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This work theoretically studies the problem of estimating a structured high-dimensional signal $x_0 \in \mathbb{R}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge…
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…
Bayesian model selection methods provide a self-consistent probabilistic framework to test the validity of competing scenarios given a set of data. We present a case study application to strong gravitational lens parametric models. Our goal…
Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…
Increasingly large parameter spaces, used to more accurately model precision observables in physics, can paradoxically lead to large deviations in the inferred parameters of interest -- a bias known as volume projection effects -- when…
The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…
Central limit theorems (CLTs) for high-dimensional random vectors with dimension possibly growing with the sample size have received a lot of attention in the recent times. Chernozhukov et al. (2017) proved a Berry--Esseen type result for…
One of the most criticized features of Bayesian statistics is the fact that credible intervals, especially when open likelihoods are involved, may strongly depend on the prior shape and range. Many analyses involving open likelihoods are…
Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have raised progressive interest recently. The purpose of this paper is to study the strong law of large numbers and the law of the…
The appearance of negative terms in quasiprobability representations of quantum theory is known to be inevitable, and, due to its equivalence with the onset of contextuality, of central interest in quantum computation and information. Until…
Identifying signals that replicate across multiple studies is essential for establishing robust scientific evidence, yet existing methods for high-dimensional replicability analysis either rely on restrictive modeling assumptions, are…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
Upper and lower bounds are derived for the Gaussian mean width of the intersection of a convex hull of $M$ points with an Euclidean ball of a given radius. The upper bound holds for any collection of extreme point bounded in Euclidean norm.…
Recent years have witnessed many successful applications of contrastive learning in diverse domains, yet its self-supervised version still remains many exciting challenges. As the negative samples are drawn from unlabeled datasets, a…
We present cosmological upper limits on the sum of active neutrino masses using large-scale power spectrum data from the WiggleZ Dark Energy Survey and from the Sloan Digital Sky Survey - Data Release 7 (SDSS-DR7) sample of Luminous Red…
The standard cosmological model, known as the LambdaCDM model, has been successful in many respects, but it has some significant discrepancies, some of which have not been resolved yet. In measuring the Hubble-Lematre parameter, there is an…
We discuss the recent proposal by Thommen and Mandel (Phys. Rev. Lett. {\bf 96}, 053601 (2006)) for electromagnetically induced negative refraction. Although the main conclusion of the paper -- the possibility to achieve negative refraction…
Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are…
The variation of the dimensionless fundamental physical constant mu = m_p/m_e (the proton to electron mass ratio) can be constrained via observation of Lyman and Werner lines of molecular hydrogen in the spectra of damped Lyman alpha…
Classically, confidence intervals are required to have consistent coverage across all values of the parameter. However, this will inevitably break down if the underlying estimation procedure is biased. For this reason, many efforts have…