Related papers: Randomisation in the Josephus Problem
In this paper, I propose a method for correcting sample selection bias when the outcome of interest is categorical, such as occupational choice, health status, or field of study. Classical approaches to sample selection rely on strong…
The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider…
In this work, we study a new approach to optimizing the margin distribution realized by binary classifiers. The classical approach to this problem is simply maximization of the expected margin, while more recent proposals consider…
We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the…
In this paper we make a survey on the so called randomization method, a recent methodology to study stochastic optimization problems. It allows to represent the value function of an optimal control problem by a suitable backward stochastic…
We present a new variant of the secretary problem. Let $A$ be a totally ordered set of $n$ \emph{applicants}. Given $P\subseteq A$ and $x\in A$, let $rr(P,x)=\vert\{z\in P \mid z\leq x\}\vert\mbox{ }$ be the \emph{relative rank of} $x$…
Random walks and Lorentz processes serve as fundamental models for Brownian motion. The study of random walks is a favorite object of probability theory, whereas that of Lorentz processes belongs to the theory of hyperbolic dynamical…
We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version,…
Inspired by an example of Grebogi et al [1], we study a class of model systems which exhibit the full two-step scenario for the nonautonomous Hopf bifurcation, as proposed by Arnold [2]. The specific structure of these models allows a…
We consider the problem of strategic classification, where a learner must build a model to classify agents based on features that have been strategically modified. Previous work in this area has concentrated on the case when the learner is…
The number of recurrent events before a terminating event is often of interest. For instance, death terminates an individual's process of rehospitalizations and the number of rehospitalizations is an important indicator of economic cost. We…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal…
Penalization of the likelihood by Jeffreys' invariant prior, or by a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial generalized linear models. The class of…
Sortition is a political system in which decisions are made by panels of randomly selected citizens. The process for selecting a sortition panel is traditionally thought of as uniform sampling without replacement, which has strong fairness…
We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…
Motivated by real-world machine learning applications, we consider a statistical classification task in a sequential setting where test samples arrive sequentially. In addition, the generating distributions are unknown and only a set of…
We define a new variant of exclusion processes in discrete time that has jump probabilities that depend on the last jump performed. In a particular limit for the jump probabilities and in suitable scaling limits for space and time, we…