Related papers: Near-Efficient and Non-Asymptotic Multiway Inferen…
We consider statistical inference under a semi-supervised setting where we have access to both a labeled dataset consisting of pairs $\{X_i, Y_i \}_{i=1}^n$ and an unlabeled dataset $\{ X_i \}_{i=n+1}^{n+N}$. We ask the question: under what…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
This paper presents an average case denoising performance analysis for the Subspace Pursuit (SP), the CoSaMP and the IHT algorithms. This analysis considers the recovery of a noisy signal, with the assumptions that (i) it is corrupted by an…
Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these…
Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional…
Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…
We consider nonlinear model predictive control (MPC) with multiple competing cost functions. In each step of the scheme, a multiobjective optimal control problem with a nonlinear system and terminal conditions is solved. We propose an…
Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…
The continuous extension of a discrete random variable is amongst the computational methods used for estimation of multivariate normal copula-based models with discrete margins. Its advantage is that the likelihood can be derived…
Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on…
This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…
Tensor parameters that are amortized or regularized over large tensor powers, often called "asymptotic" tensor parameters, play a central role in several areas including algebraic complexity theory (constructing fast matrix multiplication…
Obtaining a reliable estimate of the joint probability mass function (PMF) of a set of random variables from observed data is a significant objective in statistical signal processing and machine learning. Modelling the joint PMF as a tensor…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…
In this paper, we develop asymptotic theories for a class of latent variable models for large-scale multi-relational networks. In particular, we establish consistency results and asymptotic error bounds for the (penalized) maximum…
We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with…
A common method for deriving non-parametric tests is to reformulate a parametric test in terms of sample ranks. Despite being distribution free (even in finite samples), the resulting tests often display remarkable asymptotic power…
Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…
Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…