Related papers: The Replicator Equation as an Inference Dynamic
A representative researcher has repeated opportunities for empirical research. To process findings, she must impose an "identifying assumption." She conducts research when the assumption is sufficiently plausible (taking into account both…
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…
In a well-known paper, Jeremy England derived a bound on the free energy dissipated by a self-replicating system [England, "Statistical physics of self-replication", The Journal of Chemical Physics, 2013]. This bound is usually interpreted…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
We study a class of evolutionary game dynamics defined by balancing a gain determined by the game's payoffs against a cost of motion that captures the difficulty with which the population moves between states. Costs of motion are…
A thesaurus is one, out of many, possible representations of term (or word) connectivity. The terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph. The directionality of the links retains all…
We consider an infinite-sized population where an infinite number of traits compete simultaneously. The replicator equation with a diffusive term describes time evolution of the probability distribution over the traits due to selection and…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
This paper introduces a general class of Replicator-Mutator equations on a multi-dimensional fitness space. We establish a novel probabilistic representation of weak solutions of the equation by using the theory of Fockker-Planck-Kolmogorov…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…
Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…
Many published research results are false, and controversy continues over the roles of replication and publication policy in improving the reliability of research. Addressing these problems is frustrated by the lack of a formal framework…
Natural phenomenon of coevolution is the reciprocally induced evolutionary change between two or more species or population. Though this biological occurrence is a natural fact, there are only few attempts to use this as a simile in…
Statistical inference from data is a foundational task in science. Recently, it has received growing attention for its central role in inference systems of primary interest in data sciences and machine learning. However, the understanding…
We describe a connectionist model that attempts to capture a notion of experience-based problem solving or task learning, whereby solutions to newly encountered problems are composed from remembered solutions to prior problems. We apply…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
We describe inferactive data analysis, so-named to denote an interactive approach to data analysis with an emphasis on inference after data analysis. Our approach is a compromise between Tukey's exploratory (roughly speaking "model free")…