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

We present a method to linearize, without approximation, a specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the nonlinearities are expressed by scalar functions that are defined by a quotient of linear…

In this paper we show the extension of the Nonlinear-Diffusion Acceleration (NDA) to geometries containing small voids using a weighted least-squares (WLS) high order equation. Even though the WLS equation is well defined in voids, the…

Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…

Differential dynamic programming (DDP) is a popular technique for solving nonlinear optimal control problems with locally quadratic approximations. However, existing DDP methods are not designed for stochastic systems with unknown…

Considering the high computation cost produced in conventional computation fluid dynamic simulations, machine learning methods have been introduced to flow dynamic simulations in recent years. However, most of studies focus mainly on…

Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction, but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear…

We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs,…

Consider a two-class classification problem where we observe samples $(X_i, Y_i)$ for i = 1, ..., n, $X_i \in R^p$ and $Y_i$ in {0, 1}. Given $Y_i = k$, $X_i$ is assumed to follow a multivariate normal distribution with mean $\mu_k \in R^k$…

Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original and embedded samples while preserving clusters in the…

Quadratic discriminant analysis (QDA) is a standard tool for classification due to its simplicity and flexibility. Because the number of its parameters scales quadratically with the number of the variables, QDA is not practical, however,…

With the introduction of the variational autoencoder (VAE), probabilistic latent variable models have received renewed attention as powerful generative models. However, their performance in terms of test likelihood and quality of generated…

Anomaly detection tools and methods present a key capability in modern cyberphysical and failure prediction systems. Despite the fast-paced development in deep learning architectures for anomaly detection, model optimization for a given…

We consider the task of classification in the high dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose a heuristic, called sparse…

When learning graph neural networks (GNNs) in node-level prediction tasks, most existing loss functions are applied for each node independently, even if node embeddings and their labels are non-i.i.d. because of their graph structures. To…

We present Wasserstein introspective neural networks (WINN) that are both a generator and a discriminator within a single model. WINN provides a significant improvement over the recent introspective neural networks (INN) method by enhancing…

This paper introduces Wasserstein Adversarially Regularized Graph Autoencoder (WARGA), an implicit generative algorithm that directly regularizes the latent distribution of node embedding to a target distribution via the Wasserstein metric.…

This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…

We propose a novel end-to-end non-minimax algorithm for training optimal transport mappings for the quadratic cost (Wasserstein-2 distance). The algorithm uses input convex neural networks and a cycle-consistency regularization to…

As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the…

The proximal algorithm is a powerful tool to minimize nonlinear and nonsmooth functionals in a general metric space. Motivated by the recent progress in studying the training dynamics of the noisy gradient descent algorithm on two-layer…