相关论文: Large deviations analysis for random combinatorial…
In this paper, we present a cluster algorithm for the numerical simulations of non-additive hard-core mixtures. This algorithm allows one to simulate and equilibrate systems with a number of particles two orders of magnitude larger than…
A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
Biclustering algorithms play a central role in the biotechnological and biomedical domains. The knowledge extracted supports the extraction of putative regulatory modules, essential to understanding diseases, aiding therapy research, and…
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…
We investigate the predictability of large language model (LLM) capabilities: given records of past experiments using different model families, numbers of parameters, tasks, and numbers of in-context examples, can we accurately predict LLM…
We study high-dimensional Bayesian linear regression with a general beta prime distribution for the scale parameter. Under the assumption of sparsity, we show that appropriate selection of the hyperparameters in the beta prime prior leads…
We apply the Ginzburg criterion to the dimer problem and we solve the apparent contradiction of a system with mean field $\alpha={1\over2}$, the typical value of tricritical systems, and upper critical dimension $D_{cr}=6$. We find that the…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
We investigate trends in the data-error scaling laws of machine learning (ML) models trained on discrete combinatorial spaces that are prone-to-mutation, such as proteins or organic small molecules. We trained and evaluated kernel ridge…
Binary mixtures growing on small-world networks under far-from-equilibrium conditions are studied by means of extensive Monte Carlo simulations. For any positive value of the shortcut fraction of the network ($p>0$), the system undergoes a…
Mixture models are flexible tools in density estimation and classification problems. Bayesian estimation of such models typically relies on sampling from the posterior distribution using Markov chain Monte Carlo. Label switching arises…
In binary classification, imbalance refers to situations in which one class is heavily under-represented. This issue is due to either a data collection process or because one class is indeed rare in a population. Imbalanced classification…
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the…
In bidisperse particle mixtures varying in size or density alone, large particles rise (driven by percolation) and heavy particles sink (driven by buoyancy). When the two particle species differ from each other in both size and density, the…
Consider a branching system with particles moving according to an Ornstein-Uhlenbeck process with drift $\mu>0$ and branching according to a law in the domain of attraction of the $(1+\beta)$-stable distribution. The mean of the branching…
In this paper, I relate the phase separation transition in binary hard-core mixtures in the limit of small size ratio to a bond percolation transition. It allows to estimate the critical packing fraction at the transition as a function of…
Big data sets must be carefully partitioned into statistically similar data subsets that can be used as representative samples for big data analysis tasks. In this paper, we propose the random sample partition (RSP) data model to represent…
The Linear Ballistic Accumulator (Brown & Heathcote, 2008) model is used as a measurement tool to answer questions about applied psychology. The analyses based on this model depend upon the model selected and its estimated parameters.…