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Mixture of Experts (MoE) models enable parameter-efficient scaling through sparse expert activations, yet optimizing their inference and memory costs remains challenging due to limited understanding of their specialization behavior. We…

Mixture of Experts (MoE) models have become central to scaling large language models, yet their mechanistic differences from dense networks remain poorly understood. Previous work has explored how dense models use \textit{superposition} to…

Mixture of experts (MoE) model is a statistical machine learning design that aggregates multiple expert networks using a softmax gating function in order to form a more intricate and expressive model. Despite being commonly used in several…

Joint models of longitudinal and event-time data have been extensively studied and applied in many different fields. Estimation of joint models is challenging, most present procedures are computational expensive and have a strict…

Many learning problems involve multiple patterns and varying degrees of uncertainty dependent on the covariates. Advances in Deep Learning (DL) have addressed these issues by learning highly nonlinear input-output dependencies. However,…

The Mixture-of-Experts (MoE) model uses a set of expert networks that specialize on subsets of a dataset under the supervision of a gating network. A common issue in MoE architectures is ``expert collapse'' where overlapping class…

We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according…

Regression models, where the response variable is circular, are common in areas such as biology, geology and meteorology. A typical model assumes that the conditional distribution of the response follows a von-Mises distribution. However,…

Phase-type (PH) distributions are a popular tool for the analysis of univariate risks in numerous actuarial applications. Their multivariate counterparts (MPH$^\ast$), however, have not seen such a proliferation, due to lack of explicit…

A robust estimator for a wide family of mixtures of linear regression is presented. Robustness is based on the joint adoption of the Cluster Weighted Model and of an estimator based on trimming and restrictions. The selected model provides…

Deep mixture-of-experts models have attracted a lot of attention for survival analysis problems, particularly for their ability to cluster similar patients together. In practice, grouping often comes at the expense of key metrics such as…

Nonlinear mixed effects models have received a great deal of attention in the statistical literature in recent years because of their flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics,…

Phase-type distribution has been an important probabilistic tool in the analysis of complex stochastic system evolution. It was introduced by Neuts \cite{Neuts1975} in 1975. The model describes the lifetime distribution of a finite-state…

We propose a modified version of the three-step estimation method for the latent class model with covariates, which may be used to estimate latent Markov models for longitudinal data. The three-step estimation approach we propose is based…

The goal of this paper is to improve (upcycle) an existing large language model without the prohibitive requirements of continued pre-training of the full-model. The idea is to split the pre-training data into semantically relevant groups…

Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…

In general insurance companies, a correct estimation of liabilities plays a key role due to its impact on management and investing decisions. Since the Financial Crisis of 2007-2008 and the strengthening of regulation, the focus is not only…

In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix…

Until recently obtaining data on populations of networks was typically rare. However, with the advancement of automatic monitoring devices and the growing social and scientific interest in networks, such data has become more widely…

A pivotal advancement in the progress of large language models (LLMs) is the emergence of the Mixture-of-Experts (MoE) LLMs. Compared to traditional LLMs, MoE LLMs can achieve higher performance with fewer parameters, but it is still hard…