## CS 229T: Statistical Learning Theory (STATS 231)

How do we formalize what it means for an algorithm to learn from data? How do we use mathematical thinking to design better machine learning methods? This course focuses on developing mathematical tools for answering these questions. We will present various learning algorithms and prove theoretical guarantees about them. Topics include generalization bounds, implicit regularization, the theory of deep learning, spectral methods, and online learning and bandits problems. Prerequisites: A solid background in linear algebra (
Math 104,
Math 113 or
CS205) and probability theory (CS109 or STAT 116), statistics and machine learning (
STATS 315A,
CS 229 or
STATS 216).

Last offered: Autumn 2018

## CS 325B: Data for Sustainable Development (EARTHSYS 162, EARTHSYS 262)

The sustainable development goals (SDGs) encompass many important aspects of human and ecosystem well-being that are traditionally difficult to measure. This project-based course will focus on ways to use inexpensive, unconventional data streams to measure outcomes relevant to SDGs, including poverty, hunger, health, governance, and economic activity. Students will apply machine learning techniques to various projects outlined at the beginning of the quarter. The main learning goals are to gain experience conducting and communicating original research. Prior knowledge of machine learning techniques, such as from
CS 221,
CS 229,
CS 231N,
STATS 202, or
STATS 216 is required. Open to both undergraduate and graduate students. Enrollment limited to 24. Students must apply for the class by filling out the form at
https://goo.gl/forms/9LSZF7lPkHadix5D3. A permission code will be given to admitted students to register for the class.

Terms: Aut
| Units: 3-5
| Repeatable for credit

## EARTHSYS 162: Data for Sustainable Development (CS 325B, EARTHSYS 262)

The sustainable development goals (SDGs) encompass many important aspects of human and ecosystem well-being that are traditionally difficult to measure. This project-based course will focus on ways to use inexpensive, unconventional data streams to measure outcomes relevant to SDGs, including poverty, hunger, health, governance, and economic activity. Students will apply machine learning techniques to various projects outlined at the beginning of the quarter. The main learning goals are to gain experience conducting and communicating original research. Prior knowledge of machine learning techniques, such as from
CS 221,
CS 229,
CS 231N,
STATS 202, or
STATS 216 is required. Open to both undergraduate and graduate students. Enrollment limited to 24. Students must apply for the class by filling out the form at
https://goo.gl/forms/9LSZF7lPkHadix5D3. A permission code will be given to admitted students to register for the class.

Terms: Aut
| Units: 3-5
| Repeatable for credit

## EARTHSYS 262: Data for Sustainable Development (CS 325B, EARTHSYS 162)

The sustainable development goals (SDGs) encompass many important aspects of human and ecosystem well-being that are traditionally difficult to measure. This project-based course will focus on ways to use inexpensive, unconventional data streams to measure outcomes relevant to SDGs, including poverty, hunger, health, governance, and economic activity. Students will apply machine learning techniques to various projects outlined at the beginning of the quarter. The main learning goals are to gain experience conducting and communicating original research. Prior knowledge of machine learning techniques, such as from
CS 221,
CS 229,
CS 231N,
STATS 202, or
STATS 216 is required. Open to both undergraduate and graduate students. Enrollment limited to 24. Students must apply for the class by filling out the form at
https://goo.gl/forms/9LSZF7lPkHadix5D3. A permission code will be given to admitted students to register for the class.

Terms: Aut
| Units: 3-5
| Repeatable for credit

## MATH 51: Linear Algebra, Multivariable Calculus, and Modern Applications

This course provides unified coverage of linear algebra and multivariable differential calculus. It discusses applications connecting the material to many quantitative fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion of the course includes orthogonality, linear independence, matrix algebra, and eigenvalues as well as ubiquitious applications: least squares, linear regression, Markov chains (relevant to population dynamics, molecular chemistry, and PageRank), singular value decomposition (essential in image compression, topic modeling, and data-intensive work in the natural sciences), and more. The multivariable calculus material includes unconstrained optimization via gradients and Hessians (used for energy minimization in physics and chemistry), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underl
more »

This course provides unified coverage of linear algebra and multivariable differential calculus. It discusses applications connecting the material to many quantitative fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion of the course includes orthogonality, linear independence, matrix algebra, and eigenvalues as well as ubiquitious applications: least squares, linear regression, Markov chains (relevant to population dynamics, molecular chemistry, and PageRank), singular value decomposition (essential in image compression, topic modeling, and data-intensive work in the natural sciences), and more. The multivariable calculus material includes unconstrained optimization via gradients and Hessians (used for energy minimization in physics and chemistry), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underlie many machine learning algorithms, such as backpropagation), and Newton's method (a crucial part of how GPS works). The course emphasizes computations alongside an intuitive understanding of key ideas, making students well-prepared for further study of mathematics and its applications to other fields. The widespread use of computers makes it more important, not less, for users of math to understand concepts: in all scientific fields, novel users of quantitative tools in the future will be those who understand ideas and how they fit with applications and examples. This is the only course at Stanford whose syllabus includes nearly all the math background for
CS 229, which is why
CS 229 and
CS 230 specifically recommend it (or other courses resting on it). For frequently asked questions about the differences between
Math 51 and
CME 100, see the FAQ on the placement page on the math department website. Prerequisite: 21, 42, or the math placement diagnostic (offered through the Math Department website) in order to register for this course.

Terms: Aut, Win, Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Cant, D. (PI)
;
Chetard, B. (PI)
;
Dore, D. (PI)
;
Helfer, J. (PI)
;
Izzo, Z. (PI)
;
Lucianovic, M. (PI)
;
Perlman, M. (PI)
;
Sloman, L. (PI)
;
Taylor, C. (PI)
;
Trettel, S. (PI)
;
White, B. (PI)
;
Wieczorek, W. (PI)
;
Ying, L. (PI)
;
Arana Herrera, F. (TA)
;
Cant, D. (TA)
;
Helfer, J. (TA)
;
Izzo, Z. (TA)
;
Libkind, S. (TA)
;
Sloman, L. (TA)

## STATS 229: Machine Learning (CS 229)

Topics: statistical pattern recognition, linear and non-linear regression, non-parametric methods, exponential family, GLMs, support vector machines, kernel methods, deep learning, model/feature selection, learning theory, ML advice, clustering, density estimation, EM, dimensionality reduction, ICA, PCA, reinforcement learning and adaptive control, Markov decision processes, approximate dynamic programming, and policy search. Prerequisites: knowledge of basic computer science principles and skills at a level sufficient to write a reasonably non-trivial computer program in Python/numpy, familiarity with probability theory to the equivalency of CS109 or
STATS116, and familiarity with multivariable calculus and linear algebra to the equivalency of
MATH51.

Terms: Aut, Spr
| Units: 3-4

Instructors:
Charikar, M. (PI)
;
Ma, T. (PI)
;
Ng, A. (PI)
;
Re, C. (PI)
;
Avati, A. (TA)
;
Chen, E. (TA)
;
Ding, T. (TA)
;
Jia, Z. (TA)
;
Jin, Y. (TA)
;
Khosla, K. (TA)
;
Kurenkov, A. (TA)
;
Li, J. (TA)
;
Mehr, L. (TA)
;
She, J. (TA)
;
Steinberg, E. (TA)
;
Tlili, F. (TA)
;
Xiong, Z. (TA)
;
Yang, J. (TA)
;
Zhang, K. (TA)
;
Zhang, V. (TA)

## STATS 231: Statistical Learning Theory (CS 229T)

How do we formalize what it means for an algorithm to learn from data? How do we use mathematical thinking to design better machine learning methods? This course focuses on developing mathematical tools for answering these questions. We will present various learning algorithms and prove theoretical guarantees about them. Topics include generalization bounds, implicit regularization, the theory of deep learning, spectral methods, and online learning and bandits problems. Prerequisites: A solid background in linear algebra (
Math 104,
Math 113 or
CS205) and probability theory (CS109 or STAT 116), statistics and machine learning (
STATS 315A,
CS 229 or
STATS 216).

Last offered: Autumn 2018

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