Related papers: Optimal e-values for testing the mean of a bounded…
In this paper, we obtain bounds on the probability of convergence to the optimal solution for the compact Genetic Algorithm (cGA) and the Population Based Incremental Learning (PBIL). We also give a sufficient condition for convergence of…
Conventional methods for analyzing composite endpoints in clinical trials often only focus on the time to the first occurrence of all events in the composite. Therefore, they have inherent limitations because the individual patients' first…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…
We present a unified framework ensuring well posedness and providing stability estimates to a class of Initial Boundary Value Problems for renewal equations comprising a variety of biological or epidemiological models. This versatility is…
We analyze common types of e-variables and e-processes for composite exponential family nulls: the optimal e-variable based on the reverse information projection (RIPr), the conditional (COND) e-variable, and the universal inference (UI)…
Regression models are essential for a wide range of real-world applications. However, in practice, target values are not always precisely known; instead, they may be represented as intervals of acceptable values. This challenge has led to…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
This paper investigates and bounds the expected solution quality of combinatorial optimization problems when feasible solutions are chosen at random. Loose general bounds are discovered, as well as families of combinatorial optimization…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
We derive adjusted signed likelihood ratio statistics for a general class of extreme value regression models. The adjustments reduce the error in the standard normal approximation to the distribution of the signed likelihood ratio…
Optimal design of distributed decision policies can be a difficult task, illustrated by the famous Witsenhausen counterexample. In this paper we characterize the optimal control designs for the vector-valued setting assuming that it results…
In recent years, Machine Learning algorithms, in particular supervised learning techniques, have been shown to be very effective in solving regression problems. We compare the performance of a newly proposed regression algorithm against…
We propose an estimator for the mean of random variables in separable real Banach spaces using the empirical characteristic function. Assuming that the covariance operator of the random variable is bounded in a precise sense, we show that…
We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood…
It is well known that machine learning methods can be vulnerable to adversarially-chosen perturbations of their inputs. Despite significant progress in the area, foundational open problems remain. In this paper, we address several key…
We introduce the notion of p*-values (p*-variables), which generalizes p-values (p-variables) in several senses. The new notion has four natural interpretations: operational, probabilistic, Bayesian, and frequentist. A main example of a…
We study a counterfactual mean-variance optimization, where the mean and variance are defined as functionals of counterfactual distributions. The optimization problem defines the optimal resource allocation under various constraints in a…
The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…
The Negative Binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard Normal approximation often does not provide adequate…
The growth rate of organisms depends both on external conditions and on internal states, such as the expression levels of various genes. We show that to achieve a criterion mean growth rate over an ensemble of conditions, the internal…