Related papers: Error threshold in simple landscapes
We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0,1,...,L} and has a natural reproduction rate, a logistic death rate due to age or competition and a probability of mutation…
In this work we develop a microscopic physical model of early evolution, where phenotype,organism life expectancy, is directly related to genotype, the stability of its proteins in their native conformations which can be determined exactly…
In this paper we discuss how to evaluate the differences between fitted logistic regression models across sub-populations. Our motivating example is in studying computerized diagnosis for learning disabilities, where sub-populations based…
Two types of random evolution processes are studied for ensembles of the standard map with driving parameter $K$ that determines its degree of stochasticity. For one type of processes the parameter $K$ is chosen at random from a Gaussian…
In clinical trials and other applications, we often see regions of the feature space that appear to exhibit interesting behaviour, but it is unclear whether these observed phenomena are reflected at the population level. Focusing on a…
In considering evolution of transcribed regions, regulatory modules, and other genomic loci of interest, we are often faced with a situation in which the number of allelic states greatly exceeds the population size. In this limit, the…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
In supervised learning, the redundancy contained in random examples can be avoided by learning from queries. Using statistical mechanics, we study learning from minimum entropy queries in a large tree-committee machine. The generalization…
Neural Collapse is a phenomenon where the last-layer representations of a well-trained neural network converge to a highly structured geometry. In this paper, we focus on its first (and most basic) property, known as NC1: the within-class…
Although overparameterized models have achieved remarkable practical success, their theoretical properties, particularly their generalization behavior, remain incompletely understood. The well known double descents phenomenon suggests that…
By using a previously established exact characterization of the ground state of random potential systems in the thermodynamic limit, we determine the ground and first excited energy levels of quantum random energy models, discrete and…
In this paper we consider two continuous-mass population models as analogues of logistic branching random walks, one is supported on a finite trait space and the other one is supported on an infinite trait space. For the first model with…
We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description…
In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…
We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection…
Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…
A major effort in modern high-dimensional statistics has been devoted to the analysis of linear predictors trained on nonlinear feature embeddings via empirical risk minimization (ERM). Gaussian equivalence theory (GET) has emerged as a…
Despite empirical risk minimization (ERM) is widely applied in the machine learning community, its performance is limited on data with spurious correlation or subpopulation that is introduced by hidden attributes. Existing literature…
We explore the connection between migration patterns and emergent behaviors of evolving populations in spatially heterogeneous environments. Despite extensive studies in ecologically and medically important systems, a unifying framework…
Some species exhibit very high levels of DNA sequence variability; there is also evidence for the existence of heritable epigenetic variants that experience state changes at a much higher rate than sequence variants. In both cases, the…