Related papers: On the optimality of likelihood ratio test for pro…
The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…
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…
The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the…
We characterize the maximal attainable power-size gap in overidentified instrumental variables models with heteroskedastic or autocorrelated (HAC) errors. Using total variation distance and Kraft's theorem, we define the decision theoretic…
We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Reinforcement learning is the method of choice to train models in sampling-based setups with binary outcome feedback, such as navigation, code generation, and mathematical problem solving. In such settings, models implicitly induce a…
The paper studies distributed binary hypothesis testing over a two-hop relay network where both the relay and the receiver decide on the hypothesis. Both communication links are subject to expected rate constraints, which differs from the…
We provide a general theoretical analysis of expected out-of-sample utility, also referred to as decision-theoretic classification, for non-decomposable binary classification metrics such as F-measure and Jaccard coefficient. Our key result…
We study the population limit maximum regret (MR) of plug-in prediction when the decision problem is to choose between two treatments for the members of a population with observed covariates x. In this setting, the optimal treatment for…
This paper studies relations among axioms on individuals' intertemporal choices under risk. The focus is on Risk Averse over Time Lotteries (RATL), meaning that a fixed prize is preferred to a lottery with the same monetary prize but a…
We develop a mathematical framework to define an optimal individualized treatment rule (ITR) within the context of prioritized outcomes in a randomized controlled trial. Our optimality criterion is based on the framework of generalized…
We study a variation of Bayesian M-ary hypothesis testing in which the test outputs a list of L candidates out of the M possible upon processing the observation. We study the minimum error probability of list hypothesis testing, where an…
We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations could be defined by a biomarker or risk factor measured at…
A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…
Prior work on automatic control synthesis for cyber-physical systems under logical constraints has primarily focused on environmental disturbances or modeling uncertainties, however, the impact of deliberate and malicious attacks has been…
The proliferation of Large Language Models (LLMs) necessitates valid evaluation methods to guide downstream applications and actionable future improvements. The Item Response Theory (IRT) has recently emerged as a promising framework for…
We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988],…
Measuring the F\"{o}rster resonance energy transfer (FRET) efficiency of freely diffusing single molecules provides information about the sampled conformational states of the molecules. Under equilibrium conditions, the distribution of the…
This paper proposes and axiomatizes a new updating rule: Relative Maximum Likelihood (RML) for ambiguous beliefs represented by a set of priors (C). This rule takes the form of applying Bayes' rule to a subset of C. This subset is a linear…