相关论文: A Bi-level Nonlinear Eigenvector Algorithm for Was…

Domain adaptation (DA) is an important and emerging field of machine learning that tackles the problem occurring when the distributions of training (source domain) and test (target domain) data are similar but different. Current theoretical…

Multi-modal distributions are commonly used to model clustered data in statistical learning tasks. In this paper, we consider the Mixed Linear Regression (MLR) problem. We propose an optimal transport-based framework for MLR problems,…

Discriminant analysis, including linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA), is a popular approach to classification problems. It is well known that LDA is suboptimal to analyze heteroscedastic data, for…

This paper consider solving a class of nonconvex-strongly-convex distributed stochastic bilevel optimization (DSBO) problems with personalized inner-level objectives. Most existing algorithms require computational loops for hypergradient…

Probabilistic models with hierarchical-latent-variable structures provide state-of-the-art results amongst non-autoregressive, unsupervised density-based models. However, the most common approach to training such models based on Variational…

The use of well-disentangled representations offers many advantages for downstream tasks, e.g. an increased sample efficiency, or better interpretability. However, the quality of disentangled interpretations is often highly dependent on the…

In this paper, we propose a new variant of Linear Discriminant Analysis (LDA) to solve multi-label classification tasks. The proposed method is based on a probabilistic model for defining the weights of individual samples in a weighted…

This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement…

Linear discriminant analysis improves class separability but struggles with non-linearly separable data. To overcome this, we introduce Deep Discriminant Analysis (DDA), which directly optimizes the Fisher criterion utilizing deep networks.…

Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…

The computation of Wasserstein gradient direction is essential for posterior sampling problems and scientific computing. The approximation of the Wasserstein gradient with finite samples requires solving a variational problem. We study the…

We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…

We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning. By assigning vertex weights through the LPT…

Covariance and Hessian matrices have been analyzed separately in the literature for classification problems. However, integrating these matrices has the potential to enhance their combined power in improving classification performance. We…

It is widely acknowledged that hyperparameter selection plays a critical role in the effectiveness of sparse optimization problems. The bilevel optimization provides a robust framework for addressing this issue, but these existing methods…

We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case…

Gradient descent-ascent (GDA) flows play a central role in finding saddle points of bivariate functionals, with applications in optimization, game theory, and robust control. While they are well-understood in Hilbert and Banach spaces via…

Linear discriminant analysis (LDA) is a widely used technique for data classification. The method offers adequate performance in many classification problems, but it becomes inefficient when the data covariance matrix is ill-conditioned.…

We propose the particle dual averaging (PDA) method, which generalizes the dual averaging method in convex optimization to the optimization over probability distributions with quantitative runtime guarantee. The algorithm consists of an…

The optimal transport barycenter (a.k.a. Wasserstein barycenter) is a fundamental notion of averaging that extends from the Euclidean space to the Wasserstein space of probability distributions. Computation of the unregularized barycenter…