LassoBench: A High-Dimensional Hyperparameter Optimization Benchmark Suite for Lasso

TL;DR

LassoBench introduces a comprehensive benchmark suite for high-dimensional hyperparameter optimization in Weighted Lasso regression, facilitating the evaluation and development of HPO methods in complex, real-world high-dimensional problems.

Contribution

It provides the first dedicated benchmark suite for high-dimensional Weighted Lasso, enabling systematic testing of HPO algorithms on synthetic and real datasets.

Findings

Bayesian optimization and evolutionary strategies outperform traditional methods.

Limitations of current HPO methods are highlighted in very high-dimensional noisy settings.

Benchmark suite supports diverse experimental setups for Lasso hyperparameter tuning.

Abstract

While Weighted Lasso sparse regression has appealing statistical guarantees that would entail a major real-world impact in finance, genomics, and brain imaging applications, it is typically scarcely adopted due to its complex high-dimensional space composed by thousands of hyperparameters. On the other hand, the latest progress with high-dimensional hyperparameter optimization (HD-HPO) methods for black-box functions demonstrates that high-dimensional applications can indeed be efficiently optimized. Despite this initial success, HD-HPO approaches are mostly applied to synthetic problems with a moderate number of dimensions, which limits its impact in scientific and engineering applications. We propose LassoBench, the first benchmark suite tailored for Weighted Lasso regression. LassoBench consists of benchmarks for both well-controlled synthetic setups (number of samples, noise level, ambient and effective dimensionalities, and multiple fidelities) and real-world datasets, which enables the use of many flavors of HPO algorithms to be studied and extended to the high-dimensional Lasso setting. We evaluate 6 state-of-the-art HPO methods and 3 Lasso baselines, and demonstrate that Bayesian optimization and evolutionary strategies can improve over the methods commonly used for sparse regression while highlighting limitations of these frameworks in very high-dimensional and noisy settings.