Related papers: Hypothesis Testing via Affine Detectors
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
In this work, we consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on…
We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors. To express such models, we…
The problem of detecting anomalies in multiple processes is considered. We consider a composite hypothesis case, in which the measurements drawn when observing a process follow a common distribution with an unknown parameter (vector), whose…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the…
We propose a frequentist testing procedure that maintains a defined coverage and is optimal in the sense that it gives maximal power to detect deviations from a null hypothesis when the alternative to the null hypothesis is sampled from a…
This article extends the hypotheses assessment method to the case with two competing simple hypotheses. In doing so we further clarify the benefits that hypotheses assessments can bring to classical statistical analyses. Given that…
This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure…
Distribution testing deals with what information can be deduced about an unknown distribution over $\{1,\ldots,n\}$, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…
A fixed-confidence, finite-sample problem of active hypothesis testing arises in many safety-critical applications. Situated in the context of sequential hypothesis testing, this paper studies the effect of hypothesis elimination on the…
Detection rules have traditionally been designed for rational agents that minimize the Bayes risk (average decision cost). With the advent of crowd-sensing systems, there is a need to redesign binary hypothesis testing rules for behavioral…
Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…
Nonconvex methods have emerged as a dominant approach for low-rank matrix estimation, a problem that arises widely in machine learning and AI for learning and representing high-dimensional data. Existing analyses for these methods often…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…
In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…
We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we…
Convex polyhedral abstractions of logic programs have been found very useful in deriving numeric relationships between program arguments in order to prove program properties and in other areas such as termination and complexity analysis. We…