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In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
In this paper, we consider an $\ell_{0}$-norm penalized formulation of the generalized eigenvalue problem (GEP), aimed at extracting the leading sparse generalized eigenvector of a matrix pair. The formulation involves maximization of a…
Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…
It is well-known that the finite difference discretization of the Laplacian eigenvalue problem $-\Delta u = \lambda u$ leads to a matrix eigenvalue problem (EVP) $A x= \lambda x$ where the matrix $A$ is Toeplitz-plus-Hankel. Analytical…
Canonical correlation analysis (CCA) is a technique to find statistical dependencies between a pair of multivariate data. However, its application to high dimensional data is limited due to the resulting time complexity. While the…
In this paper, we introduce Functional Generalized Canonical Correlation Analysis (FGCCA), a new framework for exploring associations between multiple random processes observed jointly. The framework is based on the multiblock Regularized…
Genetic Programming (GP) has traditionally entangled the evolution of symbolic representations with their performance-based evaluation, often relying solely on raw fitness scores. This tight coupling makes GP solutions more fragile and…
The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language…
The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide…
Sequential learning of tasks using gradient descent leads to an unremitting decline in the accuracy of tasks for which training data is no longer available, termed catastrophic forgetting. Generative models have been explored as a means to…
We consider the problem of learning discriminative representations for data in a high-dimensional space with distribution supported on or around multiple low-dimensional linear subspaces. That is, we wish to compute a linear injective map…
Complex computer codes are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this problem consists in replacing cpu-time expensive…
The main idea of canonical correlation analysis (CCA) is to map different views onto a common latent space with maximum correlation. We propose a deep interpretable variational canonical correlation analysis (DICCA) for multi-view learning.…
Canonical correlation analysis (CCA) is a widely used technique for estimating associations between two sets of multi-dimensional variables. Recent advancements in CCA methods have expanded their application to decipher the interactions of…
Deep CCA is a recently proposed deep neural network extension to the traditional canonical correlation analysis (CCA), and has been successful for multi-view representation learning in several domains. However, stochastic optimization of…
This paper proposes a robust high-dimensional sparse canonical correlation analysis (CCA) method for investigating linear relationships between two high-dimensional random vectors, focusing on elliptical symmetric distributions. Traditional…
Graph contrastive learning (GCL) has emerged as an effective tool for learning unsupervised representations of graphs. The key idea is to maximize the agreement between two augmented views of each graph via data augmentation. Existing GCL…
Evolutionary algorithms (EAs) are increasingly implemented on graphics processing units (GPUs) to leverage parallel processing capabilities for enhanced efficiency. However, existing studies largely emphasize the raw speedup obtained by…
This paper describes an expectation propagation (EP) method for multi-class classification with Gaussian processes that scales well to very large datasets. In such a method the estimate of the log-marginal-likelihood involves a sum across…
Canonical Correlation Analysis (CCA) has been exploited immensely for learning latent representations in various fields. This study takes a step further by demonstrating the potential of CCA in identifying Elementary Discourse Units(EDUs)…