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Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…

Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prevalent approach is to take the random matrix as a standard…

Existing image recognition techniques based on convolutional neural networks (CNNs) basically assume that the training and test datasets are sampled from i.i.d distributions. However, this assumption is easily broken in the real world…

We propose a novel class of kernels to alleviate the high computational cost of large-scale nonparametric learning with kernel methods. The proposed kernel is defined based on a hierarchical partitioning of the underlying data domain, where…

We consider the stochastic gradient method with random reshuffling ($\mathsf{RR}$) for tackling smooth nonconvex optimization problems. $\mathsf{RR}$ finds broad applications in practice, notably in training neural networks. In this work,…

Active and passive thermography are two efficient techniques extensively used to measure heterogeneous thermal patterns leading to subsurface defects for diagnostic evaluations. This study conducts a comparative analysis on low-rank matrix…

Gradient compression is a popular technique for improving communication complexity of stochastic first-order methods in distributed training of machine learning models. However, the existing works consider only with-replacement sampling of…

Scalable Gaussian Process methods are computationally attractive, yet introduce modeling biases that require rigorous study. This paper analyzes two common techniques: early truncated conjugate gradients (CG) and random Fourier features…

Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization…

We propose the adaptive random Fourier features Gaussian kernel LMS (ARFF-GKLMS). Like most kernel adaptive filters based on stochastic gradient descent, this algorithm uses a preset number of random Fourier features to save computation…

Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…

Kernel-based nonparametric hazard rate estimation is considered with a special class of infinite-order kernels that achieves favorable bias and mean square error properties. A fully automatic and adaptive implementation of a density and…

This is a tutorial and survey paper on the Johnson-Lindenstrauss (JL) lemma and linear and nonlinear random projections. We start with linear random projection and then justify its correctness by JL lemma and its proof. Then, sparse random…

In this paper, we consider the problem of minimizing the average of a large number of nonsmooth and convex functions. Such problems often arise in typical machine learning problems as empirical risk minimization, but are computationally…

The primary outcome of Randomized clinical Trials (RCTs) are typically dichotomous, continuous, multivariate continuous, or time-to-event. However, what if this outcome is unstructured, e.g., a list of variables of mixed types, longitudinal…

Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely…

Large Multimodal Models (LMMs) have shown generalized zero-shot capabilities in diverse domain question-answering (QA) tasks, including graph QA that involves complex graph topologies. However, most current approaches use only a single type…

\noindent Randomized nomination sampling (RNS) is a rank-based sampling technique which has been shown to be effective in several nonparametric studies involving environmental and ecological applications. In this paper, we investigate…

We present Consistent-Recurrent Feature Flow Transformer (CRFT), a unified coarse-to-fine framework based on feature flow learning for robust cross-modal image registration. CRFT learns a modality-independent feature flow representation…

Subsampled Randomized Hadamard Transform (SRHT), a popular random projection method that can efficiently project a $d$-dimensional data into $r$-dimensional space ($r \ll d$) in $O(dlog(d))$ time, has been widely used to address the…