Related papers: Variational inference and density estimation with …
Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: $(i)$ Estimate latent variables…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…
Split computing has emerged as a recent paradigm for implementation of DNN-based AI workloads, wherein a DNN model is split into two parts, one of which is executed on a mobile/client device and the other on an edge-server (or cloud). Data…
In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…
Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…
We propose a nonparametric factorization approach for sparsely observed tensors. The sparsity does not mean zero-valued entries are massive or dominated. Rather, it implies the observed entries are very few, and even fewer with the growth…
We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…
Distributional regression aims to estimate the full conditional distribution of a target variable, given covariates. Popular methods include linear and tree-ensemble based quantile regression. We propose a neural network-based…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
We consider the solution of linear systems with tensor product structure using a GMRES algorithm. In order to cope with the computational complexity in large dimension both in terms of floating point operations and memory requirement, our…
The low-rank tensor approximation is very promising for the compression of deep neural networks. We propose a new simple and efficient iterative approach, which alternates low-rank factorization with a smart rank selection and fine-tuning.…
In scientific fields such as quantum computing, physics, chemistry, and machine learning, high dimensional data are typically represented using sparse tensors. Tensor contraction is a popular operation on tensors to exploit meaning or alter…
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…
In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high dimensional data arising from the…
Contemporary applications, such as recommendation systems and mobile health monitoring, require real-time processing and analysis of sequentially arriving high-dimensional tensor data. Traditional offline learning, involving the storage and…
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…
The Number Theoretic Transform (NTT) can be regarded as a variant of the Discrete Fourier Transform. NTT has been quite a powerful mathematical tool in developing Post-Quantum Cryptography and Homomorphic Encryption. The Fourier Transform…
Binary Neural Networks (BNNs) enable efficient deep learning by saving on storage and computational costs. However, as the size of neural networks continues to grow, meeting computational requirements remains a challenge. In this work, we…
In this work, we present the tree tensor network Nystr\"om (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker and tensor-train formats, to the more general tree tensor network format,…