# Large Deviation Methods for Approximate Probabilistic Inference

arXiv: https://arxiv.org/abs/1301.7392 · HTML: https://mlsanity.com/paper/1301.7392/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2013.

## Built on by (most cited first, 12 of 12)

- [Bregman Deviations of Generic Exponential Families](https://mlsanity.com/paper/2201.07306/) (2022)
- [DARE the Extreme: Revisiting Delta-Parameter Pruning For Fine-Tuned Models](https://mlsanity.com/paper/2410.09344/) (2024)
- [Time-uniform confidence bands for the CDF under nonstationarity](https://mlsanity.com/paper/2302.14248/) (2023)
- [SignSGD with Federated Voting](https://mlsanity.com/paper/2403.16372/) (2024)
- [Private Estimation when Data and Privacy Demands are Correlated](https://mlsanity.com/paper/2407.11274/) (2024)
- [Tight Non-asymptotic Inference via Sub-Gaussian Intrinsic Moment Norm](https://mlsanity.com/paper/2303.07287/) (2023)
- [SignSGD with Federated Defense: Harnessing Adversarial Attacks through Gradient Sign Decoding](https://mlsanity.com/paper/2402.01340/) (2024)
- [Unsupervised Opinion Aggregation -- A Statistical Perspective](https://mlsanity.com/paper/2308.10386/) (2023)
- [How to Shrink Confidence Sets for Many Equivalent Discrete Distributions?](https://mlsanity.com/paper/2407.15662/) (2024)
- [Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order](https://mlsanity.com/paper/2604.26819/) (2026)
- [Formal Concept Lattices are Good Semantic Scaffolds for Concept-Based Learning](https://mlsanity.com/paper/2606.05471/) (2026)
- [Tight Information Complexity of the Coin Problem in the Broadcast Model](https://mlsanity.com/paper/2608.02776/) (2026)

## Abstract (arXiv)

We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is intractable, we show how to compute upper and lower bounds on many probabilities of interest. In particular, using methods from large deviation theory, we derive rigorous bounds on marginal probabilities such as Pr[children] and prove rates of convergence for the accuracy of our bounds as a function of network size. Our results apply to networks with generic transfer function parameterizations of the conditional probability tables, such as sigmoid and noisy-OR. They also explicitly illustrate the types of averaging behavior that can simplify the problem of inference in large networks.