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We develop a theory of estimation when in addition to a sample of $n$ observed outcomes the underlying probabilities of the observed outcomes are known, as is typically the case in the context of numerical simulation modeling, e.g. in…
We introduce a parameterization method called Neural Bayes which allows computing statistical quantities that are in general difficult to compute and opens avenues for formulating new objectives for unsupervised representation learning.…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
Identifying leading measurement units from a large collection is a common inference task in various domains of large-scale inference. Testing approaches, which measure evidence against a null hypothesis rather than effect magnitude, tend to…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference…
In nonparametric statistics, rate-optimal estimators typically balance bias and stochastic error. The recent work on overparametrization raises the question whether rate-optimal estimators exist that do not obey this trade-off. In this work…
Although there are a few works reported in the literature considering loss tomography in the general topology, there is few well established result since all of them rely either on simulations or on experiments that have many random factors…
Measurements of quantum states form a key component in quantum-information processing. It is therefore an important task to compare measurements and furthermore decide if a measurement strategy is optimal. Entropic quantities, such as the…
A number of applications (e.g., AI bot tournaments, sports, peer grading, crowdsourcing) use pairwise comparison data and the Bradley-Terry-Luce (BTL) model to evaluate a given collection of items (e.g., bots, teams, students, search…
In quantum state tomography, the estimated frequencies do not correspond directly to a physical quantum state, due to statistical fluctuations. Thus, one resorts to point estimators that return the state that matches observations the best,…
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…
We discuss the asymptotics of the nonparametric maximum likelihood estimator (NPMLE) in the normal mixture model. We then prove the convergence rate of the NPMLE decision in the empirical Bayes problem with normal observations. We point to…
Nonparametric maximum likelihood estimators (MLEs) in inverse problems often have non-normal limit distributions, like Chernoff's distribution. However, if one considers smooth functionals of the model, with corresponding functionals of the…
General Probabilistic Theories provide the most general mathematical framework for the theory of probability in an operationally natural manner, and generalize classical and quantum theories. In this article, we study state-discrimination…
An empirical Bayes problem has an unknown prior to be estimated from data. The predictive recursion (PR) algorithm provides fast nonparametric estimation of mixing distributions and is ideally suited for empirical Bayes applications. This…
Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…
We propose a flexible and identifiable version of the two-groups model, motivated by hierarchical Bayes considerations, that features an empirical null and a semiparametric mixture model for the non-null cases. We use a computationally…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric…