# Variations on the Expectation due to Changes in the Probability Measure

arXiv: https://arxiv.org/abs/2502.02887 · HTML: https://mlsanity.com/paper/2502.02887/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 43 references that are in the map.
- First posted on arXiv 5 Feb 2025.

## Builds on (most cited first, 16 of 16)

- [On the properties of variational approximations of Gibbs posteriors](https://mlsanity.com/paper/1506.04091/) (2015)
- [Distributionally Robust Optimization: A Review](https://mlsanity.com/paper/1908.05659/) (2019)
- [Generalization Bounds: Perspectives from Information Theory and PAC-Bayes](https://mlsanity.com/paper/2309.04381/) (2023)
- [Optimal Bounds between f-Divergences and Integral Probability Metrics](https://mlsanity.com/paper/2006.05973/) (2020)
- [What is the long-run distribution of stochastic gradient descent? A large deviations analysis](https://mlsanity.com/paper/2406.09241/) (2024)
- [Characterizing and Understanding the Generalization Error of Transfer Learning with Gibbs Algorithm](https://mlsanity.com/paper/2111.01635/) (2021)
- [Empirical Risk Minimization with Relative Entropy Regularization](https://mlsanity.com/paper/2211.06617/) (2022)
- [Flow-based Distributionally Robust Optimization](https://mlsanity.com/paper/2310.19253/) (2023)
- [On the Validation of Gibbs Algorithms: Training Datasets, Test Datasets and their Aggregation](https://mlsanity.com/paper/2306.12380/) (2023)
- [Tackling Virtual and Real Concept Drifts: An Adaptive Gaussian Mixture Model](https://mlsanity.com/paper/2102.05983/) (2021)
- [Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysis](https://mlsanity.com/paper/2202.04385/) (2022)
- [Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure](https://mlsanity.com/paper/2312.12236/) (2023)
- [How Does Pseudo-Labeling Affect the Generalization Error of the Semi-Supervised Gibbs Algorithm?](https://mlsanity.com/paper/2210.08188/) (2022)
- [The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithms](https://mlsanity.com/paper/2411.12030/) (2024)
- [Proofs for Folklore Theorems on the Radon-Nikodym Derivative](https://mlsanity.com/paper/2501.18374/) (2025)
- [An Information-Theoretic Framework for Out-of-Distribution Generalization with Applications to Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2403.19895/) (2024)

## Built on by (most cited first, 3 of 3)

- [Decentralized Machine Learning with Centralized Performance Guarantees via Gibbs Algorithms](https://mlsanity.com/paper/2604.20492/) (2026)
- [Equivalence Between Nested Gibbs Measures and Log-Linear Combinations of Gibbs Measures](https://mlsanity.com/paper/2609.19988/) (2026)
- [Machine Unlearning for Gibbs Supervised Learning Algorithms](https://mlsanity.com/paper/2609.29409/) (2026)

## Abstract (arXiv)

In this paper, closed-form expressions are presented for the variation of the expectation of a given function due to changes in the probability measure used for the expectation. They unveil interesting connections with Gibbs probability measures, mutual information, and lautum information.