SRLR

Name	SRLR JSON
Version	0.1.8 JSON
	download
home_page	https://github.com/statsle/SRLR_python
Summary	A package for sketched ridgeless estimator simulations, optimizing generalization. Identify the best sketching size to minimize out-of-sample risks. Stable risk curves in optimally sketched estimator eliminate peaks found in full-sample estimator. SRLR offers practical method to discover the ideal sketching size.
upload_time	2023-08-01 20:07:13
maintainer
docs_url	None
author	Siyue Yang
requires_python	>=3.6
license	MIT
keywords	python sketched ridgeless linear regression
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bugtrack_url
requirements	No requirements were recorded.
Travis-CI	No Travis.
coveralls test coverage	No coveralls.

            # SRLR

Sketched Ridgeless Linear Regression

## Description

This repository presents numerical simulations that analyze the empirical risks of the sketched ridgeless estimator, aiming to enhance generalization performance. The simulations focus on determining optimal sketching sizes that minimize out-of-sample prediction risks. The results reveal that the optimally sketched estimator exhibits stable risk curves, effectively eliminating the peaks observed in the full-sample estimator. Additionally, we introduce a practical procedure to empirically identify the optimal sketching size.

Suppose we observe data vectors  (x<sub>i</sub>,y<sub>i</sub>) that follow a linear model y<sub>i</sub>=x<sub>i</sub><sup>T</sup>&beta;<sup>*</sup>+&epsilon;<sub>i</sub>, i=1,...n, where y<sub>i</sub> is a univariate response,  x<sub>i</sub> is a d-dimensional predictor, &beta;<sup>*</sup> denotes the vector of regression coefficients, and &epsilon;<sub>i</sub> is a random error. We consider the ridgeless least square estimator β̂=(X<sup>T</sup>X)<sup>+</sup>X<sup>T</sup>Y.

With this package, the simulation results in [this paper](https://arxiv.org/abs/2302.01088) can be reporduced.

## Examples

Please refer to [tutorial.ipynb](https://github.com/statsle/SRLR_python/blob/main/tutorial.ipynb) for a comprehensive example and step-by-step guide.


## Reference

Chen, X., Zeng, Y., Yang, S. and Sun, Q. Sketched Ridgeless Linear Regression: The Role of Downsampling. [Paper](https://arxiv.org/abs/2302.01088)

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Siyue Yang