# Online Debiasing for Adaptively Collected High-dimensional Data with Applications to Time Series Analysis

arXiv: https://arxiv.org/abs/1911.01040 · HTML: https://mlsanity.com/paper/1911.01040/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2019.

## Built on by (most cited first, 13 of 13)

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- [Avoiding the Price of Adaptivity: Inference in Linear Contextual Bandits via Stability](https://mlsanity.com/paper/2512.20368/) (2025)
- [Entropy Regularization for Population Estimation](https://mlsanity.com/paper/2208.11747/) (2022)
- [A Model-free Closeness-of-influence Test for Features in Supervised Learning](https://mlsanity.com/paper/2306.11855/) (2023)
- [Adaptive debiased SGD in high-dimensional GLMs with streaming data](https://mlsanity.com/paper/2405.18284/) (2024)
- [Design-Based Bandits Under Network Interference: Trade-Off Between Regret and Statistical Inference](https://mlsanity.com/paper/2510.07646/) (2025)
- [Transfer Learning for High-dimensional Reduced Rank Time Series Models](https://mlsanity.com/paper/2504.15691/) (2025)

## Abstract (arXiv)

Adaptive collection of data is commonplace in applications throughout science and engineering. From the point of view of statistical inference however, adaptive data collection induces memory and correlation in the samples, and poses significant challenge. We consider the high-dimensional linear regression, where the samples are collected adaptively, and the sample size n can be smaller than p, the number of covariates. In this setting, there are two distinct sources of bias: the first due to regularization imposed for consistent estimation, e.g. using the LASSO, and the second due to adaptivity in collecting the samples. We propose "online debiasing", a general procedure for estimators such as the LASSO, which addresses both sources of bias. In two concrete contexts (i) time series analysis and (ii) batched data collection, we demonstrate that online debiasing optimally debiases the LASSO estimate when the underlying parameter θ0 has sparsity of order o(√n/log p). In this regime, the debiased estimator can be used to compute p-values and confidence intervals of optimal size.