相关论文: Soft Tensor Regression

We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…

Modern machine learning forces practitioners to choose between powerful but expensive deep networks and fast but limited classical algorithms. Here we introduce Soft Learning, a framework that maintains a library of heterogeneous…

Consider the task of estimating a 3-order $n \times n \times n$ tensor from noisy observations of randomly chosen entries in the sparse regime. We introduce a similarity based collaborative filtering algorithm for estimating a tensor from…

Long-sequence transformers are designed to improve the representation of longer texts by language models and their performance on downstream document-level tasks. However, not much is understood about the quality of token-level predictions…

CNNs achieve remarkable performance by leveraging deep, over-parametrized architectures, trained on large datasets. However, they have limited generalization ability to data outside the training domain, and a lack of robustness to noise and…

Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the…

This chapter opens with a review of classic tools for regression, a subset of machine learning that seeks to find relationships between variables. With the advent of scientific machine learning this field has moved from a purely data-driven…

The focus of this work is on spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models, soft-thresholded Gaussian processes and develop the efficient posterior computation algorithms.…

This paper proposes a tensor-based parametric channel estimation technique for IRS-assisted communication systems with time-varying channel parameters. We exploit the multidimensional structure of the received signal by developing a…

Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…

Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

In this paper, we study difference-in-differences identification and estimation strategies when the parallel trends assumption holds after conditioning on covariates. We consider empirically relevant settings where the covariates can be…

Value-function (VF) approximation is a central problem in Reinforcement Learning (RL). Classical non-parametric VF estimation suffers from the curse of dimensionality. As a result, parsimonious parametric models have been adopted to…

Effective non-parametric density estimation is a key challenge in high-dimensional multivariate data analysis. In this paper,we propose a novel approach that builds upon tensor factorization tools. Any multivariate density can be…

Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the…

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…

A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…

We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals…