Annals of the Institute of Statistical Mathematics· 2026Q2
Non-asymptotic oracle inequalities for the Lasso in high-dimensional mixture of experts
- 3citations
- Q2SCImago
- 2026year
Short summary
This paper establishes non-asymptotic oracle inequalities for Lasso estimation in high-dimensional softmax-gated Gaussian mixture-of-experts (SGMoE) regression models, even when predictor dimension P exceeds sample size N.
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Key points
- Establishes non-asymptotic KL oracle inequalities for Lasso in high-dimensional SGMoE regression (P > N).
- Provides explicit bounds dependent on N, P, Q, K, and boundedness constants.
- Derives sparse well-specified and approximation-space rates, linking approximation error to KL-risk.
- Extends theory to random covariates and controls approximation error under misspecification.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Annals of the Institute of Statistical Mathematics, 2026 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics