Related papers: Statistical Inference in Tensor Completion: Optima…

In stochastic simulation, input uncertainty refers to the propagation of the statistical noise in calibrating input models to impact output accuracy, in addition to the Monte Carlo simulation noise. The vast majority of the input…

We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite…

We develop a methodology for conducting inference on extreme quantiles of unobserved individual heterogeneity (e.g., heterogeneous coefficients, treatment effects) in panel data and meta-analysis settings. Inference is challenging in such…

In many applications, such as classification of images or videos, it is of interest to develop a framework for tensor data instead of an ad-hoc way of transforming data to vectors due to the computational and under-sampling issues. In this…

We study the problem of estimation and testing in logistic regression with class-conditional noise in the observed labels, which has an important implication in the Positive-Unlabeled (PU) learning setting. With the key observation that the…

Literatures in state space models focus on parametric inference and prediction, which fail if the state space model is not fully specified and the maximum likelihood estimation does not work. In this paper, we assume the state transition…

We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise…

We study tensor completion in the agnostic setting. In the classical tensor completion problem, we receive $n$ entries of an unknown rank-$r$ tensor and wish to exactly complete the remaining entries. In agnostic tensor completion, we make…

We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…

Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to…

Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…

We determine statistical and computational limits for estimation of a rank-one matrix (the spike) corrupted by an additive gaussian noise matrix, in a sparse limit, where the underlying hidden vector (that constructs the rank-one matrix)…

For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…

While RANSAC-based methods are robust to incorrect image correspondences (outliers), their hypothesis generators are not robust to correct image correspondences (inliers) with positional error (noise). This slows down their convergence…

Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…

Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…

We study informationally overcomplete measurements for quantum state estimation so as to clarify their tomographic significance as compared with minimal informationally complete measurements. We show that informationally overcomplete…

This paper revisits the simple, but empirically salient, problem of inference on a real-valued parameter that is partially identified through upper and lower bounds with asymptotically normal estimators. A simple confidence interval is…

We propose tensor time series imputation when the missing pattern in the tensor data can be general, as long as any two data positions along a tensor fibre are both observed for enough time points. The method is based on a tensor time…