# Accurate Inference for Adaptive Linear Models

arXiv: https://arxiv.org/abs/1712.06695 · HTML: https://mlsanity.com/paper/1712.06695/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2017.

## Built on by (most cited first, 30 of 39)

- [Statistical Inference with M-Estimators on Adaptively Collected Data](https://mlsanity.com/paper/2104.14074/) (2021)
- [Deeply-Debiased Off-Policy Interval Estimation](https://mlsanity.com/paper/2105.04646/) (2021)
- [A Closer Look at the Worst-case Behavior of Multi-armed Bandit Algorithms](https://mlsanity.com/paper/2106.02126/) (2021)
- [Near-optimal inference in adaptive linear regression](https://mlsanity.com/paper/2107.02266/) (2021)
- [UCB algorithms for multi-armed bandits: Precise regret and adaptive inference](https://mlsanity.com/paper/2412.06126/) (2024)
- [Metalearning Linear Bandits by Prior Update](https://mlsanity.com/paper/2107.05320/) (2021)
- [Inference with the Upper Confidence Bound Algorithm](https://mlsanity.com/paper/2408.04595/) (2024)
- [From Finite to Countable-Armed Bandits](https://mlsanity.com/paper/2105.10721/) (2021)
- [Synthetically Controlled Bandits](https://mlsanity.com/paper/2202.07079/) (2022)
- [Online Statistical Inference for Contextual Bandits via Stochastic Gradient Descent](https://mlsanity.com/paper/2212.14883/) (2022)
- [Linear Contextual Bandits with Interference](https://mlsanity.com/paper/2409.15682/) (2024)
- [Stable Thompson Sampling: Valid Inference via Variance Inflation](https://mlsanity.com/paper/2505.23260/) (2025)
- [Efficient Inference Without Trading-off Regret in Bandits: An Allocation Probability Test for Thompson Sampling](https://mlsanity.com/paper/2111.00137/) (2021)
- [Semi-parametric inference based on adaptively collected data](https://mlsanity.com/paper/2303.02534/) (2023)
- [Contextual Online Uncertainty-Aware Preference Learning for Human Feedback](https://mlsanity.com/paper/2504.19342/) (2025)
- [Challenges in Statistical Analysis of Data Collected by a Bandit Algorithm: An Empirical Exploration in Applications to Adaptively Randomized Experiments](https://mlsanity.com/paper/2103.12198/) (2021)
- [Adaptive Linear Estimating Equations](https://mlsanity.com/paper/2307.07320/) (2023)
- [reBandit: Random Effects based Online RL algorithm for Reducing Cannabis Use](https://mlsanity.com/paper/2402.17739/) (2024)
- [Adaptive Data Debiasing through Bounded Exploration](https://mlsanity.com/paper/2110.13054/) (2021)
- [Adaptive Principal Component Regression with Applications to Panel Data](https://mlsanity.com/paper/2307.01357/) (2023)
- [Reinforcement Learning in the Real World: A Survey of Statistical Challenges and Future Directions](https://mlsanity.com/paper/2601.15353/) (2026)
- [Doubly Robust Interval Estimation for Optimal Policy Evaluation in Online Learning](https://mlsanity.com/paper/2110.15501/) (2021)
- [Online Estimation and Inference for Robust Policy Evaluation in Reinforcement Learning](https://mlsanity.com/paper/2310.02581/) (2023)
- [Best of Three Worlds: Adaptive Experimentation for Digital Marketing in Practice](https://mlsanity.com/paper/2402.10870/) (2024)
- [Adaptive Off-Policy Inference for M-Estimators Under Model Misspecification](https://mlsanity.com/paper/2509.14218/) (2025)
- [Debiasing Samples from Online Learning Using Bootstrap](https://mlsanity.com/paper/2108.00236/) (2021)
- [Statistical Limits of Adaptive Linear Models: Low-Dimensional Estimation and Inference](https://mlsanity.com/paper/2310.00532/) (2023)
- [Replicability is Asymptotically Free in Multi-armed Bandits](https://mlsanity.com/paper/2402.07391/) (2024)
- [Oralytics Reinforcement Learning Algorithm](https://mlsanity.com/paper/2406.13127/) (2024)
- [MiWaves Reinforcement Learning Algorithm](https://mlsanity.com/paper/2408.15076/) (2024)

## Abstract (arXiv)

Estimators computed from adaptively collected data do not behave like their non-adaptive brethren. Rather, the sequential dependence of the collection policy can lead to severe distributional biases that persist even in the infinite data limit. We develop a general method -- W-decorrelation -- for transforming the bias of adaptive linear regression estimators into variance. The method uses only coarse-grained information about the data collection policy and does not need access to propensity scores or exact knowledge of the policy. We bound the finite-sample bias and variance of the W-estimator and develop asymptotically correct confidence intervals based on a novel martingale central limit theorem. We then demonstrate the empirical benefits of the generic W-decorrelation procedure in two different adaptive data settings: the multi-armed bandit and the autoregressive time series.