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Course 6: Electrical Engineering and Computer Science |
 | | | 6.10/6.50 | | | 6.20/6.60 | | | 6.30/6.70 | | | 6.40/6.80 | | | 6.90/6.ZZ | | |  |
Signal Processing6.3000 Signal Processing
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(Subject meets with 21M.584) Prereq: 6.100A Units: 4-0-8  Lecture: TR2 (4-370) Lab: TR4 (4-370) Recitation: TR3 (4-370, 4-237) +final
Fundamentals of signal processing, focusing on the use of Fourier methods to analyze and process signals such as sounds and images. Topics include Fourier series, Fourier transforms, the Discrete Fourier Transform, sampling, convolution, deconvolution, filtering, noise reduction, and compression. Applications draw broadly from areas of contemporary interest with emphasis on both analysis and design. D. Freeman No textbook information available 6.3010 Signals, Systems and Inference
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Prereq: 6.3000 and (6.3700, 6.3800, or 18.05) Units: 4-0-8
Covers signals, systems and inference in communication, control and signal processing. Topics include input-output and state-space models of linear systems driven by deterministic and random signals; time- and transform-domain representations in discrete and continuous time; and group delay. State feedback and observers. Probabilistic models; stochastic processes, correlation functions, power spectra, spectral factorization. Least-mean square error estimation; Wiener filtering. Hypothesis testing; detection; matched filters. Staff 6.3020[J] Fundamentals of Music Processing
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(Same subject as 21M.387[J]) (Subject meets with 21M.587) Prereq: 6.3000 and 21M.051 Units: 3-0-9
Analyzes recorded music in digital audio form using advanced signal processing and optimization techniques to understand higher-level musical meaning. Covers fundamental tools like windowing, feature extraction, discrete and short-time Fourier transforms, chromagrams, and onset detection. Addresses analysis methods including dynamic time warping, dynamic programming, self-similarity matrices, and matrix factorization. Explores a variety of applications, such as event classification, audio alignment, chord recognition, structural analysis, tempo and beat tracking, content-based audio retrieval, and audio decomposition. Students taking graduate version complete different assignments. Staff 6.7000 Discrete-Time Signal Processing
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Prereq: 6.3010 Units: 4-0-8
Representation, analysis, and design of discrete time signals and systems. Decimation, interpolation, and sampling rate conversion. Noise shaping. Flowgraph structures for DT systems. IIR and FIR filter design techniques. Parametric signal modeling, linear prediction, and lattice filters. Discrete Fourier transform, DFT computation, and FFT algorithms. Spectral analysis, time-frequency analysis, relation to filter banks. Multirate signal processing, perfect reconstruction filter banks, and connection to wavelets. A. V. Oppenheim, J. Ward 6.7010 Digital Image Processing
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Prereq: 6.3000 and 6.3700 Units: 3-0-9
Introduces models, theories, and algorithms key to digital image processing. Core topics covered include models of image formation, image processing fundamentals, filtering in the spatial and frequency domains, image transforms, and feature extraction. Additional topics include image enhancement, image restoration and reconstruction, compression of images and videos, visual recognition, and the application of machine learning-based approaches to image processing. Includes student-driven term project. Staff 6.7020 Array Processing
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Prereq: 6.7000 and (2.687 or (6.3010 and 18.06)) Units: 3-2-7
Adaptive and non-adaptive processing of signals received at arrays of sensors. Deterministic beamforming, space-time random processes, optimal and adaptive algorithms, and the sensitivity of algorithm performance to modeling errors and limited data. Methods of improving the robustness of algorithms to modeling errors and limited data are derived. Advanced topics include an introduction to matched field processing and physics-based methods of estimating signal statistics. Homework exercises providing the opportunity to implement and analyze the performance of algorithms in processing data supplied during the course. G. Averbuch, Y. Park Control6.3100 Dynamical System Modeling and Control Design
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(Subject meets with 6.3102) Prereq: Physics II (GIR) and (18.06 or 18.C06) Units: 4-4-4 Lecture: MW3 (2-190) Lab: F10-1 (38-545) or F2-5 (38-545)
A learn-by-design introduction to modeling and control of discrete- and continuous-time systems, from intuition-building analytical techniques to more computational and data-centric strategies. Topics include: linear difference/differential equations (natural frequencies, transfer functions); controller metrics (stability, tracking, disturbance rejection); analytical techniques (PID, root-loci, lead-lag, phase margin); computational strategies (state-space, eigen-placement, LQR); and data-centric approaches (state estimation, regression, and identification). Concepts are introduced with lectures and online problems, and then mastered during weekly labs. In lab, students model, design, test, and explain systems and controllers involving sensors, actuators, and a microcontroller (e.g., optimizing thrust-driven positioners or stabilizing magnetic levitators). Students taking graduate version complete additional problems and labs. J. White No textbook information available 6.3102 Dynamical System Modeling and Control Design
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(Subject meets with 6.3100) Prereq: Physics II (GIR) and (18.06 or 18.C06) Units: 4-4-4 Lecture: MW3 (2-190) Lab: F10-1 (38-545) or F2-5 (38-545)
A learn-by-design introduction to modeling and control of discrete- and continuous-time systems, from intuition-building analytical techniques to more computational and data-centric strategies. Topics include: linear difference/differential equations (natural frequencies, transfer functions); controller metrics (stability, tracking, disturbance rejection); analytical techniques (PID, root-loci, lead-lag, phase margin); computational strategies (state-space, eigen-placement, LQR); and data-centric approaches (state estimation, regression and identification). Concepts are introduced with lectures and on-line problems, and then mastered during weekly labs. In lab, students model, design, test and explain systems and controllers involving sensors, actuators, and a microcontroller (e.g. optimizing thrust-driven positioners or stabilizing magnetic levitators). Students in the graduate version complete additional problems and labs. Fall: J. K. White Spring: J. K. White No textbook information available 6.7100[J] Dynamic Systems and Control
()Not offered regularly; consult department (Same subject as 16.338[J]) Prereq: 6.3000 and 18.06 Units: 4-0-8
Linear, discrete- and continuous-time, multi-input-output systems in control, related areas. Least squares and matrix perturbation problems. State-space models, modes, stability, controllability, observability, transfer function matrices, poles and zeros, and minimality. Internal stability of interconnected systems, feedback compensators, state feedback, optimal regulation, observers, and observer-based compensators. Measures of control performance, robustness issues using singular values of transfer functions. Introductory ideas on nonlinear systems. Recommended prerequisite: 6.3100. M. A. Dahleh, A. Megretski 6.7110 Multivariable Control Systems
()Not offered regularly; consult department Prereq: 6.7100 or 16.31 Units: 3-0-9
Computer-aided design methodologies for synthesis of multivariable feedback control systems. Performance and robustness trade-offs. Model-based compensators; Q-parameterization; ill-posed optimization problems; dynamic augmentation; linear-quadratic optimization of controllers; H-infinity controller design; Mu-synthesis; model and compensator simplification; nonlinear effects. Computer-aided (MATLAB) design homework using models of physical processes. A. Megretski 6.7120 Principles of Modeling, Computing and Control for Decarbonized Electric Energy Systems
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(Subject meets with 6.7121) Prereq: 6.2200, (6.2000 and 6.3100), or permission of instructor Units: 4-0-8
Introduces fundamentals of electric energy systems as complex dynamical network systems. Topics include coordinated and distributed modeling and control methods for efficient and reliable power generation, delivery, and consumption; data-enabled algorithms for integrating clean intermittent resources, storage, and flexible demand, including electric vehicles; examples of network congestion management, frequency, and voltage control in electrical grids at various scales; and design and operation of supporting markets. Students taking graduate version complete additional assignments. Staff 6.7121 Principles of Modeling, Computing and Control for Decarbonized Electric Energy Systems
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(Subject meets with 6.7120) Prereq: 6.2200, (6.2000 and 6.3100), or permission of instructor Units: 4-0-8
Introduces fundamentals of electric energy systems as complex dynamical network systems. Topics include coordinated and distributed modeling and control methods for efficient and reliable power generation, delivery, and consumption; data-enabled algorithms for integrating clean intermittent resources, storage, and flexible demand, including electric vehicles; examples of network congestion management, frequency, and voltage control in electrical grids at various scales; and design and operation of supporting markets. Students taking graduate version complete additional assignments. Staff Optimization & Engineering Mathematics6.3260[J] Networks
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(Same subject as 14.15[J]) (Subject meets with 14.150) Prereq: 6.3700 or 14.30 Units: 4-0-8 Lecture: MW10.30-12 (E51-149) Recitation: F3 (E51-149) +final
Highlights common principles that permeate the functioning of diverse technological, economic and social networks. Utilizes three sets of tools for analyzing networks -- random graph models, optimization, and game theory -- to study informational and learning cascades; economic and financial networks; social influence networks; formation of social groups; communication networks and the Internet; consensus and gossiping; spread and control of epidemics; control and use of energy networks; and biological networks. Students taking graduate version complete additional assignments. S. Morris No textbook information available 6.7210[J] Introduction to Mathematical Programming
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(Same subject as 15.081[J]) Prereq: 18.06 Units: 4-0-8 Lecture: TR1-2.30 (32-141) Recitation: F12 (2-105) +final
Introduction to linear optimization and its extensions emphasizing both methodology and the underlying mathematical structures and geometrical ideas. Covers classical theory of linear programming as well as some recent advances in the field. Topics: simplex method; duality theory; sensitivity analysis; network flow problems; decomposition; robust optimization; integer programming; interior point algorithms for linear programming; and introduction to combinatorial optimization and NP-completeness. P. Jaillet No textbook information available 6.7220[J] Nonlinear Optimization
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(Same subject as 15.084[J]) Prereq: 18.06 and (18.100A, 18.100B, or 18.100Q) Units: 4-0-8
Unified analytical and computational approach to nonlinear optimization problems. Unconstrained optimization methods include gradient, conjugate direction, Newton, sub-gradient and first-order methods. Constrained optimization methods include feasible directions, projection, interior point methods, and Lagrange multiplier methods. Convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. Comprehensive treatment of optimality conditions and Lagrange multipliers. Geometric approach to duality theory. Applications drawn from control, communications, machine learning, and resource allocation problems. Staff 6.7230[J] Algebraic Techniques and Semidefinite Optimization
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(Same subject as 18.456[J]) Prereq: 6.7210 or 15.093 Units: 3-0-9
Theory and computational techniques for optimization problems involving polynomial equations and inequalities with particular, emphasis on the connections with semidefinite optimization. Develops algebraic and numerical approaches of general applicability, with a view towards methods that simultaneously incorporate both elements, stressing convexity-based ideas, complexity results, and efficient implementations. Examples from several engineering areas, in particular systems and control applications. Topics include semidefinite programming, resultants/discriminants, hyperbolic polynomials, Groebner bases, quantifier elimination, and sum of squares. Staff 6.7240 Game Theory with Engineering Applications
()Not offered regularly; consult department Prereq: 6.3702 Units: 4-0-8
Introduction to fundamentals of game theory and mechanism design with motivations for each topic drawn from engineering applications (including distributed control of wireline/wireless communication networks, transportation networks, pricing). Emphasis on the foundations of the theory, mathematical tools, as well as modeling and the equilibrium notion in different environments. Topics include normal form games, supermodular games, dynamic games, repeated games, games with incomplete/imperfect information, mechanism design, cooperative game theory, and network games. A. Ozdaglar 6.7250 Optimization for Machine Learning
()Not offered regularly; consult department Prereq: 6.3900 and 18.06 Units: 3-0-9
Optimization algorithms are central to all of machine learning. Covers a variety of topics in optimization, with a focus on non-convex optimization. Focuses on both classical and cutting-edge results, including foundational topics grounded in convexity, complexity theory of first-order methods, stochastic optimization, as well as recent progress in non-Euclidean optimization, deep learning, and beyond. Prepares students to appreciate a broad spectrum of ideas in OPTML, learning to be not only informed users but also gaining exposure to research questions in the area. Staff 6.7260 Network Science and Models
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Prereq: 6.3702 and 18.06 Units: 3-0-9
Introduces the main mathematical models used to describe large networks and dynamical processes that evolve on networks. Static models of random graphs, preferential attachment, and other graph evolution models. Epidemic propagation, opinion dynamics, social learning, and inference in networks. Applications drawn from social, economic, natural, and infrastructure networks, as well as networked decision systems such as sensor networks. P. Jaillet 6.7300[J] Introduction to Modeling and Simulation
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(Same subject as 2.096[J], 16.910[J]) Prereq: 18.03 or 18.06 Units: 3-6-3 Lecture: MW1-2.30 (32-155)
Introduction to computational techniques for modeling and simulation of a variety of large and complex engineering, science, and socio-economical systems. Prepares students for practical use and development of computational engineering in their own research and future work. Topics include mathematical formulations (e.g., automatic assembly of constitutive and conservation principles); linear system solvers (sparse and iterative); nonlinear solvers (Newton and homotopy); ordinary, time-periodic and partial differential equation solvers; and model order reduction. Students develop their own models and simulators for self-proposed applications, with an emphasis on creativity, teamwork, and communication. Prior basic linear algebra required and at least one numerical programming language (e.g., MATLAB, Julia, Python, etc.) helpful. L. Daniel No textbook information available 6.7310[J] Introduction to Numerical Methods
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(Same subject as 18.335[J]) Prereq: 18.06, 18.700, or 18.701 Units: 3-0-9 Lecture: TR2.30-4 (4-265)
Advanced introduction to numerical analysis: accuracy and efficiency of numerical algorithms. In-depth coverage of sparse-matrix/iterative and dense-matrix algorithms in numerical linear algebra (for linear systems and eigenproblems). Floating-point arithmetic, backwards error analysis, conditioning, and stability. Other computational topics (e.g., numerical integration or nonlinear optimization) may also be surveyed. Final project involves some programming. R. Shah No textbook information available 6.7320[J] Parallel Computing and Scientific Machine Learning
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(Same subject as 18.337[J]) Prereq: 18.06, 18.700, or 18.701 Units: 3-0-9
Introduction to scientific machine learning with an emphasis on developing scalable differentiable programs. Covers scientific computing topics (numerical differential equations, dense and sparse linear algebra, Fourier transformations, parallelization of large-scale scientific simulation) simultaneously with modern data science (machine learning, deep neural networks, automatic differentiation), focusing on the emerging techniques at the connection between these areas, such as neural differential equations and physics-informed deep learning. Provides direct experience with the modern realities of optimizing code performance for supercomputers, GPUs, and multicores in a high-level language. Staff 6.7330[J] Numerical Methods for Partial Differential Equations
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(Same subject as 2.097[J], 16.920[J]) Prereq: 18.03 or 18.06 Units: 3-0-9 Lecture: MW9.30-11 (37-212)
Covers the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic, and hyperbolic partial differential and integral equations. Topics include mathematical formulations; finite difference, finite volume, finite element, and boundary element discretization methods; and direct and iterative solution techniques. The methodologies described form the foundation for computational approaches to engineering systems involving heat transfer, solid mechanics, fluid dynamics, and electromagnetics. Computer assignments requiring programming. J. Peraire No textbook information available 6.7340[J] Fast Methods for Partial Differential and Integral Equations
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(Same subject as 18.336[J]) Prereq: 6.7300, 16.920, 18.085, 18.335, or permission of instructor Units: 3-0-9
Unified introduction to the theory and practice of modern, near linear-time, numerical methods for large-scale partial-differential and integral equations. Topics include preconditioned iterative methods; generalized Fast Fourier Transform and other butterfly-based methods; multiresolution approaches, such as multigrid algorithms and hierarchical low-rank matrix decompositions; and low and high frequency Fast Multipole Methods. Example applications include aircraft design, cardiovascular system modeling, electronic structure computation, and tomographic imaging. Staff 6.7350 Numerical Algorithms for Computing and Machine Learning
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Prereq: (Calculus II (GIR), 6.100A, and 18.C06) or permission of instructor Units: 3-0-9
Broad survey of numerical methods used in graphics, vision, robotics, machine learning, and scientific computing, with emphasis on incorporating these algorithms into downstream applications. Focuses on challenges that arise in applying/implementing numerical algorithms and recognizing which numerical methods are relevant to different applications. Topics include numerical linear algebra (QR, LU, SVD matrix factorizations; eigenvectors; conjugate gradients), ordinary and partial differential equations (divided differences, finite element method), and nonlinear systems and optimization (gradient descent, Newton/quasi-Newton methods, gradient-free optimization, constrained optimization). Examples and case studies drawn from the computer science and machine learning literatures. Staff Communications6.3400 Introduction to EECS via Communication Networks
() Not offered regularly; consult department Prereq: 6.100A Units: 4-4-4
Studies key concepts, systems, and algorithms to reliably communicate data in settings ranging from the cellular phone network and the Internet to deep space. Weekly laboratory experiments explore these areas in depth. Topics presented in three modules - bits, signals, and packets - spanning the multiple layers of a communication system. Bits module includes information, entropy, data compression algorithms, and error correction with block and convolutional codes. Signals module includes modeling physical channels and noise, signal design, filtering and detection, modulation, and frequency-division multiplexing. Packets module includes switching and queuing principles, media access control, routing protocols, and data transport protocols. Staff 6.7410 Principles of Digital Communication
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(Subject meets with 6.7411) Prereq: (6.3000 or 6.3102) and (6.3700, 6.3800, or 18.05) Units: 3-0-9 Lecture: TR2.30-4 (56-154)
Covers communications by progressing through signal representation, sampling, quantization, compression, modulation, coding and decoding, medium access control, and queueing and principles of protocols. By providing simplified proofs, seeks to present an integrated, systems-level view of networking and communications while laying the foundations of analysis and design. Lectures are offered online; in-class time is dedicated to recitations, exercises, and weekly group labs. Homework exercises are based on theoretical derivation and software implementation. Students taking graduate version complete additional assignments. M. Medard No textbook information available 6.7411 Principles of Digital Communication
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(Subject meets with 6.7410) Prereq: (6.3000, 6.3100, or 6.3400) and (6.3700, 6.3800, or 18.05) Units: 3-0-9 Lecture: TR2.30-4 (56-154)
Covers communications by progressing through signal representation, sampling, quantization, compression, modulation, coding and decoding, medium access control, and queueing and principles of protocols. By providing simplified proofs, seeks to present an integrated, systems-level view of networking and communications while laying the foundations of analysis and design. Lectures are offered online; in-class time is dedicated to recitations, exercises, and weekly group labs. Homework exercises are based on theoretical derivation and software implementation. Students taking graduate version complete additional assignments. M. Medard No textbook information available 6.7420 Heterogeneous Networks: Architecture, Transport, Proctocols, and Management
()Not offered regularly; consult department Prereq: 6.1200 or 6.3700 Units: 4-0-8
Introduction to modern heterogeneous networks and the provision of heterogeneous services. Architectural principles, analysis, algorithmic techniques, performance analysis, and existing designs are developed and applied to understand current problems in network design and architecture. Begins with basic principles of networking. Emphasizes development of mathematical and algorithmic tools; applies them to understanding network layer design from the performance and scalability viewpoint. Concludes with network management and control, including the architecture and performance analysis of interconnected heterogeneous networks. Provides background and insight to understand current network literature and to perform research on networks with the aid of network design projects. V. W. S. Chan, R. G. Gallager 6.7430 Optical Networks
()Not offered regularly; consult department Prereq: 6.1200 or 6.3700 Units: 3-0-9
Introduces the fundamental and practical aspects of optical network technology, architecture, design and analysis tools and techniques. The treatment of optical networks are from the architecture and system design points of view. Optical hardware technologies are introduced and characterized as fundamental network building blocks on which optical transmission systems and network architectures are based. Beyond the Physical Layer, the higher network layers (Media Access Control, Network and Transport Layers) are treated together as integral parts of network design. Performance metrics, analysis and optimization techniques are developed to help guide the creation of high performance complex optical networks. Staff 6.7440 Principles of Wireless Communication
()Not offered regularly; consult department Prereq: 6.7410 Units: 3-0-9
Introduction to design, analysis, and fundamental limits of wireless transmission systems. Wireless channel and system models; fading and diversity; resource management and power control; multiple-antenna and MIMO systems; space-time codes and decoding algorithms; multiple-access techniques and multiuser detection; broadcast codes and precoding; cellular and ad-hoc network topologies; OFDM and ultrawideband systems; architectural issues. G. W. Wornell, L. Zheng 6.7450[J] Data-Communication Networks
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(Same subject as 16.37[J]) Prereq: 6.3700 or 18.204 Units: 3-0-9
Provides an introduction to data networks with an analytic perspective, using wireless networks, satellite networks, optical networks, the internet and data centers as primary applications. Presents basic tools for modeling and performance analysis. Draws upon concepts from stochastic processes, queuing theory, and optimization. E. Modiano 6.7460 Essential Coding Theory
()Not offered regularly; consult department Prereq: 6.1210 and 6.1400 Units: 3-0-9
Introduces the theory of error-correcting codes. Focuses on the essential results in the area, taught from first principles. Special focus on results of asymptotic or algorithmic significance. Principal topics include construction and existence results for error-correcting codes; limitations on the combinatorial performance of error-correcting codes; decoding algorithms; and applications to other areas of mathematics and computer science. Staff 6.7470 Information Theory
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Prereq: 6.3700 Units: 3-0-9 Credit cannot also be received for 6.7480
Mathematical definitions of information measures, convexity, continuity, and variational properties. Lossless source coding; variable-length and block compression; Slepian-Wolf theorem; ergodic sources and Shannon-McMillan theorem. Hypothesis testing, large deviations and I-projection. Fundamental limits of block coding for noisy channels: capacity, dispersion, finite blocklength bounds. Coding with feedback. Joint source-channel problem. Rate-distortion theory, vector quantizers. Advanced topics include Gelfand-Pinsker problem, multiple access channels, broadcast channels (depending on available time). M. Medard, L. Zheng 6.7480 Information Theory: From Coding to Learning
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Prereq: 6.3700, 6.3800, or 18.05 Units: 3-0-9 Credit cannot also be received for 6.7470
Introduces fundamentals of information theory and its applications to contemporary problems in statistics, machine learning, and computer science. A thorough study of information measures, including Fisher information, f-divergences, their convex duality, and variational characterizations. Covers information-theoretic treatment of inference, hypothesis testing and large deviations, universal compression, channel coding, lossy compression, and strong data-processing inequalities. Methods are applied to deriving PAC-Bayes bounds, GANs, and regret inequalities in machine learning, parametric and non-parametric estimation in statistics, communication complexity, and computation with noisy gates in computer science. Fast-paced journey through a recent textbook with the same title. For a communication-focused version, consider 6.7470. Staff Probability & Statistics6.3700 Introduction to Probability
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(Subject meets with 6.3702) Prereq: Calculus II (GIR) Units: 4-0-8 Credit cannot also be received for 18.600 Lecture: MW11-12.30 (54-100) Recitation: TR1 (E25-117) or TR2 (E25-117) +final
An introduction to probability theory, the modeling and analysis of probabilistic systems, and elements of statistical inference. Probabilistic models, conditional probability. Discrete and continuous random variables. Expectation and conditional expectation, and further topics about random variables. Limit Theorems. Bayesian estimation and hypothesis testing. Elements of classical statistical inference. Bernoulli and Poisson processes. Markov chains. Students taking graduate version complete additional assignments. M. Roozbehani No textbook information available 6.3702 Introduction to Probability
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(Subject meets with 6.3700) Prereq: Calculus II (GIR) Units: 4-0-8 Credit cannot also be received for 18.600 Lecture: MW11-12.30 (54-100) Recitation: TR1 (E25-117) or TR2 (E25-117) +final
An introduction to probability theory, the modeling and analysis of probabilistic systems, and elements of statistical inference. Probabilistic models, conditional probability. Discrete and continuous random variables. Expectation and conditional expectation, and further topics about random variables. Limit Theorems. Bayesian estimation and hypothesis testing. Elements of classical statistical inference. Bernoulli and Poisson processes. Markov chains. Students taking graduate version complete additional assignments. Fall: M. Roozbehani Spring: P. Golland No textbook information available 6.3720 Introduction to Statistical Data Analysis
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(Subject meets with 6.3722) Prereq: 6.100A and (6.3700, 6.3800, or 18.600) Units: 4-0-8
Introduction to the central concepts and methods of data science with an emphasis on statistical grounding and modern computational capabilities. Covers principles involved in extracting information from data for the purpose of making predictions or decisions, including data exploration, feature selection, model fitting, and performance assessment. Topics include learning of distributions, hypothesis testing (including multiple comparison procedures), linear and nonlinear regression and prediction, classification, time series, uncertainty quantification, model validation, causal inference, optimization, and decisions. Computational case studies and projects drawn from applications in finance, sports, engineering, and machine learning life sciences. Students taking graduate version complete additional assignments. Recommended prerequisite: 18.06. Staff 6.3722 Introduction to Statistical Data Analysis
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(Subject meets with 6.3720) Prereq: 6.100A and (6.3700, 6.3800, 18.600, or permission of instructor) Units: 4-0-8
Introduction to the central concepts and methods of data science with an emphasis on statistical grounding and modern computational capabilities. Covers principles involved in extracting information from data for the purpose of making predictions or decisions, including data exploration, feature selection, model fitting, and performance assessment. Topics include learning of distributions, hypothesis testing (including multiple comparison procedures), linear and nonlinear regression and prediction, classification, time series, uncertainty quantification, model validation, causal inference, optimization, and decisions. Computational case studies and projects drawn from applications in finance, sports, engineering, and machine learning life sciences. Students taking graduate version complete additional assignments. Recommended prerequisite: 18.06. Y. Polyanskiy, D. Shah 6.3730[J] Statistics, Computation and Applications
()Not offered regularly; consult department (Same subject as 2.092[J], IDS.012[J]) (Subject meets with 2.093[J], 6.3732[J], IDS.131[J]) Prereq: (6.100B, (18.03, 18.06, or 18.C06), and (6.3700, 6.3800, 14.30, 16.09, or 18.05)) or permission of instructor Units: 3-1-8
Hands-on analysis of data demonstrates the interplay between statistics and computation. Includes four modules, each centered on a specific data set, and introduced by a domain expert. Provides instruction in specific, relevant analysis methods and corresponding algorithmic aspects. Potential modules may include medical data, gene regulation, social networks, finance data (time series), traffic, transportation, weather forecasting, policy, or industrial web applications. Projects address a large-scale data analysis question. Students taking graduate version complete additional assignments. Enrollment limited; priority to Statistics and Data Science minors, and to juniors and seniors. Staff 6.3732[J] Statistics, Computation and Applications
()Not offered regularly; consult department (Same subject as 2.093[J], IDS.131[J]) (Subject meets with 2.092[J], 6.3730[J], IDS.012[J]) Prereq: (6.100B, (18.03, 18.06, or 18.C06), and (6.3700, 6.3800, 14.30, 16.09, or 18.05)) or permission of instructor Units: 3-1-8
Hands-on analysis of data demonstrates the interplay between statistics and computation. Includes four modules, each centered on a specific data set, and introduced by a domain expert. Provides instruction in specific, relevant analysis methods and corresponding algorithmic aspects. Potential modules may include medical data, gene regulation, social networks, finance data (time series), traffic, transportation, weather forecasting, policy, or industrial web applications. Projects address a large-scale data analysis question. Students taking graduate version complete additional assignments. Limited enrollment; priority to Statistics and Data Science minors and to juniors and seniors. Staff 6.7700[J] Fundamentals of Probability
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(Same subject as 15.085[J]) Prereq: Calculus II (GIR) Units: 4-0-8 Lecture: MW2.30-4 (45-230) Recitation: F1 (3-333) or F2 (3-333) +final
Introduction to probability theory. Probability spaces and measures. Discrete and continuous random variables. Conditioning and independence. Multivariate normal distribution. Abstract integration, expectation, and related convergence results. Moment generating and characteristic functions. Bernoulli and Poisson process. Finite-state Markov chains. Convergence notions and their relations. Limit theorems. Familiarity with elementary probability and real analysis is desirable. D. Gamarnik No textbook information available 6.7710 Discrete Stochastic Processes
()Not offered regularly; consult department Prereq: 6.3702 or 18.204 Units: 4-0-8
Review of probability and laws of large numbers; Poisson counting process and renewal processes; Markov chains (including Markov decision theory), branching processes, birth-death processes, and semi-Markov processes; continuous-time Markov chains and reversibility; random walks, martingales, and large deviations; applications from queueing, communication, control, and operations research. R. G. Gallager, V. W. S. Chan 6.7720[J] Discrete Probability and Stochastic Processes
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(Same subject as 15.070[J], 18.619[J]) Prereq: 6.3702, 6.7700, 18.100A, 18.100B, or 18.100Q Units: 3-0-9
Provides an introduction to tools used for probabilistic reasoning in the context of discrete systems and processes. Tools such as the probabilistic method, first and second moment method, martingales, concentration and correlation inequalities, theory of random graphs, weak convergence, random walks and Brownian motion, branching processes, Markov chains, Markov random fields, correlation decay method, isoperimetry, coupling, influences and other basic tools of modern research in probability will be presented. Algorithmic aspects and connections to statistics and machine learning will be emphasized. Staff 6.7730 Modern Mathematical Statistics
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Prereq: 18.100A, 18.C06, (6.3700 or 18.600), and (6.3720 or 18.650) Units: 3-0-9 Lecture: MW9.30-11 (45-102) +final
Presents mathematical statistics as a formal language for reasoning about data and uncertainty. Introduction to the basic framework of statistical decision theory, along with core concepts such as sufficiency, Bayes and minimax optimality of statistical procedures, with applications to optimal estimation, hypothesis testing, and prediction. Discussion topics include causality, multiple hypothesis testing, nonparametric and semiparametric statistics, and results for model misspecification. Targeted to students interested in statistical and machine learning research, with an emphasis on proofs and fundamental understanding. S. Bates No textbook information available 6.7740[J] Mathematical Statistics: a Non-Asymptotic Approach
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(Same subject as 9.521[J], 18.656[J], IDS.160[J]) Prereq: (6.7700, 18.06, and 18.6501) or permission of instructor Units: 3-0-9
Introduces students to modern non-asymptotic statistical analysis. Topics include high-dimensional models, nonparametric regression, covariance estimation, principal component analysis, oracle inequalities, prediction and margin analysis for classification. Develops a rigorous probabilistic toolkit, including tail bounds and a basic theory of empirical processes S. Rakhlin, M. Wainwright Inference6.3800 Introduction to Inference
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Prereq: Calculus II (GIR) or permission of instructor Units: 4-4-4 Lecture: MW10 (32-141) Lab: TBA Recitation: TR1 (2-105) or TR2 (2-105) +final
Introduces probabilistic modeling for problems of inference and machine learning from data, emphasizing analytical and computational aspects. Distributions, marginalization, conditioning, and structure, including graphical and neural network representations. Belief propagation, decision-making, classification, estimation, and prediction. Sampling methods and analysis. Introduces asymptotic analysis and information measures. Computational laboratory component explores the concepts introduced in class in the context of contemporary applications. Students design inference algorithms, investigate their behavior on real data, and discuss experimental results. G. Wornell No textbook information available 6.7800 Inference and Information
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Prereq: 6.3700, 6.3800, or 6.7700 Units: 4-0-8
Introduction to principles of Bayesian and non-Bayesian statistical inference and its information theoretic foundations. Hypothesis testing and parameter estimation, sufficient statistics, exponential families. Loss functions, information measures, model capacity, and information geometry. Variational inference and EM algorithm; MCMC and other Monte Carlo methods. Asymptotic analysis and large deviations theory; universal inference and learning. Selected topics such as representation learning, score-matching, diffusion, and nonparametric statistics. Staff 6.7810 Algorithms for Inference
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Prereq: 18.06 and (6.3700, 6.3800, or 6.7700) Units: 4-0-8 Lecture: TR9.30-11 (32-123) Recitation: F10 (32-155) +final
Introduction to computational aspects of statistical inference via probabilistic graphical models. Directed and undirected graphical models, and factor graphs, over discrete and Gaussian distributions; hidden Markov models, linear dynamical systems. Sum-product and junction tree algorithms; forward-backward algorithm, Kalman filtering and smoothing. Min-sum and Viterbi algorithms. Variational methods, mean-field theory, and loopy belief propagation. Sampling methods; Glauber dynamics and mixing time analysis. Parameter structure learning for graphical models; Baum-Welch and Chow-Liu algorithms. Selected topics such as causal inference, particle filtering, restricted Boltzmann machines, and graph neural networks. D. Shah No textbook information available 6.7820[J] Graphical Models: A Geometric, Algebraic, and Combinatorial Perspective
()Not offered regularly; consult department (Same subject as IDS.136[J]) Prereq: 6.3702 and 18.06 Units: 3-0-9
Provides instruction in the geometric, algebraic and combinatorial perspective on graphical models. Presents methods for learning the underlying graph and inferring its parameters. Topics include exponential families, duality theory, conic duality, polyhedral geometry, undirected graphical models, Bayesian networks, Markov properties, total positivity of distributions, hidden variables, and tensor decompositions. C. Uhler 6.7830 Bayesian Modeling and Inference
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Prereq: 6.7700 and 6.7900 Units: 3-0-9
Covers Bayesian modeling and inference at an advanced graduate level. Topics include de Finetti's theorem, decision theory, approximate inference (modern approaches and analysis of Monte Carlo, variational inference, etc.), hierarchical modeling, (continuous and discrete) nonparametric Bayesian approaches, sensitivity and robustness, and evaluation. Staff Machine Learning6.3900 Introduction to Machine Learning
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Prereq: (6.1000 or 6.1210) and (18.03 or 18.06) Units: 4-0-8 URL: https://introml.mit.edu/?from=registrar Lecture: M2.30-4 (10-250) Lab: W9.30-11 (34-501) or W11-12.30 (34-501) or W1-2.30 (34-501) or W2.30-4 (34-501) or W11-12.30 (32-044) or W1-2.30 (32-044) Recitation: R1-2.30 (32-044) or R2.30-4 (32-044) or F9.30-11 (32-044) or F11-12.30 (32-044) +final
Introduction to the principles and algorithms of machine learning from an optimization perspective. Topics include linear and non-linear models for supervised, unsupervised, and reinforcement learning, with a focus on gradient-based methods and neural-network architectures. Previous experience with algorithms may be helpful. S. Shen No textbook information available 6.3930 AI and Decision Making in Medicine: From Disease to Therapy
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| | | 6.10/6.50 | | | 6.20/6.60 | | | 6.30/6.70 | | | 6.40/6.80 | | | 6.90/6.ZZ | | | |
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