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Forward regression is a classical and effective tool for variable screening in ultra-high dimensional linear models, but its standard projection-based implementation can be computationally costly and numerically unstable when predictors are…

Real-world scientific applications frequently encounter incomplete observational data due to sensor limitations, geographic constraints, or measurement costs. Although neural operators significantly advanced PDE solving in terms of…

Humans can often predict physical outcomes after only a few observations, a capability known as physical intuition. The mechanisms underlying this efficient learning remain elusive. Here, we introduce a variational learning framework in…

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We…

Under partial-label learning (PLL) where, for each training instance, only a set of ambiguous candidate labels containing the unknown true label is accessible, contrastive learning has recently boosted the performance of PLL on vision…

A core problem in machine learning is to learn expressive latent variables for model prediction on complex data that involves multiple sub-components in a flexible and interpretable fashion. Here, we develop an approach that improves…

Generalized additive index models (GAIMs) offer a flexible semiparametric framework for capturing complex data relationships, balancing the interpretability of parametric models with the flexibility of nonparametric approaches. However,…

While Reinforcement Learning from Verifiable Rewards (RLVR) has advanced reasoning in Large Vision-Language Models (LVLMs), prevailing frameworks suffer from a foundational methodological flaw: by distributing identical advantages across…

We address tracking and prediction of multiple moving objects in visual data streams as inference and sampling in a disentangled latent state-space model. By encoding objects separately and including explicit position information in the…

Graph matching is a fundamental tool in computer vision and pattern recognition. In this paper, we introduce an algorithm for graph matching based on the proximal operator, referred to as differentiable proximal graph matching (DPGM).…

Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent…

In the early days of machine learning (ML), the emphasis was on developing complex algorithms to achieve best predictive performance. To understand and explain the model results, one had to rely on post hoc explainability techniques, which…

Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and slow training times,…

Transparent models, which provide inherently interpretable predictions, are receiving significant attention in high-stakes domains. However, despite much real-world data being collected as time series, there is a lack of studies on…

We introduce CogVLM, a powerful open-source visual language foundation model. Different from the popular shallow alignment method which maps image features into the input space of language model, CogVLM bridges the gap between the frozen…

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…

We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…

Many applications of deep learning for image generation use perceptual losses for either training or fine-tuning of the generator networks. The use of perceptual loss however incurs repeated forward-backward passes in a large image…

Generalized additive models (GAM) have been successfully applied to high dimensional data analysis. However, most existing methods cannot simultaneously estimate the link function, the component functions and the variable interaction. To…

The limitations of purely neural learning have sparked an interest in probabilistic neurosymbolic models, which combine neural networks with probabilistic logical reasoning. As these neurosymbolic models are trained with gradient descent,…