arXiv subjects

Ziwen Gao

Publications and source records attributed to Ziwen Gao.

3 recordsLinked to original sources

arXiv2026

Towards a Statistical Understanding of Mixture-of-Experts

Mixture-of-experts (MoE) architectures increase model capacity by combining a collection of expert predictors through input-dependent routing, while often activating only a small subset of experts for each input. Despite their growing importance in modern large-scale models, the statistical roles of their design choices, especially routing, sparse activation, and shared experts, remain only partially understood, as existing theory has largely focused on parametric or correctly specified MoE models. In this paper, we view MoE as a form of localized aggregation and show how this localization reshapes the approximation-estimation-computation tradeoff. We derive oracle risk bounds for learning dense and sparse routing with evolving experts, separating approximation, expert-learning, and router-estimation errors, and characterize how sparse Top-K routing can retain the benefits of localized aggregation while controlling per-input computation. We also interpret gating through the geometry of input space, relating routing performance to regions of local expert advantage, and show how shared experts, as adopted in architectures such as DeepSeekMoE, can extract common predictive structure so that routed experts focus on residual local variation. Together, these results provide a unified statistical framework for understanding MoE through input-dependent expert aggregation, in which expert specialization and computational tradeoffs are governed by local predictive structure.

stat.ML↗

arXiv2026

Combining pre-trained models via localized model averaging

Many pre-trained models (PTMs) are available in modern applications. Because different PTMs are often trained on different datasets, their performances can vary substantially for different new tasks, and the ranking of the candidates may depend heavily on the input. Motivated by this, we propose a localized model averaging method with weights modeled as functions of the covariates, making it substantially more versatile than existing model averaging methods. This formulation allows the model averaging procedure to adaptively capture the varying relative advantages of different PTMs across heterogeneous contexts. Specifically, we learn flexible local weights under a general loss framework that accommodates a broad class of prediction tasks. We further establish the asymptotic optimality of the proposed method for both in-sample and out-of-sample risks, as well as the consistency of the estimated weights. Extensive numerical experiments further demonstrate the effectiveness of the proposed method.

stat.ME↗

arXiv2024

Semi-supervised learning using copula-based regression and model averaging

The available data in semi-supervised learning usually consists of relatively small sized labeled data and much larger sized unlabeled data. How to effectively exploit unlabeled data is the key issue. In this paper, we write the regression function in the form of a copula and marginal distributions, and the unlabeled data can be exploited to improve the estimation of the marginal distributions. The predictions based on different copulas are weighted, where the weights are obtained by minimizing an asymptotic unbiased estimator of the prediction risk. Error-ambiguity decomposition of the prediction risk is performed such that unlabeled data can be exploited to improve the prediction risk estimation. We demonstrate the asymptotic normality of copula parameters and regression function estimators of the candidate models under the semi-supervised framework, as well as the asymptotic optimality and weight consistency of the model averaging estimator. Our model averaging estimator achieves faster convergence rates of asymptotic optimality and weight consistency than the supervised counterpart. Extensive simulation experiments and the California housing dataset demonstrate the effectiveness of the proposed method.

stat.ME↗