# From Predictions to Decisions: The Importance of Joint Predictive Distributions

arXiv: https://arxiv.org/abs/2107.09224 · HTML: https://mlsanity.com/paper/2107.09224/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 20 Jul 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [An Information-Theoretic Analysis of Thompson Sampling](https://mlsanity.com/paper/1403.5341/) (2014)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [Learning to Optimize via Information-Directed Sampling](https://mlsanity.com/paper/1403.5556/) (2014)
- [Ensemble Sampling](https://mlsanity.com/paper/1705.07347/) (2017)
- [Reinforcement Learning, Bit by Bit](https://mlsanity.com/paper/2103.04047/) (2021)
- [Bootstrapped Thompson Sampling and Deep Exploration](https://mlsanity.com/paper/1507.00300/) (2015)
- [Beyond Marginal Uncertainty: How Accurately can Bayesian Regression Models Estimate Posterior Predictive Correlations?](https://mlsanity.com/paper/2011.03178/) (2020)
- [Thompson Sampling with Approximate Inference](https://mlsanity.com/paper/1908.04970/) (2019)
- [Scalable Thompson Sampling via Optimal Transport](https://mlsanity.com/paper/1902.07239/) (2019)

## Built on by (most cited first, 29 of 29)

- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [Bayesian Model Selection, the Marginal Likelihood, and Generalization](https://mlsanity.com/paper/2202.11678/) (2022)
- [Rethinking Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2412.20892/) (2024)
- [Approximate Thompson Sampling via Epistemic Neural Networks](https://mlsanity.com/paper/2302.09205/) (2023)
- [An Analysis of Ensemble Sampling](https://mlsanity.com/paper/2203.01303/) (2022)
- [The Neural Testbed: Evaluating Joint Predictions](https://mlsanity.com/paper/2110.04629/) (2021)
- [Fine-Tuning Language Models via Epistemic Neural Networks](https://mlsanity.com/paper/2211.01568/) (2022)
- [Non-Stationary Bandit Learning via Predictive Sampling](https://mlsanity.com/paper/2205.01970/) (2022)
- [Ensembles for Uncertainty Estimation: Benefits of Prior Functions and Bootstrapping](https://mlsanity.com/paper/2206.03633/) (2022)
- [Experts Don't Cheat: Learning What You Don't Know By Predicting Pairs](https://mlsanity.com/paper/2402.08733/) (2024)
- [On Subjective Uncertainty Quantification and Calibration in Natural Language Generation](https://mlsanity.com/paper/2406.05213/) (2024)
- [(Implicit) Ensembles of Ensembles: Epistemic Uncertainty Collapse in Large Models](https://mlsanity.com/paper/2409.02628/) (2024)
- [Evaluating High-Order Predictive Distributions in Deep Learning](https://mlsanity.com/paper/2202.13509/) (2022)
- [Promises and Pitfalls of the Linearized Laplace in Bayesian Optimization](https://mlsanity.com/paper/2304.08309/) (2023)
- [Provable Uncertainty Decomposition via Higher-Order Calibration](https://mlsanity.com/paper/2412.18808/) (2024)
- [Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions](https://mlsanity.com/paper/2401.04305/) (2024)
- [Adaptive Elicitation of Latent Information Using Natural Language](https://mlsanity.com/paper/2504.04204/) (2025)
- [Contextual Thompson Sampling via Generation of Missing Data](https://mlsanity.com/paper/2502.07064/) (2025)
- [Efficiently Generating Correlated Sample Paths from Multi-step Time Series Foundation Models](https://mlsanity.com/paper/2510.02224/) (2025)
- [Marginal and Joint Cross-Entropies & Predictives for Online Bayesian Inference, Active Learning, and Active Sampling](https://mlsanity.com/paper/2205.08766/) (2022)
- [Information-theoretic Analysis of Test Data Sensitivity in Uncertainty](https://mlsanity.com/paper/2307.12456/) (2023)
- [Architectural and Inferential Inductive Biases For Exchangeable Sequence Modeling](https://mlsanity.com/paper/2503.01215/) (2025)
- [SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty](https://mlsanity.com/paper/2505.13501/) (2025)
- [PICProp: Physics-Informed Confidence Propagation for Uncertainty Quantification](https://mlsanity.com/paper/2310.06923/) (2023)
- [Improved Exploration in GFlownets via Enhanced Epistemic Neural Networks](https://mlsanity.com/paper/2506.16313/) (2025)
- [Robustness of Epinets against Distributional Shifts](https://mlsanity.com/paper/2207.00137/) (2022)
- [Prediction-Oriented Subsampling from Data Streams](https://mlsanity.com/paper/2508.03868/) (2025)
- [In-Context Learning for Data-Driven Censored Inventory Control](https://mlsanity.com/paper/2605.14840/) (2026)

## Abstract (arXiv)

A fundamental challenge for any intelligent system is prediction: given some inputs, can you predict corresponding outcomes? Most work on supervised learning has focused on producing accurate marginal predictions for each input. However, we show that for a broad class of decision problems, accurate joint predictions are required to deliver good performance. In particular, we establish several results pertaining to combinatorial decision problems, sequential predictions, and multi-armed bandits to elucidate the essential role of joint predictive distributions. Our treatment of multi-armed bandits introduces an approximate Thompson sampling algorithm and analytic techniques that lead to a new kind of regret bound.