Related papers: On Optimal Solutions to Compound Statistical Decis…
We consider adaptive decision-making problems where an agent optimizes a cumulative performance objective by repeatedly choosing among a finite set of options. Compared to the classical prediction-with-expert-advice set-up, we consider…
The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…
As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…
Anomaly detection in large populations is a challenging but highly relevant problem. The problem is essentially a multi-hypothesis problem, with a hypothesis for every division of the systems into normal and anomal systems. The number of…
We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample average estimator for a stochastic…
We present a general theorem for distributed synthesis problems in coordination games with $\omega$-regular objectives of the form: If there exists a winning strategy for the coalition, then there exists an "essential" winning strategy,…
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…
We consider the problem of sensitivity of threshold risk, defined as the probability of a function of a random variable falling below a specified threshold level $\delta >0.$ We demonstrate that for polynomial and rational functions of that…
We propose a new approach to solving dynamic decision problems with rewards that are unbounded below. The approach involves transforming the Bellman equation in order to convert an unbounded problem into a bounded one. The major advantage…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
Causal inference problems often involve continuous treatments, such as dose, duration, or frequency. However, identifying and estimating standard dose-response estimands requires that everyone has some chance of receiving any level of the…
Let $\mathbb{K}$ be a field of characteristic $0$. For each choice of distinct $a_1, \ldots, a_n\in \mathbb{K}$ and distinct $b_1, \ldots, b_n\in \mathbb{K}$, consider the sum $S=\sum_{i=1}^n a_i b_{\pi(i)}$ as $\pi$ ranges over the…
New lower bounds involving sum, difference, product, and ratio sets for a set $A\subset \C$ are given. The estimates involving the sum set match, up to constants, the one obtained by Solymosi for the reals and are obtained by generalising…
We characterize the optimal reward functions (scoring rules) that incentivize an agent to acquire information and report it truthfully to the principal. The optimal scoring rules let the agent make a simple binary bet in single-dimensional…
We apply classical statistical decision theory to a large class of treatment choice problems with partial identification. We show that, in a general class of problems with Gaussian likelihood, all decision rules are admissible; it is…
This work explores use of novel advances in best subset selection for regression modelling via continuous optimization for offline change point detection and estimation in univariate Gaussian data sequences. The approach exploits…
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…
An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…
Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…