Work

Non-asymptotic oracle inequalities for the Lasso in high-dimensional mixture of experts

Year: 2026

Type: article

Abstract: We study Lasso estimation for high-dimensional softmax-gated Gaussian mixture-of-experts (SGMoE) regression models, where the predictor dimension P may exceed the sample size N . Under bounded parameters, we establish a non-asymptotic Kullback–Leibler (KL) oracle inequality with an explicit sufficient regularization level and explicit dependence on N , P , response dimension Q , number of experts K , and boundedness constants. We derive sparse well-specified and approximation-space rates, showing how deterministic SGMoE approximation error transfers into statistical KL-risk bounds. The theory extends to random covariates and, under misspecification, controls the best Gaussian SGMoE approximation in the candidate class. Reproducible experiments validate KL decay and density recovery, compare Lasso with SCAD when $$P>N$$ P > N , evaluate model-selection criteria, handle multivariate covariance structures, and assess high-dimensional biological benchmarks relevant to heterogeneous genotype–phenotype mapping, omics-to-trait prediction, and AI-enabled virtual-cell modelling in systems biology.

Source: Annals of the Institute of Statistical Mathematics

DOI: 10.1007/s10463-026-01007-5

Authors: TrungTin Nguyen, Hien D. Nguyen, Faicel Chamroukhi, Geoffrey J. McLachlan

Institutions: ARC Centre of Excellence for Mathematical and Statistical Frontiers, Kyushu University, La Trobe University, Institut de Recherche Technologique SystemX, The University of Queensland

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4296563174

FWCI:

Cites:

Cited by: 3

Related to: 10