Related papers: Analyzing Generalized P\'olya Urn Models using Mar…
Random walks (RWs) are fundamental stochastic processes with applications across physics, computer science, and information processing. A recent extension, the laser chaos decision-maker, employs chaotic time series from semiconductor…
The universe involves many independent co-learning agents as an ever-evolving part of our observed environment. Yet, in practice, Multi-Agent Reinforcement Learning (MARL) applications are typically constrained to small, homogeneous…
We used the random walk to model the problem of reserves. The classic case of a stochastic process is the example of random walks, which are used to study a set of phenomena and, particularly, as in this article, models of reserves…
The purpose of this paper is to investigate the asymptotic behavior of the multi-dimensional elephant random walk (MERW). It is a non-Markovian random walk which has a complete memory of its entire history. A wide range of literature is…
We consider a general class of Markovian models describing the growth in a randomly fluctuating environment of a clonal biological population having several phenotypes related by stochastic switching. Phenotypes differ e.g. by the level of…
Of theories for why large-scale machine learning models generalize despite being vastly overparameterized, which of their assumptions are needed to capture the qualitative phenomena of generalization in the real world? On one hand, we find…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via…
We consider a recent innovative theory by Chastain et al. on the role of sex in evolution [PNAS'14]. In short, the theory suggests that the evolutionary process of gene recombination implements the celebrated multiplicative weights updates…
In this paper, we introduce the elephant random walk (ERW) with memory consisting of randomly selected steps from its history. It is a time-changed variant of the standard elephant random walk with memory consisting of its full history. At…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
This paper analyzes a simplified model of viral infection and evolution using the 'grand canonical ensemble' and formalisms from statistical mechanics and thermodynamics to enumerate all possible viruses and to derive thermodynamic…
Tournament solutions are standard tools for identifying winners based on pairwise comparisons between competing alternatives. The recently studied notion of margin of victory (MoV) offers a general method for refining the winner set of any…
Randomized trials are considered the gold standard for estimating causal effects. Trial findings are often used to inform policy and programming efforts, yet their results may not generalize well to a relevant target population due to…
Consider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn…
The random vector of frequencies in a generalized urn model is viewed as conditionally independent random variables, given their sum. Such a representation is exploited to derive Edgeworth expansions for a sum of functions of such…
The behaviour of gene regulatory networks (GRNs) is typically analysed using simulation-based statistical testing-like methods. In this paper, we demonstrate that we can replace this approach by a formal verification-like method that gives…
Composite endpoints are widely used in cardiovascular clinical trials to improve statistical efficiency while preserving clinical relevance. The Win Ratio (WR) measure and more general frameworks of Win Statistics have emerged as…
The Generalized P\'{o}lya Urn (GPU) is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we propose a sequential…
We consider the problem of correctly identifying the \textit{mode} of a discrete distribution $\mathcal{P}$ with sufficiently high probability by observing a sequence of i.i.d. samples drawn from $\mathcal{P}$. This problem reduces to the…