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Finite mixture models have been widely used to model and analyze data from a heterogeneous populations. Moreover, data of this kind can be missing or subject to some upper and/or lower detection limits because of the restriction of…

We consider a semiparametric mixture of two univariate density functions where one of them is known while the weight and the other function are unknown. Such mixtures have a history of application to the problem of detecting differentially…

Mixture-of-Experts (MoE) language models can reduce computational costs by 2-4$\times$ compared to dense models without sacrificing performance, making them more efficient in computation-bounded scenarios. However, MoE models generally…

Mixture-of-Experts (MoE) models can achieve promising results with outrageous large amount of parameters but constant computation cost, and thus it has become a trend in model scaling. Still it is a mystery how MoE layers bring quality…

The Expectation-Maximization (EM) algorithm (Dempster, Laird and Rubin, 1977) is a popular method for computing maximum likelihood estimates (MLEs) in problems with missing data. Each iteration of the al- gorithm formally consists of an…

Mixture model-based clustering, usually applied to multidimensional data, has become a popular approach in many data analysis problems, both for its good statistical properties and for the simplicity of implementation of the…

Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…

The recent rapid progress in (self) supervised learning models is in large part predicted by empirical scaling laws: a model's performance scales proportionally to its size. Analogous scaling laws remain elusive for reinforcement learning…

Mixture Markov Model (MMM) is a widely used tool to cluster sequences of events coming from a finite state-space. However the MMM likelihood being multi-modal, the challenge remains in its maximization. Although Expectation-Maximization…

Large-scale pre-training of deep models, followed by fine-tuning them, has become the cornerstone of natural language processing (NLP). The prevalence of data coupled with computational resources has led to large models with a considerable…

Mixture-of-Experts (MoE) has emerged as an effective approach to reduce the computational overhead of Transformer architectures by sparsely activating a subset of parameters for each token while preserving high model capacity. This paradigm…

Mixture-of-Experts (MoE) layers have emerged as an important tool in scaling up modern neural networks by decoupling total trainable parameters from activated parameters in the forward pass for each token. However, sparse MoEs add…

Sparse Mixture of Experts (SMoEs) models scale the capacity of models while maintaining constant computational overhead. Early designs typically relied on a fixed value of $k$, where $k$ represents either the number of experts selected per…

Sparse Mixture of Experts (SMoE) enables efficient training of large language models by routing input tokens to a select number of experts. However, training SMoE remains challenging due to the issue of representation collapse. Recent…

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…

Finite mixture of skew distributions have emerged as an effective tool in modelling heterogeneous data with asymmetric features. With various proposals appearing rapidly in the recent years, which are similar but not identical, the…

Mixture-of-Experts (MoE) models enable scalable performance by activating large parameter sets sparsely, minimizing computational overhead. To mitigate the prohibitive cost of training MoEs from scratch, recent work employs upcycling,…

In cross-border e-commerce, search relevance modeling faces the dual challenge of extreme linguistic diversity and fine-grained semantic nuances. Existing approaches typically rely on scaling up a single monolithic Large Language Model…

The Expectation Maximization (EM) algorithm is a versatile tool for model parameter estimation in latent data models. When processing large data sets or data stream however, EM becomes intractable since it requires the whole data set to be…

Sparse Mixture-of-Experts (MoE) models offer a powerful way to scale model size without increasing compute, as per-token FLOPs depend only on k active experts rather than the total pool of E experts. Yet, this asymmetry creates an MoE…