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The growth of data today poses a challenge in management and inference. While feature extraction methods are capable of reducing the size of the data for inference, they do not help in minimizing the cost of data storage. On the other hand,…
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…
Support Vector Machines (SVM), a popular machine learning technique, has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. Whether it is identifying high-risk patients by…
This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…
Unsupervised/self-supervised time series representation learning is a challenging problem because of its complex dynamics and sparse annotations. Existing works mainly adopt the framework of contrastive learning with the time-based…
This paper discusses the trapezoidal fuzzy number(TrFN); Interval-valued intuitionistic fuzzy number(IVIFN); neutrosophic set and its operational laws; and, trapezoidal neutrosophic set(TrNS) and its operational laws. Based on the…
L-BFGS is the state-of-the-art optimization method for many large scale inverse problems. It has a small memory footprint and achieves superlinear convergence. The method approximates Hessian based on an initial approximation and an update…
Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with…
A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by…
We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…
Two-stage least squares (TSLS) estimators and variants thereof are widely used to infer the effect of an exposure on an outcome using instrumental variables (IVs). They belong to a wider class of two-stage IV estimators, which are based on…
Scaling laws motivate the development of Time Series Foundation Models (TSFMs) that pre-train vast parameters and achieve remarkable zero-shot forecasting performance. Surprisingly, even after fine-tuning, TSFMs cannot consistently…
This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…
Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pre-trained…
Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD…
Feature Selection is a crucial procedure in Data Science tasks such as Classification, since it identifies the relevant variables, making thus the classification procedures more interpretable, cheaper in terms of measurement and more…
Type-2 fuzzy set (T2 FS) were introduced by Zadeh in 1965, and the membership degrees of T2 FSs are type-1 fuzzy sets (T1 FSs). Owing to the fuzziness of membership degrees, T2 FSs can better model the uncertainty of real life, and thus,…
This article aims to seek a selection and estimation procedure for a class of tensor regression problems with multivariate covariates and matrix responses, which can provide theoretical guarantees for model selection in finite samples.…
In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…
We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…