Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define heterogeneous subgroups and handling data that are missing not at random, a prevalent issue in fields like transcriptomics. While several notable methods have been proposed to address these problems, they typically tackle each issue in isolation, thereby limiting their flexibility and adaptability. This paper introduces a unified framework designed to address these challenges simultaneously. Our approach incorporates a data-driven penalty matrix into penalized clustering to enable more flexible variable selection, along with a mechanism that explicitly models the relationship between missingness and latent class membership. We demonstrate that, under certain regularity conditions, the proposed framework achieves both asymptotic consistency and selection consistency, even in the presence of missing data. This unified strategy significantly enhances the capability and efficiency of model-based clustering, advancing methodologies for identifying informative variables that define homogeneous subgroups in the presence of complex missing data patterns. The performance of the framework, including its computational efficiency, is evaluated through simulations and demonstrated using both synthetic and real-world transcriptomic datasets.

State-of-the-art medical multi-modal LLMs (med-MLLMs), such as LLaVA-Med and BioMedGPT, primarily depend on scaling model size and data volume, with training driven largely by autoregressive objectives. However, we reveal that this approach can lead to weak vision-language alignment, making these models overly dependent on costly instruction-following data. To address this, we introduce ExGra-Med, a novel multi-graph alignment framework that jointly aligns images, instruction responses, and extended captions in the latent space, advancing semantic grounding and cross-modal coherence. To scale to large LLMs (e.g., LLaMa-7B), we develop an efficient end-to-end training scheme using black-box gradient estimation, enabling fast and scalable optimization. Empirically, ExGra-Med matches LLaVA-Med’s performance using just 10\% of pre-training data, achieving a 20.13\% gain on VQA-RAD and approaching full-data performance. It also outperforms strong baselines like BioMedGPT and RadFM on visual chatbot and zero-shot classification tasks, demonstrating its promise for efficient, high-quality vision-language integration in medical AI.

Originally introduced as a neural network for ensemble learning, mixture of experts (MoE) has recently become a fundamental building block of highly successful modern deep neural networks for heterogeneous data analysis in several applications of machine learning and statistics. Despite its popularity in practice, a satisfactory level of theoretical understanding of the MoE model is far from complete. To shed new light on this problem, we provide a convergence analysis for maximum likelihood estimation (MLE) in the Gaussian-gated MoE model. The main challenge of that analysis comes from the inclusion of covariates in the Gaussian gating functions and expert networks, which leads to their intrinsic interaction via some partial differential equations with respect to their parameters. We tackle these issues by designing novel Voronoi loss functions among parameters to accurately capture the heterogeneity of parameter estimation rates. Our findings reveal that the MLE has distinct behaviors under two complement settings of location parameters of the Gaussian gating functions, namely when all these parameters are non-zero versus when at least one among them vanishes. Notably, these behaviors can be characterized by the solvability of two different systems of polynomial equations. Finally, we conduct a simulation study to empirically verify our theoretical results.

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been previous attempts to comprehend the behavior of that model under the regression settings through the convergence analysis of maximum likelihood estimation in the Gaussian MoE model, such analysis under the setting of a classification problem has remained missing in the literature. We close this gap by establishing the convergence rates of density estimation and parameter estimation in the softmax gating multinomial logistic MoE model. Notably, when part of the expert parameters vanish, these rates are shown to be slower than polynomial rates owing to an inherent interaction between the softmax gating and expert functions via partial differential equations. To address this issue, we propose using a novel class of modified softmax gating functions which transform the input before delivering them to the gating functions. As a result, the previous interaction disappears and the parameter estimation rates are significantly improved.

A molecule’s 2D representation consists of its atoms, their attributes, and the molecule’s covalent bonds. A 3D (geometric) representation of a molecule is called a conformer and consists of its atom types and Cartesian coordinates. Every conformer has a potential energy, and the lower this energy, the more likely it occurs in nature. Most existing machine learning methods for molecular property prediction consider either 2D molecular graphs or 3D conformer structure representations in isolation. Inspired by recent work on using ensembles of conformers in conjunction with 2D graph representations, we propose E(3)-invariant molecular conformer aggregation networks. The method integrates a molecule’s 2D representation with that of multiple of its conformers. Contrary to prior work, we propose a novel 2D–3D aggregation mechanism based on a differentiable solver for the Fused Gromov-Wasserstein Barycenter problem and the use of an efficient conformer generation method based on distance geometry. We show that the proposed aggregation mechanism is E(3) invariant and propose an efficient GPU implementation. Moreover, we demonstrate that the aggregation mechanism helps to significantly outperform state-of-the-art molecule property prediction methods on established datasets.

Empirical risk minimization (ERM) is a foundational framework for the estimation of solutions to statistical and machine learning problems. Characterizing the distributional properties of the minimum empirical risk (MER) provides valuable tools for conducting inference and assessing the goodness of model fit. We provide a comprehensive account of the asymptotic distribution for the order-$\sqrt{n}$ blowup of the MER under generic and abstract assumptions, and present practical conditions under which our theorems hold. Our results improve upon and relax the assumptions made in previous works. Specifically, we provide asymptotic distributions for MERs for non-independent and identically distributed data, and when the loss functions may be discontinuous or indexed by non-Euclidean spaces. We further present results that enable the application of these asymptotics for statistical inference. Specifically, the construction of consistent confidence sets using the bootstrap and consistent hypothesis tests using penalized model selection. We illustrate the utility of our approach by applying our results to neural network problems.

We extend Bayesian Synthetic Likelihood (BSL) methods to non-Gaussian approximations of the likelihood function. In this setting, we introduce Mixtures of Experts (MoEs), a class of neural network models, as surrogate likelihoods that exhibit desirable approximation theoretic properties. Moreover, MoEs can be estimated using Expectation-Maximization algorithm-based approaches, such as the Gaussian Locally Linear Mapping model estimators that we implement. Further, we provide theoretical evidence towards the ability of our procedure to estimate and approximate a wide range of likelihood functions. Through simulations, we demonstrate the superiority of our approach over existing BSL variants in terms of both posterior approximation accuracy and computational efficiency.

Increasing the throughput of the Transformer architecture, a foundational component used in numerous state-of-the-art models for vision and language tasks (e.g., GPT, LLaVa), is an important problem in machine learning. One recent and effective strategy is to merge token representations within Transformer models, aiming to reduce computational and memory requirements while maintaining accuracy. Prior work has proposed algorithms based on Bipartite Soft Matching (BSM), which divides tokens into distinct sets and merges the top $k$ similar tokens. However, these methods have significant drawbacks, such as sensitivity to token-splitting strategies and damage to informative tokens in later layers. This paper presents a novel paradigm called PiToMe, which prioritizes the preservation of informative tokens using an additional metric termed the \textit{energy score}. This score identifies large clusters of similar tokens as high-energy, indicating potential candidates for merging, while smaller (unique and isolated) clusters are considered as low-energy and preserved. Experimental findings demonstrate that PiToMe saved from 40-60\% FLOPs of the base models while exhibiting superior off-the-shelf performance on image classification (0.5\% average performance drop of ViT-MAEH compared to 2.6\% as baselines), image-text retrieval (0.3\% average performance drop of Clip on Flick30k compared to 4.5\% as others), and analogously in visual questions answering with LLaVa-7B. Furthermore, PiToMe is theoretically shown to preserve intrinsic spectral properties to the original token space under mild conditions.

Truong Do, Le Khiem, Quang Pham, TrungTin Nguyen, Thanh-Nam Doan, Binh Nguyen, Chenghao Liu, Savitha Ramasamy, Xiaoli Li, Steven Hoi. Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing. 2023.

Understanding the parameter estimation of softmax gating Gaussian mixture of experts has remained a long-standing open problem in the literature. It is mainly due to three fundamental theoretical challenges associated with the softmax gating function: (i) the identifiability only up to the translation of parameters; (ii) the intrinsic interaction via partial differential equations between the softmax gating and the expert functions in the Gaussian density; (iii) the complex dependence between the numerator and denominator of the conditional density of softmax gating Gaussian mixture of experts. We resolve these challenges by proposing novel Voronoi loss functions among parameters and establishing the convergence rates of maximum likelihood estimator (MLE) for solving parameter estimation in these models. When the true number of experts is unknown and over-specified, our findings show a connection between the convergence rate of the MLE and a solvability problem of a system of polynomial equations.