Related papers: A Link Between The Continuous And The Discrete Log…
While normalizing flows have led to significant advances in modeling high-dimensional continuous distributions, their applicability to discrete distributions remains unknown. In this paper, we show that flows can in fact be extended to…
Evolutionary game theory, encompassing discrete, continuous, and mixed strategies, is pivotal for understanding cooperation dynamics. Discrete strategies involve deterministic actions with a fixed probability of one, whereas continuous…
The use of continuous probability distributions has been widespread in problems with purely discrete nature. In general, such distributions are not appropriate in this scenario. In this paper, we introduce a class of discrete and asymmetric…
Discrete and Continuous Dynamics is the first in a series of articles on Network Models for Epidemiology. This project began in the Fall quarter of 2014 in my continuous modeling course. Since then, it has taken off and turned into a series…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
Using results from convex analysis, we investigate a novel approach to identification and estimation of discrete choice models which we call the Mass Transport Approach (MTA). We show that the conditional choice probabilities and the…
Classical Biplot Methods allow for the simultaneous representation of individuals (rows) and variables (columns) of a data matrix. For Binary data, Logistic biplots have been recently developed.When data are nominal, linear or even binary…
The problem of multi-agent learning and adaptation has attracted a great deal of attention in recent years. It has been suggested that the dynamics of multi agent learning can be studied using replicator equations from population biology.…
In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour, whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to…
Large Language Models (LLMs) are increasingly used in tasks such as psychological text analysis and decision-making in automated workflows. However, their reliability remains a concern due to potential biases inherited from their training…
In this paper we analyze a continuous-time epidemic model and its discrete counterpart, where infection spreads both horizontally and vertically. We consider three cases: model with horizontal and imperfect vertical transmissions, model…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Linear approximations to the decision boundary of a complex model have become one of the most popular tools for interpreting predictions. In this paper, we study such linear explanations produced either post-hoc by a few recent methods or…
Biological systems are generally complicated and/or complex. In the former approach, one sets up a model with a large number of parameters to describe the system in detail. The latter approach focuses on understanding the universal aspects…
Accurately predicting future behaviors of surrounding vehicles is an essential capability for autonomous vehicles in order to plan safe and feasible trajectories. The behaviors of others, however, are full of uncertainties. Both rational…
Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven to be expressive tools for…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game…