# Confidence Estimation via Sequential Likelihood Mixing

arXiv: https://arxiv.org/abs/2502.14689 · HTML: https://mlsanity.com/paper/2502.14689/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2025.

## Built on by (most cited first, 7 of 7)

- [Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update](https://mlsanity.com/paper/2507.11847/) (2025)
- [Confidence Sequences for Generalized Linear Models via Regret Analysis](https://mlsanity.com/paper/2504.16555/) (2025)
- [A variational approach to dimension-free self-normalized concentration](https://mlsanity.com/paper/2508.06483/) (2025)
- [Principled Confidence Estimation for Deep Computed Tomography](https://mlsanity.com/paper/2602.05812/) (2026)
- [A Jointly Efficient and Optimal Algorithm for Heteroskedastic Generalized Linear Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2602.10971/) (2026)
- [Best Arm Identification in Generalized Linear Bandits via Hybrid Feedback](https://mlsanity.com/paper/2605.05745/) (2026)
- [Beyond Modern Asymptotics for Log-Likelihood Ratios in Logistic Regression](https://mlsanity.com/paper/2608.02507/) (2026)

## Abstract (arXiv)

We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and establish fundamental connections between sequential mixing, Bayesian inference and regret inequalities from online estimation. The framework applies to any realizable family of likelihood functions and allows for non-i.i.d. data and anytime validity. Moreover, the framework seamlessly integrates standard approximate inference techniques, such as variational inference and sampling-based methods, and extends to misspecified model classes, while preserving provable coverage guarantees. We illustrate the power of the framework by deriving tighter confidence sequences for classical settings, including sequential linear regression and sparse estimation, with simplified proofs.