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Course# MATH-685: Learning Theory of Nonparametric Regression

Summary

This course is intended to give a brief overview of how to prove consistency results in nonparametric regression. In particular, we will focus on least-square regression estimators. Some connections to the empirical risk minimization (ERM) problem will be discussed from time to time.

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Related concepts (23)

Consistency

In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic d

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number

Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by

Nonparametric regression

Nonparametric regression is a category of regression analysis in which the predictor does not take a predetermined form but is constructed according to information derived from the data. That is, no p

Density estimation

In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. Th