Related papers: The averaging principle
The mean field games (MFG) paradigm was introduced to provide tractable approximations of games involving very large populations. The theory typically rests on two key assumptions: homogeneity, meaning that all players share the same…
Modelling a complex system is almost invariably a challenging task. The incorporation of experimental observations can be used to improve the quality of a model, and thus to obtain better predictions about the behavior of the corresponding…
Auction data often contain information on only the most competitive bids as opposed to all bids. The usual measurement error approaches to unobserved heterogeneity are inapplicable due to dependence among order statistics. We bridge this…
Fairness is desirable yet challenging to achieve within multi-agent systems, especially when agents differ in latent traits that affect their abilities. This hidden heterogeneity often leads to unequal distributions of wealth, even when…
We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Inhomogeneous models of populations and communities allow for birth and death rates to vary among…
Reciprocity, or the tendency of individuals to mirror behavior, is a key measure that describes information exchange in a social network. Users in social networks tend to engage in different levels of reciprocal behavior. Differences in…
An averaging principle is derived for the abstract nonlinear evolution equation where the almost periodic right hand-side is a continuous perturbation of the time-dependent family of linear operators determining a linear evolution system.…
We develop a Bayesian hierarchical semiparametric model for phenomena related to time series of counts. The main feature of the model is its capability to learn a latent pattern of heterogeneity in the distribution of the process innovation…
Alignment with human preferences is commonly framed using a universal reward function, even though human preferences are inherently heterogeneous. We formalize this heterogeneity by introducing user types and examine the limits of the…
Interactions between people are the basis on which the structure of our society arises as a complex system and, at the same time, are the starting point of any physical description of it. In the last few years, much theoretical research has…
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
The minority model was introduced to study the competition between agents with limited information. It has the remarkable feature that, as the amount of information available increases, the collective gain made by the agents is reduced.…
We present a macroeconomic agent-based model that combines several mechanisms operating at the same timescale, while remaining mathematically tractable. It comprises enterprises and workers who compete in a job market and a commodity goods…
Inbreeding homophily is a prevalent feature of human social networks with important individual and group-level social, economic, and health consequences. The literature has proposed an overwhelming number of dimensions along which human…
The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but do not incorporate population-level heterogeneity in infection susceptibility.…
Ensembling is commonly regarded as an effective way to improve the general performance of models in machine learning, while also increasing the robustness of predictions. When it comes to algorithmic fairness, heterogeneous ensembles,…
Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can…