Lecture

Rademacher Complexity Control: Empirical Risk

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

MATH-412: Statistical machine learning

A course on statistical machine learning for supervised and unsupervised learning ...

Description

This lecture introduces the goals of statistical learning theory, presents an upper bound on the expected estimation error, defines Rademacher complexity, and discusses a lemma on empirical process control with Rademacher complexity. It also explores how to bound the expected estimation error using Rademacher complexity.

Instructor

Yoav Zemel

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (28)

Exchangeable random variables

In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear are altered. Thus, for example the sequences both have the same joint probability distribution. It is closely related to the use of independent and identically distributed random variables in statistical models.

Complex random variable

In probability theory and statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take are complex numbers. Complex random variables can always be considered as pairs of real random variables: their real and imaginary parts. Therefore, the distribution of one complex random variable may be interpreted as the joint distribution of two real random variables.

Convergence of random variables

In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied.

Multivariate random variable

In probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value. The individual variables in a random vector are grouped together because they are all part of a single mathematical system — often they represent different properties of an individual statistical unit.

Statistical inference

Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.

Related lectures (64)

Statistical Theory: Fundamentals

Covers the basics of statistical theory, including probability models, random variables, and sampling distributions.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Generalized Linear Models

Covers probability, random variables, expectation, GLMs, hypothesis testing, and Bayesian statistics with practical examples.

Probability and Statistics

Delves into probability, statistics, paradoxes, and random variables, showcasing their real-world applications and properties.

Law of Large Numbers: Strong Convergence