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Many biochemical applications such as molecular property prediction require models to generalize beyond their training domains (environments). Moreover, natural environments in these tasks are structured, defined by complex descriptors such…

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…

Traditional empirical risk minimization (ERM) for semantic segmentation can disproportionately advantage or disadvantage certain target classes in favor of an (unfair but) improved overall performance. Inspired by the recently introduced…

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced-order methods are demanded. Combining these…

A prominent family of methods for learning data distributions relies on density ratio estimation (DRE), where a model is trained to $\textit{classify}$ between data samples and samples from some reference distribution. DRE-based models can…

Invariant risk minimization (IRM) has received increasing attention as a way to acquire environment-agnostic data representations and predictions, and as a principled solution for preventing spurious correlations from being learned and for…

Domain generalization (DG) aims to enhance the ability of models trained on source domains to generalize effectively to unseen domains. Recently, Sharpness-Aware Minimization (SAM) has shown promise in this area by reducing the sharpness of…

Understanding interaction effects among variables is important for regression modeling in various applications. The conventional approach of quantifying interactions as the product of variables often lacks clear interpretability, especially…

Inference of gene regulatory networks (GRNs) based on experimental data is a challenging task in bioinformatics. In this paper, we present a bi-objective minimization model (BoMM) for inference of GRNs, where one objective is the fitting…

It is well known that open dynamical systems can admit an uncountable number of (absolutely continuous) conditionally invariant measures (ACCIMs) for each prescribed escape rate. We propose and illustrate a convex optimisation based…

In this paper, we develop the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions (Dirichlet and Neumann) for the elasticity equations in high contrast media. By a special…

Inertial measurement units (IMUs) are fundamental sensing components in multi-source integrated navigation systems, and their performance directly determines the accuracy and reliability of solutions. However, the precision of low-cost IMUs…

The theoretical and empirical performance of Empirical Risk Minimization (ERM) often suffers when loss functions are poorly behaved with large Lipschitz moduli and spurious sharp minimizers. We propose and analyze a counterpart to ERM…

This paper studies cross-domain lossy compression through the lens of minimum entropy coupling (MEC) with rate and classification constraints. In this setting, an encoder observes samples from a degraded source domain, while the decoder is…

Adversarial Training (AT) is known as an effective approach to enhance the robustness of deep neural networks. Recently researchers notice that robust models with AT have good generative ability and can synthesize realistic images, while…

A new method for estimating structural equation models (SEM) is proposed and evaluated. In contrast to most other methods, it is based directly on the data, not on the covariance matrix of the data. The new approach is flexible enough to…

Entropy minimization has been widely used in unsupervised domain adaptation (UDA). However, existing works reveal that entropy minimization only may result into collapsed trivial solutions. In this paper, we propose to avoid trivial…

Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction over fifty years ago, and is now commonly utilized within a family setting. Families of mixture models arise when the component…

How to effectively learn from unlabeled data from the target domain is crucial for domain adaptation, as it helps reduce the large performance gap due to domain shift or distribution change. In this paper, we propose an easy-to-implement…

Domain Generalization (DG) aims to learn a model that can generalize well to unseen target domains from a set of source domains. With the idea of invariant causal mechanism, a lot of efforts have been put into learning robust causal effects…