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Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…

Piecewise Aggregate Approximation (PAA) is a competitive basic dimension reduction method for high-dimensional time series mining. When deployed, however, the limitations are obvious that some important information will be missed,…

We consider convex optimization problems with a possibly nonsmooth objective function in the form of a mathematical expectation. The proposed framework (AN-SPS) employs Sample Average Approximations (SAA) to approximate the objective…

In computer vision, traditional ensemble learning methods exhibit either a low training efficiency or the limited performance to enhance the reliability of deep neural networks. In this paper, we propose a lightweight, loss-function-free,…

In the field of unsupervised feature selection, sparse principal component analysis (SPCA) methods have attracted more and more attention recently. Compared to spectral-based methods, SPCA methods don't rely on the construction of a…

Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and…

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Time series forecasting is traditionally dominated by sequence-based architectures such as recurrent neural networks and attention mechanisms, which process all time steps uniformly and often incur substantial computational cost. However,…

In this paper, we consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which…

The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…

Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…

Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. We develop a spectral domain method for multivariate second-order stationary time…

Many estimation problems in astrophysics are highly complex, with high-dimensional, non-standard data objects (e.g., images, spectra, entire distributions, etc.) that are not amenable to formal statistical analysis. To utilize such data and…

We study high-dimensional two-sample mean comparison and address the curse of dimensionality through data-adaptive projections. Leveraging the low-dimensional and localized signal structures commonly seen in single-cell genomics data, our…

Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions…

We propose a method for non-projective dependency parsing by incrementally predicting a set of edges. Since the edges do not have a pre-specified order, we propose a set-based learning method. Our method blends graph, transition, and…

Self-supervised adaptation (SSA) improves foundation model transfer to medical domains but is computationally prohibitive. Although parameter efficient fine-tuning methods such as LoRA have been explored for supervised adaptation, their…

In this paper, we propose a new semiparametric regression estimator by using a hybrid technique of a parametric approach and a nonparametric penalized spline method. The overall shape of the true regression function is captured by the…