Related papers: On universal inference in Gaussian mixture models
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
The inferential model (IM) framework offers alternatives to the familiar probabilistic (e.g., Bayesian and fiducial) uncertainty quantification in statistical inference. Allowing this uncertainty quantification to be imprecise makes it…
The Gaussian graphical model is routinely employed to model the joint distribution of multiple random variables. The graph it induces is not only useful for describing the relationship between random variables but also critical for…
The universality phenomenon asserts that the distribution of the eigenvalues of random matrix with i.i.d. zero mean, unit variance entries does not depend on the underlying structure of the random entries. For example, a plot of the…
Generalized causal effect estimands, including the Mann-Whitney parameter and causal net benefit, provide flexible summaries of treatment effects in randomized experiments with non-Gaussian or multivariate outcomes. We develop a unified…
We compute the probability distribution of the interface width at the depinning threshold, using recent powerful algorithms. It confirms the universality classes found previously. In all cases, the distribution is surprisingly well…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
In this work, we investigate Gaussian Mixture Models ({\it abbrv} GMM) and the related problem of non parametric maximum likelihood estimation ({\it abbrv} NPMLE) from the perspective of statistical mechanics. In particular, we establish…
Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models,…
We obtain the explicit rate of convergence $N^{-1/2 + \epsilon}$ for the gaps of generalized Wigner matrices in the bulk of the spectrum, for distributions of matrix entries possibly atomic and supported on enough points. The proof proceeds…
This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…
We investigate the performance of the scan (maximum likelihood ratio statistic) and of the average likelihood ratio statistic in the problem of detecting a deterministic signal with unknown spatial extent in the prototypical univariate…
Over the last decade, a wave of research has characterized the exact asymptotic risk of many high-dimensional models in the proportional regime. Two foundational results have driven this progress: Gaussian universality, which shows that the…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
We introduce a new cross-validation method based on an equicorrelated Gaussian randomization scheme. Our method is well-suited for problems where sample splitting is infeasible, either because the data violate the assumption of independent…
Universal outlier hypothesis testing refers to a hypothesis testing problem where one observes a large number of length-$n$ sequences -- the majority of which are distributed according to the typical distribution $\pi$ and a small number…
I propose two U-statistics to test coefficients in generalized linear models. One of them is used to deal with global hypothesis and the other one to test with the nuisance parameter. Both the statistics proposed are within high-dimensional…
This short note considers the problem of testing the null hypothesis that the mean values of two multivariate normal variables are proportional. We show that the usual likelihood ratio $\chi^2$-test is valid non-asymptotically. Our proof…
Residual-based goodness-of-fit tests for parametric time-series models are often complicated by parameter-estimation effects, which can alter the limiting behavior of diagnostic statistics. We propose a sample-splitting generalized spectral…
In 1976, Lai constructed a nontrivial confidence sequence for the mean $\mu$ of a Gaussian distribution with unknown variance $\sigma^2$. Curiously, he employed both an improper (right Haar) mixture over $\sigma$ and an improper (flat)…