Lecture

Statistical Inference for Bandit Data

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.

Description

This lecture covers statistical inference for bandit data, focusing on personalized treatment actions in sequential decision-making studies. It discusses contextual bandit problems, adaptive weighting in least squares, and the challenges of standard estimators on bandit data. The instructor presents simulations with continuous and binary rewards, confidence regions, and the role of adaptive weights. The lecture concludes with a discussion on model misspecification, causal inference, and regret minimization. The content is based on the paper 'Statistical Inference with M-Estimators on Adaptively Collected Data' by Kelly Wang Zhang, Lucas Janson, and Susan Murphy, presented at NeurIPS 2021.

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Related concepts (32)

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 minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.

Linear least squares

Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods. The three main linear least squares formulations are: Ordinary least squares (OLS) is the most common estimator.

Non-linear least squares

Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences.

Generalized least squares

In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model when there is a certain degree of correlation between the residuals in the regression model. Least squares and weighted least squares may need to be more statistically efficient and prevent misleading inferences. GLS was first described by Alexander Aitken in 1935. In standard linear regression models one observes data on n statistical units.

Ordinary least squares

In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable.

Related lectures (64)

Regression: Linear Models

Explores linear regression, least squares, residuals, and confidence intervals in regression models.

Linear Regression: Estimation and Inference

Explores linear regression estimation, linearity assumptions, and statistical tests in the context of model comparison.

Multilinear Regression: Basics and Applications

Covers the basics of multilinear regression and its application in analyzing material properties.

Linear Regression: Basics and Principle of Least Squares

Covers linear regression basics, focusing on minimizing error using the principle of least squares and includes an ANOVA table and practical example in R.

Multilinear Regression: Least Square Fit