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).
Terms: not given this year, last offered Autumn 2018

Units: 3

Grading: Letter or Credit/No Credit
MATH 230A: Theory of Probability I (STATS 310A)
Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, BorelCantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites:
STATS 116,
MATH 171.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Montanari, A. (PI)
STATS 116: Theory of Probability
Probability spaces as models for phenomena with statistical regularity. Discrete spaces (binomial, hypergeometric, Poisson). Continuous spaces (normal, exponential) and densities. Random variables, expectation, independence, conditional probability. Introduction to the laws of large numbers and central limit theorem. Prerequisites:
MATH 52 and familiarity with infinite series, or equivalent.
Terms: Aut, Spr, Sum

Units: 4

UG Reqs: GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
STATS 116U: Theory of Probability
For Summer UG Visitors only. Same as
Stats 116. This course is offered remotely only via video segments. TAs will host remote weekly office hours using an online platform such as Zoom.
Terms: Sum

Units: 4

Grading: Letter or Credit/No Credit
Instructors:
Kaluwa Devage, P. (PI)
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).
Terms: not given this year, last offered Autumn 2018

Units: 3

Grading: Letter or Credit/No Credit
STATS 300A: Theory of Statistics I
Finite sample optimality of statistical procedures; Decision theory: loss, risk, admissibility; Principles of data reduction: sufficiency, ancillarity, completeness; Statistical models: exponential families, group families, nonparametric families; Point estimation: optimal unbiased and equivariant estimation, Bayes estimation, minimax estimation; Hypothesis testing and confidence intervals: uniformly most powerful tests, uniformly most accurate confidence intervals, optimal unbiased and invariant tests. Prerequisites: Real analysis, introductory probability (at the level of
STATS 116), and introductory statistics.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
STATS 310A: Theory of Probability I (MATH 230A)
Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, BorelCantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites:
STATS 116,
MATH 171.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Montanari, A. (PI)
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