# Two-Stage Robust and Sparse Distributed Statistical Inference for Large-Scale Data

arXiv: https://arxiv.org/abs/2208.08230 · HTML: https://mlsanity.com/paper/2208.08230/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 56 references that are in the map.
- First posted on arXiv 17 Aug 2022.

## Builds on (most cited first, 11 of 11)

- [Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview](https://mlsanity.com/paper/1809.09573/) (2018)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [A significance test for the lasso](https://mlsanity.com/paper/1301.7161/) (2013)
- [Tuning parameter selection in high dimensional penalized likelihood](https://mlsanity.com/paper/1605.03321/) (2016)
- [A Bootstrap Lasso + Partial Ridge Method to Construct Confidence Intervals for Parameters in High-dimensional Sparse Linear Models](https://mlsanity.com/paper/1706.02150/) (2017)
- [Ultrahigh-dimensional Robust and Efficient Sparse Regression using Non-Concave Penalized Density Power Divergence](https://mlsanity.com/paper/1802.04906/) (2018)
- [The regularized tau estimator: A robust and efficient solution to ill-posed linear inverse problems](https://mlsanity.com/paper/1606.00812/) (2016)
- [Robust, scalable and fast bootstrap method for analyzing large scale data](https://mlsanity.com/paper/1504.02382/) (2015)
- [A robust variable screening procedure for ultra-high dimensional data](https://mlsanity.com/paper/2004.14851/) (2020)

## Built on by (most cited first, 1 of 1)

- [The Adaptive τ-Lasso: Robustness and Oracle Properties](https://mlsanity.com/paper/2304.09310/) (2023)

## Abstract (arXiv)

In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed processing and storage solutions. We propose a two-stage distributed and robust statistical inference procedures coping with high-dimensional models by promoting sparsity. In the first stage, known as model selection, relevant predictors are locally selected by applying robust Lasso estimators to the distinct subsets of data. The variable selections from each computation node are then fused by a voting scheme to find the sparse basis for the complete data set. It identifies the relevant variables in a robust manner. In the second stage, the developed statistically robust and computationally efficient bootstrap methods are employed. The actual inference constructs confidence intervals, finds parameter estimates and quantifies standard deviation. Similar to stage 1, the results of local inference are communicated to the fusion center and combined there. By using analytical methods, we establish the favorable statistical properties of the robust and computationally efficient bootstrap methods including consistency for a fixed number of predictors, and robustness. The proposed two-stage robust and distributed inference procedures demonstrate reliable performance and robustness in variable selection, finding confidence intervals and bootstrap approximations of standard deviations even when data is high-dimensional and contaminated by outliers.