# Slow Kill for Big Data Learning

arXiv: https://arxiv.org/abs/2305.01726 · HTML: https://mlsanity.com/paper/2305.01726/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 51 references that are in the map.
- First posted on arXiv 2 May 2023.

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

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima](https://mlsanity.com/paper/1305.2436/) (2013)
- [On Iterative Hard Thresholding Methods for High-dimensional M-Estimation](https://mlsanity.com/paper/1410.5137/) (2014)
- [Between hard and soft thresholding: optimal iterative thresholding algorithms](https://mlsanity.com/paper/1804.08841/) (2018)
- [Optimal computational and statistical rates of convergence for sparse nonconvex learning problems](https://mlsanity.com/paper/1306.4960/) (2013)
- [Robust Reduced Rank Regression](https://mlsanity.com/paper/1509.03938/) (2015)
- [On Cross-validation for Sparse Reduced Rank Regression](https://mlsanity.com/paper/1812.11555/) (2018)
- [Pathwise Coordinate Optimization for Sparse Learning: Algorithm and Theory](https://mlsanity.com/paper/1412.7477/) (2014)
- [Picasso: A Sparse Learning Library for High Dimensional Data Analysis in R and Python](https://mlsanity.com/paper/2006.15261/) (2020)
- [Gaining Outlier Resistance with Progressive Quantiles: Fast Algorithms and Theoretical Studies](https://mlsanity.com/paper/2112.08471/) (2021)
- [Analysis of Generalized Bregman Surrogate Algorithms for Nonsmooth Nonconvex Statistical Learning](https://mlsanity.com/paper/2112.09191/) (2021)

## Built on by (most cited first, 2 of 2)

- [Mind the Jumps: A Scalable Robust Local Gaussian Process for Multidimensional Response Surfaces with Discontinuities](https://mlsanity.com/paper/2512.12574/) (2025)
- [High-dimensional online learning via asynchronous decomposition: Non-divergent results, dynamic regularization, and beyond](https://mlsanity.com/paper/2603.20696/) (2026)

## Abstract (arXiv)

Big-data applications often involve a vast number of observations and features, creating new challenges for variable selection and parameter estimation. This paper presents a novel technique called ``slow kill,'' which utilizes nonconvex constrained optimization, adaptive ℓ2-shrinkage, and increasing learning rates. The fact that the problem size can decrease during the slow kill iterations makes it particularly effective for large-scale variable screening. The interaction between statistics and optimization provides valuable insights into controlling quantiles, stepsize, and shrinkage parameters in order to relax the regularity conditions required to achieve the desired level of statistical accuracy. Experimental results on real and synthetic data show that slow kill outperforms state-of-the-art algorithms in various situations while being computationally efficient for large-scale data.