Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Towards Bayesian Data Selection

Julian Rodemann

TL;DR

The paper addresses distribution shifts induced by reciprocal learning, where iterative data augmentation affects the training distribution. It proposes a Bayesian decision-theoretic framework for data selection, deriving a Bayes-optimal criterion and instantiating it with Bayesian Pseudo-Label Selection (BPLS) for self-training. The key contribution is linking data selection to the posterior predictive of augmented data via the pseudo-label likelihood, with a Laplace-based computable approximation that works beyond i.i.d. assumptions and across models such as generalized linear, semi-parametric GAMs, and Bayesian neural networks, mitigating confirmation bias without hyperparameter tuning. It further shows that the resulting inclusion probabilities enable principled importance sampling for debiasing and outlines extensions to multi-objective utilities and broader reciprocal learning, highlighting practical implications for robust data-efficiency and uncertainty quantification under distribution shift.

Abstract

A wide range of machine learning algorithms iteratively add data to the training sample. Examples include semi-supervised learning, active learning, multi-armed bandits, and Bayesian optimization. We embed this kind of data addition into decision theory by framing data selection as a decision problem. This paves the way for finding Bayes-optimal selections of data. For the illustrative case of self-training in semi-supervised learning, we derive the respective Bayes criterion. We further show that deploying this criterion mitigates the issue of confirmation bias by empirically assessing our method for generalized linear models, semi-parametric generalized additive models, and Bayesian neural networks on simulated and real-world data.

Towards Bayesian Data Selection

TL;DR

The paper addresses distribution shifts induced by reciprocal learning, where iterative data augmentation affects the training distribution. It proposes a Bayesian decision-theoretic framework for data selection, deriving a Bayes-optimal criterion and instantiating it with Bayesian Pseudo-Label Selection (BPLS) for self-training. The key contribution is linking data selection to the posterior predictive of augmented data via the pseudo-label likelihood, with a Laplace-based computable approximation that works beyond i.i.d. assumptions and across models such as generalized linear, semi-parametric GAMs, and Bayesian neural networks, mitigating confirmation bias without hyperparameter tuning. It further shows that the resulting inclusion probabilities enable principled importance sampling for debiasing and outlines extensions to multi-objective utilities and broader reciprocal learning, highlighting practical implications for robust data-efficiency and uncertainty quantification under distribution shift.

Abstract

A wide range of machine learning algorithms iteratively add data to the training sample. Examples include semi-supervised learning, active learning, multi-armed bandits, and Bayesian optimization. We embed this kind of data addition into decision theory by framing data selection as a decision problem. This paves the way for finding Bayes-optimal selections of data. For the illustrative case of self-training in semi-supervised learning, we derive the respective Bayes criterion. We further show that deploying this criterion mitigates the issue of confirmation bias by empirically assessing our method for generalized linear models, semi-parametric generalized additive models, and Bayesian neural networks on simulated and real-world data.
Paper Structure (4 sections, 1 theorem, 3 equations, 1 algorithm)

This paper contains 4 sections, 1 theorem, 3 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Selecting Data is a Decision Problem
  3. Example: Bayesian PLeaSe! Bayesian Pseudo-Label Selection (PLS)
  4. Outlook: Decision Criteria Allow Importance Sampling

Key Result

Theorem 3

In the decision problem $(\mathbb{A}_{\mathcal{U}}, \Theta, u(\cdot))$ and the pseudo-label likelihood as utility function (definition def:pseud-lik) and the prior updated by the posterior $\pi(\theta) = p(\theta \mid \mathcal{D})$ on $\Theta$, the Bayes criterion $\Phi(\cdot, \pi) \colon \mathcal{U

Theorems & Definitions (3)

  • Definition 1: Canonical Decision Problem
  • Definition 2: Pseudo-Label Likelihood as Utility
  • Theorem 3: Pseudo Posterior Predictive rodemann2023-bpls