Online Master in Data Science (MSDS)

This course provides the theoretical basis for studying the properties of modern statistical and machine learning methods. Students will learn the definitions and properties of probability spaces, random variables, distributions, expectations and limit theorems. Students will work with density functions, conditional expectations, and convergence of random variables. After successful completion of this course, students will be able to determine the probability distribution function and density of random variables/vectors, use the properties of expectations and higher-order moments in computations, and examine the appropriate convergence of random variables given specific situations. Students will also be able to apply results from probability theory to study the properties of sample statistics such as estimators.

This course provides students with the essential background in calculus and linear algebra needed to pursue the study of Data Science. Topics include limits, derivatives and integrals of (multivariable) functions; vectors and matrices; vector spaces and subspaces; norms and projections; basis and dimension; eigenvalues and eigenvectors; singular values; continuous optimization; and maps between Euclidean spaces and Jacobians. Throughout, various applications to Data Science will be considered, with hands-on numerical and coding exercises supplementing the theory.

This course offers an introduction to exploratory data analysis and the use of basic statistical tools. Topics will include data collection; descriptive statistics, and graphical and tabular treatment of quantitative, qualitative, and count data; detecting relations between variables; confidence intervals and hypothesis testing for one and two samples; simple and multiple linear regression; analysis of variance; design of experiments; and nonparametric methods. Selected topics, such as quality control and time series analysis, may also be included. Statistical software will be used throughout the course and statistical inference will be based on examples using real data. Students will participate in group projects of data analysis. They will be trained in the different phases of the professional statistician’s work, namely: data collection, description, analysis, testing, and presentation of the conclusions. Prerequisite: MA 540.

This course will introduce foundational ideas as well as advanced techniques in linear algebra that are employed in computational science of Big Data. Students will work with vector-matrix representation of various types of structured and unstructured data and how different models and processes could be understood in terms of linear algebra operations and algorithms. Efficient implementation of algorithms for high dimensional data by using Randomized Numerical Linear Algebra will be one of the focal points. Students will develop and improve their coding skills in Python and MATLAB for implementation of several algorithms. In addition, students will read past and current literature in machine learning and data science to familiarize themselves with current trends and challenges in linear algebra for solving real life problems. Prerequisites: MA 123, MA 124 or equivalent, MA 232 or equivalent, MA 222 or equivalent, and have basic knowledge of MATLAB (FE 516) or Python (FE 520).

The objective of this course is to introduce the students to the theory and methods of optimization used in data science. The first portion of the class focuses on elements of convex analysis and subgradient calculus for non-smooth functions, optimality conditions for differentiable and for non-smooth optimization problems, and Lagrangian duality. The main part of the class discusses numerical methods for optimization with a focus and application to problems arising in data science. Approaches to large-scale/big-data optimization include decomposition methods, design of distributed and parallel methods of optimization, as well as stochastic approximation methods. Examples of optimization models in classification, clustering, statistical learning, compressed sensing will be discussed in order to illustrate the theoretical and numerical challenges and to demonstrate the scope of applications.

An introductory course for machine learning theory, algorithms, and applications. Content aims to provide students with the knowledge to understand key elements of how to design algorithms/systems that automatically learn, improve, and accumulate knowledge with experience. Topics covered in this course include decision tree learning, neural networks, Bayesian learning, reinforcement learning, ensembling multiple learning algorithms, and various application problems. Students will be provided opportunities to simulate their algorithms in a programming language and apply them to solve real-world problems. Cross-listed with: EE 695.

Deep learning (DL) is a family of the most powerful and popular machine learning (ML) methods and has wide real-world applications including face recognition, machine translation, self-driving car, recommender system, and playing the Go game. This course is designed for students either with or without ML background. The course will cover fundamental ML, computer vision, and natural language problems and DL tools for solving the problems. The students will be able to use DL methods for solving real-world ML problems. The homework is mostly implementation and programming using the Python language and popular DL frameworks such as TensorFlow and Keras. Knowledge and skills in Python programming and linear algebra are strictly required. Knowledge of probability theory, statistics, and numerical analysis are recommended but not required. Knowledge of machine learning and artificial intelligence is helpful but unnecessary.

This course provides a broad and systematic introduction to time series models and their applications to modeling and prediction. It utilizes real-world examples to apply a variety of time series models and methods. After successful completion of this course, students will be able to work with stationarity and measures of dependency, time series regression, graphical analysis, trend and seasonality detection and removal, and moving-average filtering. Students will also be able to apply linear time series analysis, spectral analysis, and multivariate time series methods. Additional topics that will be covered include long-memory processes, unit root testing, volatility modeling, state space models and Kalman filtering.

The objective of this course is to give students a basic grounding in designing and implementing distributed and cloud systems, including issues in the implementation of backend services in the cloud itself. What are global consensus and Paxos, and what is their application in building cloud systems? What are the advantages and disadvantages of using distributed NoSQL stores such as Cassandra instead of relational stores such as MySQL? What are strong and weak consistency, what are the “CAP Theorem” and the “CALM Theorem,” and what are their implications for building highly available services? What is a blockchain, such as the Bitcoin blockchain, and how does it relate to issues in coordinating distributed systems? What are the roles of REST, Websockets, and stream processing in cloud applications? This course will combine hands-on experience in developing cloud services, with a firm grounding in the tools and principles for building distributed and cloud applications, including advanced architectures such as peer-to-peer and publish-subscribe. Besides cloud services, we will also be looking at cloud support for batch processing, such as the Hadoop framework, and its use with NoSQL data stores, such as Cassandra.

This course will provide an introduction to the design and querying of relational databases. Topics include relational schemas; keys and foreign key references; relational algebra (as an introduction to SQL); SQL in depth; Entity-Relationship (ER) database design; translating from ER models to relational schemas and from relational schemas to ER models; functional dependencies; and normalization. Prerequisite: CS 590 or CS 570.

This course will provide an introduction to exploratory data analysis and the use of basic statistical tools. Topics will include: data collection; descriptive statistics, and graphical and tabular treatment of quantitative, qualitative, and count data; detecting relations between variables; confidence intervals and hypothesis testing for one and two samples; simple and multiple linear regression; analysis of variance; design of experiments; and nonparametric methods. Selected topics, such as quality control and time series analysis, may also be included. Statistical software will be used throughout the course and statistical inference will be based on examples using real data. Students will participate in group projects of data analysis. They will be trained in the different phases of the professional statistician’s work, namely: data collection, description, analysis, testing, and presentation of the conclusions. Prerequisite: MA 540.

This course will provide foundational ideas as well as advanced techniques in linear algebra that are employed in computational science of Big Data. Students will work with vector-matrix representation of various types of structured and unstructured data and how different models and processes could be understood in terms of linear algebra operations and algorithms. Efficient implementation of algorithms for high dimensional data by using Randomized Numerical Linear Algebra will be one of the focal points. Students will develop and improve their coding skills in Python and MATLAB for implementation of several algorithms. In addition, students will read past and current literature in machine learning and data science to familiarize themselves with current trends and challenges in linear algebra for solving real life problems. Prerequisites: MA 123, MA 124 or equivalent, MA 232 or equivalent, MA 222 or equivalent, and have basic knowledge of MATLAB (FE 516) or Python (FE 520).

The objective of this course is to introduce the students to the theory and methods of optimization used in data science. The first portion of the class focuses on elements of convex analysis and subgradient calculus for non-smooth functions, optimality conditions for differentiable and for non-smooth optimization problems, and Lagrangian duality. The main part of the class discusses numerical methods for optimization with a focus and application to problems arising in data science. Approaches to large-scale/big-data optimization include decomposition methods, design of distributed and parallel methods of optimization, as well as stochastic approximation methods. Examples of optimization models in classification, clustering, statistical learning, compressed sensing will be discussed in order to illustrate the theoretical and numerical challenges and to demonstrate the scope of applications.

This course will provide an introduction to machine learning theory, algorithms, and applications. Content aims to provide students with the knowledge to understand key elements of how to design algorithms/systems that automatically learn, improve, and accumulate knowledge with experience. Topics covered in this course include decision tree learning, neural networks, Bayesian learning, reinforcement learning, ensembling multiple learning algorithms, and various application problems. Students will be provided opportunities to simulate their algorithms in a programming language and apply them to solve real-world problems. Cross-listed with: EE 695.

Deep learning (DL) is a family of the most powerful and popular machine learning (ML) methods and has wide real-world applications including face recognition, machine translation, self-driving car, recommender system, and playing the Go game. This course is designed for students either with or without ML background. The course will cover fundamental ML, computer vision, and natural language problems and DL tools for solving the problems. The students will be able to use DL methods for solving real-world ML problems. The homework is mostly implementation and programming using the Python language and popular DL frameworks such as TensorFlow and Keras. Knowledge and skills in Python programming and linear algebra are strictly required. Probability theory, statistics, and numerical analysis are recommended by not required. Knowledge of machine learning and artificial intelligence is helpful but unnecessary.

This course provides a broad and systematic introduction to time series models and their applications to modeling and prediction. It utilizes real-world examples to apply a variety of time series models and methods. After successful completion of this course, students will be able to work with stationarity and measures of dependency, time series regression, graphical analysis, trend and seasonality detection and removal, and moving-average filtering. Students will also be able to apply linear time series analysis, spectral analysis, and multivariate time series methods. Additional topics that will be covered include long-memory processes, unit root testing, volatility modeling, state space models and Kalman filtering.

The objective of this course is to give students a basic grounding in designing and implementing distributed and cloud systems, including issues in the implementation of backend services in the cloud itself. What are global consensus and Paxos, and what is their application in building cloud systems? What are the advantages and disadvantages of using distributed NoSQL stores such as Cassandra instead of relational stores such as MySQL? What are strong and weak consistency, what are the “CAP Theorem” and the “CALM Theorem,” and what are their implications for building highly available services? What is a blockchain, such as the Bitcoin blockchain, and how does it relate to issues in coordinating distributed systems? What are the roles of REST, Websockets, and stream processing in cloud applications? This course will combine hands-on experience in developing cloud services, with a firm grounding in the tools and principles for building distributed and cloud applications, including advanced architectures such as peer-to-peer and publish-subscribe. Besides cloud services, we will also be looking at cloud support for batch processing, such as the Hadoop framework, and its use with NoSQL data stores, such as Cassandra.

This course will provide an introduction to the design and querying of relational databases. Topics include relational schemas; keys and foreign key references; relational algebra (as an introduction to SQL); SQL in depth; Entity-Relationship (ER) database design; translating from ER models to relational schemas and from relational schemas to ER models; functional dependencies; and normalization. Prerequisite: CS 590 or CS 570.

This course will provide an introduction to dynamic programming as the most popular methodology for learning and control of dynamic stochastic systems. We discuss basic models, some theoretical results, and numerical methods for these problems. They will be developed starting from basic models of dynamical systems, through finite-horizon stochastic problems, to infinite-horizon stochastic models of fully or partially observable systems. Throughout the class, special attention will be paid to the application of dynamic programming to statistical learning. The class will include introduction to approximate dynamic programming techniques, which are used in statistical learning, such as tree-based methods for classification, Bayesian learning, among others. The concepts and methods will be illustrated by various applications including learning in stochastic networks, engineering, business, and finance. Prerequisites: MA 547, MA 623.