Related papers: Tensor rank problem in statistical high-dimensiona…
In pursuit of reinforcement learning systems that could train in physical environments, we investigate multi-task approaches as a means to alleviate the need for massive data acquisition. In a tabular scenario where the Q-functions are…
The PageRank algorithm is used to rank web pages by their importance. Since its development, the PageRank algorithm is a critical and fundamental part of search engines today. PageRank is a graph-based algorithm that ranks pages based on…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
We study nondeterministic multiparty quantum communication with a quantum generalization of broadcasts. We show that, with number-in-hand classical inputs, the communication complexity of a Boolean function in this communication model…
Topic modeling is a popular method used to describe biological count data. With topic models, the user must specify the number of topics $K$. Since there is no definitive way to choose $K$ and since a true value might not exist, we develop…
Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical…
Tensors or {\em multi-way arrays} are functions of three or more indices $(i,j,k,\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column). Tensors have a rich history, stretching over…
Two classically identical expressions for the mutual information generally differ when the two systems involved are quantum. We investigate this difference -- quantum discord -- and show that it can be used as a criterion for the…
Making binary decisions is a common data analytical task in scientific research and industrial applications. In data sciences, there are two related but distinct strategies: hypothesis testing and binary classification. In practice, how to…
We consider rank-one symmetric tensor estimation when the tensor is corrupted by Gaussian noise and the spike forming the tensor is a structured signal coming from a generalized linear model. The latter is a mathematically tractable model…
Uncertainty quantification based on stochastic spectral methods suffers from the curse of dimensionality. This issue was mitigated recently by low-rank tensor methods. However, there exist two fundamental challenges in low-rank tensor-based…
We suggest a model of a multi-agent society of decision makers taking decisions being based on two criteria, one is the utility of the prospects and the other is the attractiveness of the considered prospects. The model is the…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
The theory of majorization has seen substantial application in quantum information. Its framework predicates on the comparability between real vectors. We explore the antithesis of this premise, namely, incomparability. Specifically, we…
The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…
We formulate coherence modeling as a regression task and propose two novel methods to combine techniques from our setup with pairwise approaches. The first of our methods is a model that we call "first-next," which operates similarly to…
We investigate the computational complexity of tensor rank, a concept that plays fundamental role in different topics of modern applied mathematics. For tensors over any integral domain, we prove that the rank problem is polynomial time…
Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the {\em count-tracking} problem, where there are $k$ players, each holding a counter $n_i$ that gets…