Related papers: Gaussian Mean Testing under Truncation
This paper considers a vector Gaussian channel of fixed identity covariance matrix and binary input signalling as the mean of it. A linear transformation is performed on the vector input signal. The objective is to find the optimal scaling…
Learning with a {\it convex loss} function has been a dominating paradigm for many years. It remains an interesting question how non-convex loss functions help improve the generalization of learning with broad applicability. In this paper,…
This paper aims to test the number of spikes in a generalized spiked covariance matrix, the spiked eigenvalues of which may be extremely larger or smaller than the non-spiked ones. For a high-dimensional problem, we first propose a general…
This paper analyzes the detection of a M-dimensional useful signal modeled as the output of a M xK MIMO filter driven by a K-dimensional white Gaussian noise, and corrupted by a M-dimensional Gaussian noise with mutually uncorrelated…
The sample selection approach is very popular in learning with noisy labels. As deep networks learn pattern first, prior methods built on sample selection share a similar training procedure: the small-loss examples can be regarded as clean…
Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates.…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
We provide a fully statistical analysis of the results of a Bell test beyond mean values. This is possible in a practical scheme where all the observables involved in the test are simultaneously measured at the expense of unavoidably…
The continuous variable quantum computing platform constitutes a promising candidate for realizing quantum advantage, as exemplified in Gaussian Boson Sampling. While noise in the experiments makes the computation attainable for classical…
We uncover the quantum fluctuation-response inequality, which, in the most general setting, establishes a bound for the mean difference of an observable at two different quantum states, in terms of the quantum relative entropy. When the…
Gaussian boson sampling is originally proposed to show quantum advantage with quantum linear optical elements. Recently, several experimental breakthroughs based on Gaussian boson sampling pointing to quantum computing supremacy have been…
The observational limitations of astronomical surveys lead to significant statistical inference challenges. One such challenge is the estimation of luminosity functions given redshift $z$ and absolute magnitude $M$ measurements from an…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
Neural models, in particular the d-vector and x-vector architectures, have produced state-of-the-art performance on many speaker verification tasks. However, two potential problems of these neural models deserve more investigation. Firstly,…
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…
Gaussian boson sampling (GBS) is a promising candidate for an experimental demonstration of quantum advantage using photons. However, sufficiently large noise might hinder a GBS implementation from entering the regime where quantum speedup…
We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum…
Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving…
We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including genomics and medical imaging, it is natural to assume that…
While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings…