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The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…
We present a new method for estimating multivariate, second-order stationary Gaussian Random Field (GRF) models based on the Sparse Precision matrix Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating scalar GRF…
Compact finite-difference (FD) schemes specify derivative approximations implicitly, thus to achieve parallelism with domain-decomposition suitable partitioning of linear systems is required. Consistent order of accuracy, dispersion, and…
Tools from random matrix theory have become central to deep learning theory, using spectral information to provide mechanisms for modeling generalization, robustness, scaling, and failure modes. While often capable of modeling empirical…
Recognizing degraded faces from low resolution and blurred images are common yet challenging task. Local Frequency Descriptor (LFD) has been proved to be effective for this task yet it is extracted from a spatial neighborhood of a pixel of…
The applications of traditional statistical feature selection methods to high-dimension, low sample-size data often struggle and encounter challenging problems, such as overfitting, curse of dimensionality, computational infeasibility, and…
This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much…
In contrastive self-supervised learning, the common way to learn discriminative representation is to pull different augmented "views" of the same image closer while pushing all other images further apart, which has been proven to be…
We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the…
Federated learning has become a popular tool in the big data era nowadays. It trains a centralized model based on data from different clients while keeping data decentralized. In this paper, we propose a federated sparse sliced inverse…
Light field (LF) images acquired by hand-held devices usually suffer from low spatial resolution as the limited sampling resources have to be shared with the angular dimension. LF spatial super-resolution (SR) thus becomes an indispensable…
Recently a deterministic method, frequent directions (FD) is proposed to solve the high dimensional low rank approximation problem. It works well in practice, but experiences high computational cost. In this paper, we establish a fast…
In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and…
This paper proposes a federated learning technique for deep algorithm unfolding with applications to sparse signal recovery and compressed sensing. We refer to this architecture as Fed-CS. Specifically, we unfold and learn the iterative…
Feature whitening is a known technique for speeding up training of DNN. Under certain assumptions, whitening the activations reduces the Fisher information matrix to a simple identity matrix, in which case stochastic gradient descent is…
We consider the problem of high-dimensional light field reconstruction and develop a learning-based framework for spatial and angular super-resolution. Many current approaches either require disparity clues or restore the spatial and…
Transformer-based self-supervised models are trained as feature extractors and have empowered many downstream speech tasks to achieve state-of-the-art performance. However, both the training and inference process of these models may…
A fast forward feature selection algorithm is presented in this paper. It is based on a Gaussian mixture model (GMM) classifier. GMM are used for classifying hyperspectral images. The algorithm selects iteratively spectral features that…
Densest Subgraph Problem (DSP) is an important primitive problem with a wide range of applications, including fraud detection, community detection and DNA motif discovery. Edge-based density is one of the most common metrics in DSP.…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…