Related papers: Natural selection maximizes Fisher information
This paper focuses on the maximum speed at which biological evolution can occur. I derive inequalities that limit the rate of evolutionary processes driven by natural selection, mutations, or genetic drift. These \emph{rate limits} link the…
The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…
We show how Fisher's information already known particular character as the fundamental information geometric object which plays the role of a metric tensor for a statistical differential manifold, can be derived in a relatively easy manner…
For a given metric $g_{\mu\nu}$, which is identified as Fisher information metric, we generate new constraints for the probability distributions for physical systems. We postulate the existence of intrinsic probability distributions for…
Fisher information and natural gradient provided deep insights and powerful tools to artificial neural networks. However related analysis becomes more and more difficult as the learner's structure turns large and complex. This paper makes a…
Suppose we have $n$ different types of self-replicating entity, with the population $P_i$ of the $i$th type changing at a rate equal to $P_i$ times the fitness $f_i$ of that type. Suppose the fitness $f_i$ is any continuous function of all…
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…
Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from bio-medical imaging to precision measurements. In all of these fields, the central aim is to gather as much information…
In this paper we develop a theory of general selection systems with discrete time and explore the evolution of selection systems, in particular, inhomogeneous populations. We show that the knowledge of the initial distribution of the…
Here we postulate three laws which form a mathematical framework to capture the essence of Darwinian evolutionary dynamics. The second law is most quantitative and is explicitly expressed by a unique form of stochastic differential…
We show that the mathematical form of the information measure of Fisher's I for a Gibbs' canonical probability distribution (the most important one in statistical mechanics) incorporates important features of the intrinsic structure of…
Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between population genetics and evolutionary optimization and formulate a…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
As artificial intelligence systems (AIs) become increasingly produced by recursive self-improvement, a form of evolution may emerge, with the traits of AI systems shaped by the success of earlier AIs in designing and propagating their…
Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that…
Fisher information is a measure of the best precision with which a parameter can be estimated from statistical data. It can also be defined for a continuous random variable without reference to any parameters, in which case it has a…
Many of the mathematical frameworks describing natural selection are equivalent to Bayes Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude…
Mathematical theory of selection systems is developed for a wide class of dynamical models of inhomogeneous populations with discrete time. The Price equation and its particular case, the Fisher Fundamental theorem of natural selection…
There is little doubt in scientific circles that--counting from the origin of life towards today--evolution has led to an increase in the amount of information stored within the genomes of the biosphere. This trend of increasing information…