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The demonstrated success of sparsely-gated Mixture-of-Experts (MoE) architectures, exemplified by models such as DeepSeek and Grok, has motivated researchers to investigate their adaptation to diverse domains. In real-world image…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
The sparsely gated mixture of experts (MoE) architecture sends different inputs to different subnetworks, i.e., experts, through trainable routers. MoE reduces the training computation significantly for large models, but its deployment can…
This paper presents a comprehensive review of the Mixture-of-Experts (MoE) architecture in large language models, highlighting its ability to significantly enhance model performance while maintaining minimal computational overhead. Through…
We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists in coupling the recently…
While federated learning (FL) enables fine-tuning of large language models (LLMs) without compromising data privacy, the substantial size of an LLM renders on-device training impractical for resource-constrained clients, such as mobile…
Mixture of autoregressions (MoAR) models provide a model-based approach to the clustering of time series data. The maximum likelihood (ML) estimation of MoAR models requires the evaluation of products of large numbers of densities of normal…
We introduce a Mixture of Raytraced Experts, a stacked Mixture of Experts (MoE) architecture which can dynamically select sequences of experts, producing computational graphs of variable width and depth. Existing MoE architectures generally…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
Clustered data is ubiquitous in a variety of scientific fields. In this paper, we propose a flexible and interpretable modeling approach, called grouped heterogenous mixture modeling, for clustered data, which models cluster-wise…
The two primary approaches for high-dimensional regression problems are sparse methods (e.g., best subset selection, which uses the L0-norm in the penalty) and ensemble methods (e.g., random forests). Although sparse methods typically yield…
Empirical scaling laws have driven the evolution of large language models (LLMs), yet their coefficients shift whenever the model architecture or data pipeline changes. Mixture-of-Experts (MoE) models, now standard in state-of-the-art…
The Mixture of Experts (MoE) for language models has been proven effective in augmenting the capacity of models by dynamically routing each input token to a specific subset of experts for processing. Despite the success, most existing…
Sparse Mixture of Experts (MoE) models offer a scalable and efficient architecture for training large neural networks by activating only a subset of parameters ("experts") for each input. A learned router computes a distribution over these…
Finite mixture models are among the most popular statistical models used in different data science disciplines. Despite their broad applicability, inference under these models typically leads to computationally challenging non-convex…
Mixture-of-Experts (MoE) large language models (LLMs), which leverage dynamic routing and sparse activation to enhance efficiency and scalability, have achieved higher performance while reducing computational costs. However, these models…
The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter…
Mixture-of-experts (MoE) architectures used in large language models (LLMs) achieve state-of-the-art performance across diverse tasks yet face practical challenges such as deployment complexity and low activation efficiency. Expert pruning…
Mixture-of-Experts (MoE) architectures have become standard in large language models, yet many of their core design choices - expert count, granularity, shared experts, load balancing, token dropping - have only been studied one or two at a…
Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical…