arXiv research

Missing data is an important challenge when dealing with high dimensional data arranged in the form of an array. In this paper, we propose methods for estimation of the parameters of array variate normal probability model from partially observed multiway data. The methods developed here are useful for missing data impu…

Developed a multiway classification method for sparse data.

Paper develops efficient DML estimators for multiway clustered data without cross-fitting.

A new tensor completion method handles missing data with missing not at random entries.

We describe a probabilistic PARAFAC/CANDECOMP (CP) factorization for multiway (i.e., tensor) data that incorporates auxiliary covariates, SupCP. SupCP generalizes the supervised singular value decomposition (SupSVD) for vector-valued observations, to allow for observations that have the form of a matrix or higher-order…

We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or…

The paper explores how multiway data from PDEs can be accurately tracked using EnKF with specific covariance and precision estimators.

New method for multiway clustering of 3rd order tensors.

Efficient tensor decomposition for count data models achieves near-optimal multiway analysis.

Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…

Tensor analysis tackles complex multidimensional data across fields.

The paper develops methods for causal function estimation and inference with multiway clustered data.

We consider the problem of identifying multiway block structure from a large noisy tensor. Such problems arise frequently in applications such as genomics, recommendation system, topic modeling, and sensor network localization. We propose a tensor block model, develop a unified least-square estimation, and obtain the t…

We extend contrastive learning theory for multiway classification and prove convergence guarantees.

The growing use of neuroimaging technologies generates a massive amount of biomedical data that exhibit high dimensionality. Tensor-based analysis of brain imaging data has been proved quite effective in exploiting their multiway nature. The advantages of tensorial methods over matrix-based approaches have also been de…

We introduce a Bayesian nonparametric regression model for data with multiway (tensor) structure, motivated by an application to periodontal disease (PD) data. Our outcome is the number of diseased sites measured over four different tooth types for each subject, with subject-specific covariates available as predictors.…

New algorithm for multiway spectral clustering on Grassmann manifolds.

Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.

dCMF models evolving patterns in multiway data with temporal dynamics.

Bayesian hierarchical tensor factorization model for international trade flows

The paper ranks items based on top choices in multiway comparisons.

Improves magnetic field mapping using an array of magnetometers with noisy input.

Simpler proof for non-basic sets in 2D.

Paper improves DOA estimation in sparse arrays using Siamese neural networks.

Direction of arrival (DoA) estimation of targets improves with the number of elements employed by a phased array radar antenna. Since larger arrays have high associated cost, area and computational load, there is recent interest in thinning the antenna arrays without loss of far-field DoA accuracy. In this context, a c…

Physical activity levels are an important predictor of cardiovascular health and increasingly being measured by sensors, like accelerometers. Accelerometers produce rich multivariate data that can inform important clinical decisions related to individual patients and public health. The CHAMPION study, a study of youth …

Analog arrays are a promising upcoming hardware technology with the potential to drastically speed up deep learning. Their main advantage is that they compute matrix-vector products in constant time, irrespective of the size of the matrix. However, early convolution layers in ConvNets map very unfavorably onto analog a…

Develops a new tensor model for clustering with degree correction.

Novel CNN array for sign language recognition using wearable IMUs.

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 $\mathbb{R}^{n_1 \times n_2 \times \cdots \times n_d}$. It focuses on the task of estimatin…

A neural network, IHT-Net, improves DOA estimation with sparse arrays.

This work tackles sparse coding in DLRA for interpretable multiway data.

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifier…

Nonsingular estimation of high dimensional covariance matrices is an important step in many statistical procedures like classification, clustering, variable selection an future extraction. After a review of the essential background material, this paper introduces a technique we call slicing for obtaining a nonsingular …

Paper proposes a learning-based sparse Bayesian method for accurate off-grid DOA estimation.

We present a system for the automatic differentiation of a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source automatic differentiation and global optimizations such as loop transformations. Thanks to this feature, we demo…

Infinite Tucker Decomposition (InfTucker) and random function prior models, as nonparametric Bayesian models on infinite exchangeable arrays, are more powerful models than widely-used multilinear factorization methods including Tucker and PARAFAC decomposition, (partly) due to their capability of modeling nonlinear rel…

Paper proposes a new tensor model for mixed memberships and provides error bounds.

We augment the nonnegative matrix factorization method for audio source separation with cues about directionality of sound propagation. This improves separation quality greatly and removes the need for training data, with only a twofold increase in run time. This is the first method which can exploit directional inform…

Hardware architectures composed of resistive cross-point device arrays can provide significant power and speed benefits for deep neural network training workloads using stochastic gradient descent (SGD) and backpropagation (BP) algorithm. The training accuracy on this imminent analog hardware however strongly depends o…

The paper improves spectral ranking methods for diverse comparison graphs.

Anomaly detection is one of the frequent and important subroutines deployed in large-scale data processing systems. Even being a well-studied topic, existing techniques for unsupervised anomaly detection require storing significant amounts of data, which is prohibitive from memory and latency perspective. In the big-da…

This paper proposes a learning framework for n-bit quantized neural networks that improves accuracy and speed on FPGAs.

Dual-Channel Tensor Neural Network (DC-TNN) decomposes tensor data into low-rank and sparse components for better estimation and inference.

We consider two eigenvalue problems for Laplacian on some specific doubly connected domain. In particular, we study the following two eigenvalue problems. Let $B_1$ be an open ball in $\mathbb{R}^n$ and $B_0$ be a ball contained in $B_1$. Let $ν$ be the outward unit normal on $\partial B_1$. Then the first eigenvalue o…

New method for tensor completion from specific mode observations.

Sorting an array is a fundamental routine in machine learning, one that is used to compute rank-based statistics, cumulative distribution functions (CDFs), quantiles, or to select closest neighbors and labels. The sorting function is however piece-wise constant (the sorting permutation of a vector does not change if th…

In this paper we prove the following geometric inequality in the hyperbolic space $\H^n$ ($n\ge 5)$, which is a hyperbolic Alexandrov-Fenchel inequality, \[\begin{array}{rcl} \ds \int_Σ\s_4 d μ\ge \ds\vs C_{n-1}^4ω_{n-1}\left\{\left(\frac{|Σ|}{ω_{n-1}} \right)^\frac 12 + \left(\frac{|Σ|}{ω_{n-1}} \right)^{\frac 12\frac…