Related papers: The Absent-Minded Passengers Problem via Computer …
We study $|A + A|$ as a random variable, where $A \subseteq \{0, \dots, N\}$ is a random subset such that each $0 \le n \le N$ is included with probability $0 < p < 1$, and where $A + A$ is the set of sums $a + b$ for $a,b$ in $A$. Lazarev,…
A team of anonymous mobile agents represented by points freely moving in the plane have to gather at a single point and stop. Agents start at different points of the plane and at possibly different times chosen by the adversary. They are…
Large Language Models (LLMs) often produce fluent but factually incorrect responses, a phenomenon known as hallucination. Abstention, where the model chooses not to answer and instead outputs phrases such as "I don't know", is a common…
Nowadays, reaching a high level of employee satisfaction in efficient schedules is an important and difficult task faced by companies. We tackle a new variant of the personnel scheduling problem under unknown demand by considering employee…
Latent variable models can be used to probabilistically "fill-in" missing data entries. The variational autoencoder architecture (Kingma and Welling, 2014; Rezende et al., 2014) includes a "recognition" or "encoder" network that infers the…
In the preceding decade, Andrews and Newman resurrected the concept of a `minimal excludant' of a partition ($mex$, for short), namely, the least positive missing integer in a partition. Subsequently, several authors have not only studied…
Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…
Probability models have been proposed in the literature to account for "intelligent" behavior in many contexts. In this paper, probability propagation is applied to model agent's motion in potentially complex scenarios that include goals…
We have introduced excluded volume effect, which is an important factor to model a realistic pedestrian queue, into queueing theory. The probability distributions of pedestrian number and pedestrian waiting time in a queue have been…
Most practical data science problems encounter missing data. A wide variety of solutions exist, each with strengths and weaknesses that depend upon the missingness-generating process. Here we develop a theoretical framework for training and…
We introduce a new approach to solving path-finding problems under uncertainty by representing them as probabilistic models and applying domain-independent inference algorithms to the models. This approach separates problem representation…
Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This…
We propose an aproach for asymptotic analysis of plane partition statistics related to counts of parts whose sizes exceed a certain suitably chosen level. In our study, we use the concept of conjugate trace of a plane partition of the…
We study a random bisection problem where an initial interval of length x is cut into two random fragments at the first stage, then each of these two fragments is cut further, etc. We compute the probability P_n(x) that at the n-th stage,…
A random variable is sampled from a discrete distribution. The missing mass is the probability of the set of points not observed in the sample. We sharpen and simplify McAllester and Ortiz's results (JMLR, 2003) bounding the probability of…
The goal of the paper is to study asymptotic behavior of the number of lost messages. Long messages are assumed to be divided into a random number of packets which are transmitted independently of one another. An error in transmission of a…
A statistical analysis is performed for a random unrestricted local crew scheduling problem, expressed in terms of pairing arrivals with departures. The analysis is aimed at understanding the structure of similar problems with global…
Hallucinations, a phenomenon where a language model (LM) generates nonfactual content, pose a significant challenge to the practical deployment of LMs. While many empirical methods have been proposed to mitigate hallucinations, recent…
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…
Random flights in $\mathbb{R}^d,d\geq 2,$ with Dirichlet-distributed displacements and uniformly distributed orientation are analyzed. The explicit characteristic functions of the position $\underline{\bf X}_d(t),\,t>0,$ when the number of…