**Group A: Introductory courses: maximum of four course credit**

These courses seek to provide five critical foundational knowledge and skills that each student graduating from the master’s program is expected to receive at a graduate level: programming skills, data organization and methods skills, numerical linear algebra, multivariate calculus, probability and statistics.

**DSC 200: Data Science Programming**

*DSC 200: Data Science Programming*; 4 units:

Computing structures and programming concepts such as object orientation, data structures such as queues, heaps, lists, search trees and hash tables. Laboratory skills include Jupyte notebooks, RESTful interfaces and various software development kits (SDKs). See sample problems here:

**DSC 202: Data Management for Data Science**

*DSC 202: Data management for Data Science*; 4 Unit:

Principles of data management, relational data model, relational algebra, SQL for data science, NoSQL Databases (document, key–value, graph, column-family), Multidimensional data management (data warehousing, OLAP Queries, OLAP Cubes, Visualizing multidimensional data). Sample problems can be found here: DSC 202 Sample Problems

**DSC 210: Numerical Linear Algebra**

*DSC 210: Numerical Linear Algebra*; 4 units:

Linear algebraic systems, least squares problems, orthogonalization methods, ill-conditioned problems, eigenvalue and singular value decomposition, principal component analysis. Sample problems can be found here: DSC 210 Sample Problems

**DSC 211: Introduction to Optimization**

*DSC 211: Introduction to Optimization*; 4 units:

Continuity and differentiability of a function of several variables, gradient vector, Hessian matrices, Taylor approximation, fundamentals of optimization, Lagrange multipliers, convexity, gradient descent. Sample problems can be found here: DSC 211 Sample Problems

**DSC 212: Probability and Statistics for Data Science**

*DSC 212: Probability and Statistics for Data Science*; 4 units:

Probability, random variables, distributions, central limit theorem, maximum likelihood estimation, method of moments, confidence intervals, hypothesis testing, Bayesian estimation, introduction to simulation and the bootstrap. Sample problems can be found here: DSC 212 Sample Problems

**Group B: Core Courses: 3 required courses, minimum of six courses**

These courses build upon foundational courses. All students must take three required core courses: DSC 240, DSC 241, and DSC 260. In addition, students can select at least three out of the following core courses: DSC 203, DSC 204A, DSC 204B, DSC 206, DSC 215, DSC 242, DSC 243, DSC 244, DSC 245, DSC 250, DSC 261.

Depending on academic preparation, a M.S. students can take an advanced course on Applied Statistics, such as MATH 282B instead of DSC 241. Similarly, instead of DSC204A, a student can take a course on Algorithms, such as CSE 202: Design and Analysis of Algorithms.

**Required Core Courses [minimum 3 courses]**

**DSC 240: Machine Learning**

*DSC 240: Machine Learning*; 4 units:

A graduate level course in machine learning algorithms: decision trees, principal component analysis, k-means, clustering, logistic regression, random forests, boosting, neural networks, deep learning.

[Comprehensive Exam Eligible Course]

**DSC 241: Statistical Models (or MATH 282B)**

*DSC 241: Statistical Models*; 4 units:

linear/nonlinear models, generalized linear models, model fitting and model selection (cross-validation, knockoffs, etc.), regularization and penalization (ridge regression, lasso, etc.), robust methods, nonparametric regression, conformal prediction, causal inference.

[Comprehensive Exam Eligible Course]

**DSC 260: Data Ethics and Fairness**

*DSC 260: Data Ethics and Fairness*; 4 units:

Ethical considerations regarding privacy and control of information. Principles of fairness, accountability, and transparency. Use of metadata to information algorithms. Algorithmic fairness. Policy issues such as the Fair Information Practices Principles Act, and laws concerning the “right to be forgotten.”

**Elective Core Courses [minimum 3 courses]**

**DSC 203: Data Visualization and Scalable Visual Analytics**

*DSC 203: Data Visualization and Scalable Visual Analytics*; 4 units:

Commonly used algorithms and techniques in data visualization. Interactive reasoning and exploratory analysis though visual interfaces. Application of data visualization in various domains including science, engineering, and medicine. Scalable interactive methods involving exploring with big data and visualization methods. Techniques to evaluate effectivity and interpretability of analytical products for diverse users to obtain insights in support of assessment, planning, and decision making.

[Prerequisite: DSC 202]

**DSC 204A: Scalable Data Systems (or CSE 202)**

*DSC 204A: Scalable Data Systems*; 4 units:

Storage/memory hierarchy, distributed scalable computing (i.e., cluster, cloud, edge) principles. Big Data storage, management and processing at scale. Dataflow programming systems and programming models (MapReduce/Hadoop and Spark).

[Prerequisite: DSC 202]

[Comprehensive Exam Eligible Course]

**DSC 204B: Big Data Analytics and Applications**

*DSC 204B: Big Data Analytics & Applications*:

This course is a hands-on introduction to big data analytics. Topics covered include:

I/O bottleneck and the memory hierarchy; HDFS and Spark; RMS error minimization, PCA and percent of variance explained. Analysis of NOAA weather data. Data collection and curation. Limitations of train/test methodology and leaderboards. Kmeans and intrinsic dimension. Classification, Boosting and XGBoost. Margins. Neural Networks and tensorflow.

Students will develop the skills and attitudes required to write jupyter notebooks that can be understood by domain experts.

[Prerequisite: DSC 204A]

[Comprehensive Exam Eligible Course]

**DSC 206: Algorithms for Data Science**

*DSC 206: Algorithms for Data Science; *4 units:

*With the advent of large-scale machine learning, online social networks, and computationally intensive models, data scientists must deal with data that is massive in size, arrives fast, and must be processed within an interactive or online manner. This course studies the mathematical foundations of massive data processing, developing algorithms and analyzing them. We explore methods for sampling, sketching, and distributed processing of large scale databases, clustering, dimensionality reduction, and methods of optimization for the purpose of scalable statistical description, querying, pattern mining, and learning from data. Prerequisites: Linear Algebra and DSC212 (or equivalent). *

[Comprehensive Exam Eligible Course]

**DSC 215: Statistical Critical Thinking**

*DSC 215: Statistical Critical Thinking; *4 units:

We hold science in high regard, however, not all scientific claims are correct. How do we know which claims to trust and which not to? This fundamental question is at the heart of this course. The goal of this course is to enable the student to evaluate any paper in data science, regardless of application area. Topics covered include experimental design, claims, evidence and statistical significance, The Replication Crisis, falsifiability, philosophy of science, history of probability and statistics. About half of the class meetings, as well as the final project, would be devoted to evaluating contemporary papers in data science. This class will be in the form of an open discussion, based on provided reading materials. The only prerequisite is a statistics class that covers hypothesis testing and P-values.

**DSC 242: High-dimensional Probability and Statistics**

*DSC 242: High-dimensional Probability and Statistics*; 4 units:

Concentration inequalities, Markov processes and ergodicity, martingale inequalities, empirical processes, sparse linear models in high dimensions, Principal component analysis in high dimensions, estimation of large covariance matrices.

[This class may be cross-listed with the Mathematics Department.]

**DSC 243: Advanced Optimization**

*DSC 243: Advanced Optimization*; 4 units:

Linear/quadratic programming, optimization under constraints, gradient descent (deterministic and stochastic), convergence rate of gradient descent, acceleration phenomena in convex optimization, stochastic optimization with large data sets, complexity lower bounds for convex

optimization.

[Comprehensive Exam Eligible Course]

**DSC 244: Large-Scale Statistical Analysis**

*DSC 244: Large-Scale Statistical Analysis*; 4 units:

Exploratory data analysis, diagnostics, bootstrap, large-scale (multiple) hypothesis testing, false discovery rate, empirical Bayes methods.

[This class may be cross-listed with Mathematics and/or Biostatistics.]

[Comprehensive Exam Eligible Course]

**DSC 245: Introduction to Causal Inference**

*DSC 245: Introduction to Causal Inference*; 4 units:

Causal versus predictive inference, potential outcomes and randomized experiments (A/B testing), structural causal models (interventions, counterfactuals, causal diagram, do-operator, d-separation), identification of causal effect (back-door and front-door criterion, do-calculus), estimation of causal effect (matching, propensity score, g-computation, doubly robust estimation, regression discontinuity and instrumental variables, conditional effects), structure learning (constraint and score-based algorithms), advanced topics (mediation and path-specific effects, bounding causal effect, selection bias, external validity and transportability, processing missing data, causal inference in networks)

[Prerequisite: DSC 212, 240]

[Comprehensive Exam Eligible Course]

**DSC 250: Advanced Data Mining**

*DSC 250: Advanced Data Mining*; 4 units:

Graph mining and basic text analysis (including keyphrase extraction and generation), set expansion and taxonomy construction, graph representation learning, graph convolutional neural networks, heterogeneous information networks, label propagation, and truth findings.

[Prerequisite: DSC 190A or CSE158 or equivalent]

**DSC 261: Responsible Data Science**

*DSC 261: Responsible Data Science*; 4 units:

responsible data management, algorithmic fairness (fairness definitions, impossibility results, causal fairness, building fair ML models, fairness beyond classification), algorithmic transparency (interpretability vs explainability, auditing-black-box algorithms, algorithmic recourse), privacy and data protection, sampling bias, reproducibility

[Prerequisite: DSC 260, 240, 245]

**Group C: Elective and Specialization Courses: remaining course credit requirements**

**DSC 205: Geometry of Data **

*DSC 205: Geometry of Data; *4 units:

Graph-based data modeling, analysis and representation. Topics include: spectral graph theory, spectral clustering, kernel-based manifold learning, dimensionality reduction and visualization, multiway data analysis, multimodal and multiview data representation, graph neural networks.

**DSC 231: Embedded Sensing and IOT Data Models and Methods**

*DSC 231: Embedded Sensing and IOT Data Models and Methods*; 4 units:

Sensory data and control is mediated by devices near the edge of sensor networks, referred to as IOT (Internet of Things) devices. Components of IOT platforms: signal processing, communications/networking, control, real-time operating systems. Interfaces to cloud computing stack, publish-subscribe protocols such as MQTT, embedded software/middleware components, metadata schema, metadata normalization methods, applications in selected CPS (cyber-physical system) applications.

**DSC 251: Machine Learning in Control**

*DSC 251: Machine Learning in Control; *4 units:

Estimation of stability and uncertainty, optimal control, and sequential decision making.

**DSC 252: Statistical Natural Language Processing**

*DSC 252: Statistical Natural Language Processing*; 4 units:

Diving deep to the classical NLP pipeline: tokenization, stemming, lemmatization, part-of-speech tagging, named entity recognition, parsing, and machine translation. Finite-state transducer, context-free grammar, Hidden Markov Models (HMM), and Conditional Random Fields (CRF) will be covered in detail.

**DSC 253: Advanced Data-driven Text Mining**

*DSC 253: Advanced Data-driven Text Mining*; 4 units:

Unsupervised, weakly supervised, and distantly supervised methods for text mining problems, including information retrieval, open-domain information extraction, text summarization (both extractive and generative), and knowledge graph construction. Bootstrapping, comparative analysis, learning from seed words and existing knowledge bases will be the key methodologies.

**DSC 254: Statistical Signal and Image Analysis**

*DSC 254: Statistical Signal and Image Analysis*; 4 units.

A graduate level course on signal and image analysis spanning three main themes. Statistical signal processing: random processes, stochasticity, stationarity, Wiener filter, Kalman filter, matched filter ; Signal processing: time-frequency representations, wavelets, signal processing with sparse representation (dictionary learning) ; Image processing: registration, image degradation and restoration: noise models + denoising, image pyramids, random fields.

**DSC 213: Statistics on Manifolds**

*DSC 213: Statistics on Manifolds*; 4 units:

This is a graduate topics course covering statistics with manifold constraints. Topics include: Frechet means and variances, principal geodesic analysis, directional statistics, random fields on manifolds, statistical distances between distributions, transport problems, and information geometry. Manifold constraints will be considered on simplexes, spheres, Stiefel manifold, stratified manifolds, cone of positive definite matrices, trees, compositional data, and other relevant manifolds.

**DSC 214: Topological Data Analysis**

*DSC 214: Topological Data Analysis*; 4 units:

Topological methods provide powerful tools for analyzing complex data. This course introduces basic concepts and topological structures, as well as recent theoretical and algorithmic developments, together with examples of applications. Some topics include: basics in topology, simplicial complexes to model data, persistent homology, discrete Morse theory, topology inference, the Mapper methodology, hierarchical clustering, and integration of topological methods with machine learning.

**CSE 234: Data Systems for Machine Learning**

*CSE **234: Data Systems for Machine Learning*; 4 units.

Data management and systems issues across the whole lifecycle of ML-based analytics in real-world applications, including: data sourcing, preparation, and organization for ML; programming models and systems for scalable ML training, feature engineering, and model selection; systems for ML inference, deployment, and explanations; and governed ML platforms and feature stores.

**MATH 181 A-B-C: Mathematical Statistics**

*MATH** 281A-B-C: Mathematical Statistics *(4-4-4 units).

Math 281A consists of statistical models, sufficiency, efficiency, optimal estimation, least squares and maximum likelihood, large sample theory. Math 281B continues and discusses Hypothesis testing and confidence intervals, one-sample and two-sample problems. Bayes theory, statistical decision theory, linear models and regression. Math 281C finished the sequence with nonparametrics: tests, regression, density estimation, bootstrap and jackknife.

**MATH 284: Survival Analysis**

*MATH** 284: Survival Analysis*; 4 units.

Survival analysis is an important tool in many areas of applications including biomedicine, economics, engineering. It deals with the analysis of time to events data with censoring. This course discusses the concepts and theories associated with survival data and censoring, comparing survival distributions, proportional hazards regression, nonparametric tests, competing risk models, and frailty models. The emphasis is on semiparametric inference, and material is drawn from recent literature.

**MATH 285: Stochastic Processes**

*MATH** 285. Stochastic Processes;* 4 units.

Elements of stochastic processes, Markov chains, hidden Markov models, martingales, Brownian motion, Gaussian processes.

[Recommended preparation: undergraduate probability theory. ]

**MATH 287A-B: Time Series Analysis**

*MATH** 287A. Time Series Analysis*; 4 units.

Discussion of finite parameter schemes in the Gaussian and non-Gaussian context. Estimation

for finite parameter schemes. Linear vs. nonlinear time series. Stationary processes and their spectral representation. Spectral estimation.

[Students who have not taken MATH 282A may enroll with consent of the instructor.]

**COGS 243: Statistical Inference and data analysis**

*COGS** 243: Statistical Inference and data analysis;* 4 units:

This course provides a rigorous treatment of hypothesis testing, statistical inference, model fitting, and exploratory data analysis techniques used in the cognitive and neural sciences. Students will acquire an understanding of mathematical foundations and hands-on experience in applying these methods using Matlab.

Cognitive science PhD students must enroll for four units and will be required to do assignments

and a final project. All other students can enroll for two units and will be required to complete all

assignments but not a final project (or by request of a project and no assignments).