Related papers: Error threshold in simple landscapes
We investigate an simple evolutionary game of sequences and demonstrate on this example the structure of fitness landscapes in discrete problems. We show the smoothing action of the genotype-phenotype mapping which still makes it feasible…
Reinforcement learning (RL) enables an agent interacting with an unknown MDP $M$ to optimise its behaviour by observing transitions sampled from $M$. A natural entity that emerges in the agent's reasoning is $\widehat{M}$, the maximum…
Accurate and high-resolution Earth system model (ESM) simulations are essential to assess the ecological and socio-economic impacts of anthropogenic climate change, but are computationally too expensive to be run at sufficiently high…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased…
Multiple phenotypic states often arise in a single cell with different gene-expression states that undergo transcription regulation with positive feedback. Recent experiments have shown that at least in E. coli, the gene state switching can…
Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…
In empirical risk optimization, it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly. Recent works…
Markov Population Model is a commonly used framework to describe stochastic systems. Their exact analysis is unfeasible in most cases because of the state space explosion. Approximations are usually sought, often with the goal of reducing…
Chung and Graham define quasirandom subsets of $\mathbb{Z}_n$ to be those with any one of a large collection of equivalent random-like properties. We weaken their definition and call a subset of $\mathbb{Z}_n$ $\epsilon$-balanced if its…
In this manuscript we consider Kernel Ridge Regression (KRR) under the Gaussian design. Exponents for the decay of the excess generalization error of KRR have been reported in various works under the assumption of power-law decay of…
We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is…
We offer theoretical and empirical insights into the impact of exogenous randomness on the effectiveness of random forests with tree-building rules independent of training data. We formally introduce the concept of exogenous randomness and…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…
Random forests are a learning algorithm proposed by Breiman [Mach. Learn. 45 (2001) 5--32] that combines several randomized decision trees and aggregates their predictions by averaging. Despite its wide usage and outstanding practical…
Although a number of studies have shown that natural and laboratory populations initially well-adapted to their environment can evolve rapidly when conditions suddenly change, the dynamics of rapid adaptation are not well understood. Here a…
In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling…
We investigate the learning dynamics of classifiers in scenarios where classes are separable or classifiers are over-parameterized. In both cases, Empirical Risk Minimization (ERM) results in zero training error. However, there are many…
We consider supervised learning with random decision trees, where the tree construction is completely random. The method is popularly used and works well in practice despite the simplicity of the setting, but its statistical mechanism is…
Language models famously improve under a smooth scaling law, but some specific capabilities exhibit sudden breakthroughs in performance. Advocates of "emergence" view these capabilities as unlocked at a specific scale, but others attribute…