modeling of volatilities. Hands-on experience with financial data.

• F 10:10 a.m.-12:40 p.m.
• Instructor: Hammou El Barmi
  CULPA: 8 Info
• 3 points

STAT INF/TIME-SERIES MODELLING

Available to SSP, SMP Modeling and inference for random processes, from natural sciences to finance and economics. ARMA, ARCH, GARCH and nonlinear models, parameter estimation, prediction and filtering.

• S 10:10 a.m.-12:40 p.m.
• Instructor: Franz Rembart
  Info
• 3 points

STOCHASTC PROCSSES-APPLICTNS I

Prerequisites: STAT GR5203 or the equivalent. Basics of continuous-time stochastic processes. Wiener processes. Stochastic integrals. Ito's formula, stochastic calculus. Stochastic exponentials and Girsanov's theorem. Gaussian processes. Stochastic differential equations. Additional topics as time permits.

• MW 1:10 p.m.-2:25 p.m.
• MW 4:10 p.m.-5:25 p.m.
• Instructor: Steven Campbell
  Info
• 3 points

STOCHASTIC METHODS IN FINANCE

Prerequisites: STAT GR5264 Available to SSP, SMP. Mathematical theory and probabilistic tools for modeling and analyzing security markets are developed. Pricing options in complete and incomplete markets, equivalent martingale measures, utility maximization, term structure of interest rates.

• MW 4:10 p.m.-5:25 p.m.
• Instructor: Graeme Baker
  Info
• 3 points

ADVANCED DATA ANALYSIS

Course Description

STAT GR5291 Advanced Data Analysis serves as one of the required capstone experiences for MA students in statistics. This course is project-based and covers advanced topics in traditional data analysis. Students are presented with a mix of theory and application in homework assignments.  The final project  is a major contribution to the final grade and is arguably considered the capstone project for the MA in Statistics Program.

Students will learn a myriad of topics related to data analysis and hypothesis testing, and are responsible for application through statistical packages or manual programming. Topics include, exploratory data analysis & descriptive statistics, review of sampling distribution, point estimation, review of hypothesis testing & confidence interval procedures, non-parametric tests, computational methods (Monte Carlo, bootstrap, permutation tests), categorical data analysis, linear regression, diagnostics & residual analysis, robust regression, model selection, non-linear regression & smoothers, aspects of experimental design (ANOVA, two-way ANOVA, blocking, multiple comparisons, ANCOVA, semi-parametric procedures, random effects models, mixed effects models, nested models, repeated measures), and general linear models (logistic regression, penalized logistic, multinomial regression, link functions).

Also, time permitting the class covers:
survival analysis (hazard function, survival curve), time series analysis (stationarity, ACF/PACF, MA, AR, ARMA, ARIMA, order selection, forecasting).

• F 5:10 p.m.-7:40 p.m.
• Instructor: Demissie Alemayehu
  h-index: 14 Info
• 3 points

TOPICS IN MODERN STATISTICS

Stat Aspects of Finance

Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.

• R 10:10 a.m.-12:40 p.m.
• Instructor: Jeremy Shen
  Info
• 3 points

TOPICS IN MODERN STATISTICS

ML Engineering for Stats

Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.

• MW 6:10 p.m.-7:25 p.m.
• Instructor: Iordan I Slavov
  Info
• 3 points

TOPICS IN MODERN STATISTICS

STAT ANALYSIS-NEURAL DATA

Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.

• R 1:10 p.m.-3 p.m.
• Instructor: Liam M Paninski
  CULPA: 4 Info
• 3 points

TOPICS IN MODERN STATISTICS

APP MACH LEARN COMP VIS

Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.

• M 1:10 p.m.-3:40 p.m.
• Instructor: Xiaofu He
  h-index: 21 Info
• 3 points

TOPICS IN MODERN STATISTICS

Decode AI w/Info Theory

Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.

• M 4:10 p.m.-6:40 p.m.
• Instructor: Ori Shental
  Info
• 3 points

TOPICS IN MODERN STATISTICS

DESIGN&ANALY/ONLINE EXPRM

Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.

• W 6:10 p.m.-8:40 p.m.
• Instructor: Lei Kang
  Info
• 3 points

TOPICS IN MODERN STATISTICS

DRUG DEV IN BIG PHARMA

Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.

• MW 6:10 p.m.-7:25 p.m.
• Instructor: Paula C Abreu
  Info
• 3 points

TOPICS IN MACHINE LEARNING AND AI

THEORY OF DIFFUSION MODEL

TOPICS IN MACHINE LEARNING AND AI will provide MA Statistics students with an opportunity to study specialized areas of statistics in more depth and to meet the educational needs of a rapidly growing field.

• MW 11:40 a.m.-1:40 p.m.
• Instructor: Anthimos Vardis Kandiros
  Info
• 0 points

PROFESSIONAL DEVELOPMENT

The course aims to teach MA in Statistics students how to manage their careers and develop professionally. Topics include resume and cover-letter writing, negotiation, mentoring, interviewing skills and communication across global teams. Top professionals from across the globe speak to students and help improve leadership skills.

• W 4:10 p.m.-5:25 p.m.
• F 1:10 p.m.-3:40 p.m.
• Instructor: Banu Baydil
  CULPA: 10 Info
• Instructor: Gabriel Young
  CULPA: 7 Info
• 0 points

MA Mentored Research

MA MENTORED RESEARCH

This course is intended to provide a mechanism to MA students in Statistics who undertake on-campus project work or research. The course may be signed up with a faculty member from the Department of Statistics for academic credit. Students seeking to enroll in the course should identify an on-campus project and a congenial faculty member whose research is appealing to them, and who are able to serve as their mentor. Students should then submit an application to enroll in this course, which will be reviewed and approved by the Faculty Director of the MA in Statistics program.

• Instructor: Gabriel Young
  CULPA: 7 Info
• 0-3 points

Statistical Fieldwork

Prerequisites: GR5203; GR5204 &GR5205 and at least 4 approved electives This course is an elective course for students in the M.A. in Statistics program that counts towards the degree requirements. To receive a grade and academic credits for this course, students are expected to engage in approved off-campus internships that can be counted as an elective. Statistical Fieldwork should provide students an opportunity to apply their statistical skills and gain practical knowledge on how statistics can be applied to solve real-world challenges.

• Instructor: Demissie Alemayehu
  h-index: 14 Info
• 1 points

Honors Probability Theory

A rigorous introduction to probability theory. Topics covered include probability spaces and measures, Borel-Cantelli lemma, zero-one laws, conditional probability, Bayes rule, independence, random variables and distribution functions, random vectors and multivariate distributions, expectation, important distributions, characteristic functions, conditional distributions, transformations of random variables, probability and expectation inequalities, laws of large numbers, central limit theorem.

• TR 1:10 p.m.-3:40 p.m.
• Instructor: Michael Sobel
  CULPA: 5 Wikipedia h-index: 35 Info
• 3 points

Honors Statistical Inference

A rigorous introduction to the theory of statistics. Topics covered include elementary decision theory, distribution of the sample mean, point estimation methods and asymptotic properties, the bias variance tradeoff, exponential families, sufficiency and minimal sufficiency, completeness, Lehmann Scheffe, UMVUE and BLUE, Bayes inference, Neyman-Pearson theory, hypothesis testing, most powerful unbiased tests, likelihood ratio tests, confidence sets.

• TR 1:10 p.m.-3:40 p.m.
• Instructor: Zhiliang Ying
  CULPA: 1 Wikipedia h-index: 62 Info
• 3 points

Honors Linear Regression Models

Hon Linear Regression Mod

This high-level course in linear regression delves deeply into the theoretical and geometric aspects of regression analysis, offering a comprehensive exploration of its foundational principles and advanced topics. Students will study regression within vector space contexts, emphasizing the role of inner products and orthogonal projections. The analysis of projection matrices will include their properties, such as idempotence and symmetry, and their implications for regression diagnostics and metrics. Students will explore why various test statistics follow t- and F-distributions, with careful attention to degrees of freedom and their derivations. As the course progresses, it will address the complexities of high dimensional regression scenarios.

• MW 6:10 p.m.-7:25 p.m.
• Instructor: Yisha Yao
  Info
• 3 points

Statistics - Graduate Recitation

Statistics - Grad Recitat

This course is an introduction to probability and statistics for data science. Topics
include probability theory, probability distributions, simulations, parameters estima-
tion, hypothesis testing, simple regression. Python examples will be used throughout
the course for illustrations.

• M 10:10 a.m.-11:25 a.m.
• W 4:10 p.m.-5:25 p.m.
• T 7:10 p.m.-8:25 p.m.
• Instructor: Dobrin Marchev
  Info
• 0 points

PROBABILITY & STAT FOR DATA SC

This course covers the following topics: Fundamentals of probability theory and statistical inference used in data science; Probabilistic models, random variables, useful distributions, expectations, law of large numbers, central limit theorem; Statistical inference; point and confidence interval estimation, hypothesis tests, linear regression.

• MW 6:10 p.m.-7:25 p.m.
• TR 4:10 p.m.-5:25 p.m.
• Instructor: Dobrin Marchev
  Info
• 3 points

EXPLORATORY DATA ANALYSIS/VISUAL

This course is covers the following topics: fundamentals of data visualization, layered grammer of graphics, perception of discrete and continuous variables, intreoduction to Mondran, mosaic pots, parallel coordinate plots, introduction to ggobi, linked pots, brushing, dynamic graphics, model visualization, clustering and classification.

• MW 4:10 p.m.-5:25 p.m.
• TR 4:10 p.m.-5:25 p.m.
• Instructor: Joyce T Robbins
  CULPA: 5 Info
• 3 points

STAT INFERENCE & MODELING

Prerequisites: (STAT GR5701) working knowledge of calculus and linear algebra (vectors and matrices), STAT GR5701 or equivalent, and familiarity with a programming language (e.g. R, Python) for statistical data analysis. In this course, we will systematically cover fundamentals of statistical inference and modeling, with special attention to models and methods that address practical data issues. The course will be focused on inference and modeling approaches such as the EM algorithm, MCMC methods and Bayesian modeling, linear regression models, generalized linear regression models, nonparametric regressions, and statistical computing. In addition, the course will provide introduction to statistical methods and modeling that addresses various practical issues such as design of experiments, analysis of time-dependent data, missing values, etc. Throughpout the course, real-data examples will be used in lecture discussion and homework problems. This course lays the statistical foundation for inference and modeling using data, preparing the MS in Data Science students, for other courses in machine learning, data mining and visualization.

• TR 6:10 p.m.-7:25 p.m.
• Instructor: Dobrin Marchev
  Info
• 3 points

MA Research Specialization in Statistics

Research Specialization/S

Each year, approximately 10–15% of MA in Statistics students participate in on-campus academic research, contributing to advances in statistical methodology and applied areas. Some projects demonstrate exceptional promise and benefit from additional time and support for further development. The MA Research Specialization in Statistics allows qualified students to extend their MA program to a fourth semester to continue their research under the supervision of a faculty mentor. This competitive, merit-based program requires demonstrated research progress, a nomination from a faculty mentor, and an outstanding academic record. STAT GR5999 serves as the course through which students admitted to the MA Research Specialization fulfill their research requirements.

• Instructor: Gabriel Young
  CULPA: 7 Info
• 6 points

APPLIED STATISTICS I

First semester of the doctoral program sequence in applied statistics.

• MW 10:10 a.m.-11:25 a.m.
• Instructor: Ming Yuan
  h-index: 45 Info
• 4 points

APPLIED STATISTICS III

Prerequisites: STAT GR6102 Modern Bayesian methods offer an amazing toolbox for solving science and engineering problems. We will go through the book Bayesian Data Analysis and do applied statistical modeling using Stan, using R (or Python or Julia if you prefer) to preprocess the data and postprocess the analysis. We will also discuss the relevant theory and get to open questions in model building, computing, evaluation, and expansion. The course is intended for students who want to do applied statistics and also those who are interested in working on statistics research problems.

• TR 11:40 a.m.-12:55 p.m.
• Instructor: Andrew Gelman
  CULPA: 6 Wikipedia h-index: 112 Info
• 4 points

Statistical Consulting

Prerequisites: STAT GR6102 or instructor permission. The Deparatments doctoral student consulting practicum. Students undertake pro bono consulting activities for Columbia community researchers under the tutelage of a faculty mentor.

• T 12:10 p.m.-2 p.m.
• Instructor: Tian Zheng
  CULPA: 13 Wikipedia h-index: 25 Info
• 3 points

THEORETICAL STATISTICS I

Prerequisites: students in a masters program must seek the director of the M.A. program in statistics' permission; students in an undergraduate program must seek the director of undergraduate studies in statistics' permission. A general introduction to mathematical statistics and statistical decision theory. Elementary decision theory, Bayes inference, Neyman-Pearson theory, hypothesis testing, most powerful unbiased tests, confidence sets. Estimation: methods, theory, and asymptotic properties. Likelihood ratio tests, multivariate distribution. Elements of general linear hypothesis, invariance, nonparametric methods, sequential analysis.

• MW 2:40 p.m.-3:55 p.m.
• Instructor: Sumit Mukherjee
  CULPA: 4 h-index: 13 Info
• 4 points

THEORETICAL STATISTICS III

Prerequisites: STAT G6201 and STAT G6201 This course will mainly focus on nonparametric methods in statistics. A tentavie list of topics to be covered include nonparametric density and regression function estimation -- upper bounds on the risk of kernel estimators and matching lower bounds on the minimax risk, reproducing kernel Hilbert spaces, bootstrap and resampling methods, multiple hypothesis testing, and high dimensional stastistical analysis.

• TR 4:10 p.m.-5:25 p.m.
• Instructor: Marco A Avella Medina
  Info
• 4 points

Probabilistic Models and Machine Learnin

Stat ML: Theory to Practi

Probabilistic Models and Machine Learning is a PhD-level course about how to design and use probability models. We study their mathematical properties, algorithms for computing with them, and applications to real problems. We study both the foundations and modern methods in this field. Our goals are to understand probabilistic modeling, to begin research that makes contributions to this field, and to develop good practices for building and applying probabilistic models.

• MW 1:10 p.m.-2:25 p.m.
• Instructor: David Blei
  Wikipedia h-index: 98 Info
• 3 points

Graduate Independent Research

Independent Study with Faculty Advisor must be registered for every semester after first academic year

• Instructor: Marco A Avella Medina
  Info
• Instructor: David Blei
  Wikipedia h-index: 98 Info
• Instructor: John P Cunningham
  CULPA: 7 Info
• Instructor: Richard Davis
  CULPA: 3 h-index: 60 Info
• Instructor: Victor H de la Pena
  h-index: 20 Info
• Instructor: Bianca Dumitrascu
  Info
• Instructor: Andrew Gelman
  CULPA: 6 Wikipedia h-index: 112 Info
• Instructor: Yuqi Gu
  h-index: 6 Info
• Instructor: Ioannis Karatzas
  CULPA: 7 h-index: 58 Info
• Instructor: Samory Kpotufe
  CULPA: 2 Info
• Instructor: Jingchen Liu
  CULPA: 2 h-index: 19 Info
• Instructor: Ivan Corwin
  CULPA: 1 Wikipedia h-index: 34 Info
• Instructor: Arian Maleki
  h-index: 31 Info
• Instructor: Sumit Mukherjee
  CULPA: 4 h-index: 13 Info
• Instructor: Marcel F Nutz
  CULPA: 9 Info
• Instructor: Liam M Paninski
  CULPA: 4 Info
• Instructor: Daniel Rabinowitz
  CULPA: 19 h-index: 34 Info
• Instructor: Cynthia Rush
  CULPA: 1 h-index: 12 Info
• Instructor: Bodhisattva Sen
  h-index: 24 Info
• Instructor: Michael Sobel
  CULPA: 5 Wikipedia h-index: 35 Info
• Instructor: Simon Tavare
  Wikipedia Info
• Instructor: Anne Van Delft
  CULPA: 2 h-index: 5 Info
• Instructor: Zhiliang Ying
  CULPA: 1 Wikipedia h-index: 62 Info
• Instructor: Ming Yuan
  h-index: 45 Info
• Instructor: Tian Zheng
  CULPA: 13 Wikipedia h-index: 25 Info
• Instructor: Genevera Allen
  Info
• Instructor: Christopher Harshaw
  Info
• 3 points

Graduate Independent Research

Independent Study with Faculty Advisor must be registered for every semester after first academic year

• 3 points

Theoretical Statistics

STAT ANALYSIS-NEURAL DATA

.

• R 1:10 p.m.-3 p.m.
• Instructor: Liam M Paninski
  CULPA: 4 Info
• 3 points

SEM-THEORETICAL STATISTIC

Departmental colloquium in statistics.

• M 4:10 p.m.-5:25 p.m.
• Instructor: Christopher Harshaw
  Info
• 3 points

SEMINAR PROBABILITY THEORY

Departmental colloquium in probability theory.

• F 11:40 a.m.-12:55 p.m.
• Instructor: Ivan Corwin
  CULPA: 1 Wikipedia h-index: 34 Info
• 3 points

SEMINAR IN APPLIED PROB & RISK

A colloquiim in applied probability and risk.

• R 1:10 p.m.-2:25 p.m.
• Instructor: Sumit Mukherjee
  CULPA: 4 h-index: 13 Info
• 1 points

SEM IN MATHEMATICAL FINANCE

Seminar in Mathematical Financ

A colloquium on topics in mathematical finance

• R 4:10 p.m.-5:25 p.m.
• Instructor: Marcel F Nutz
  CULPA: 9 Info
• 3 points