Related papers: Generalized Nonlinear Yule Models

In this work, a novel approach for the construction and training of time series models is presented that deals with the problem of learning on large time series with non-equispaced observations, which at the same time may possess features…

This paper develops the asymptotic theory for parametric and nonparametric regression models when the errors have a fractional local to unity root (FLUR) model structure. FLUR models are stationary time series with semi-long range…

The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…

Neural network have achieved remarkable successes in many scientific fields. However, the interpretability of the neural network model is still a major bottlenecks to deploy such technique into our daily life. The challenge can dive into…

We study the evolution of the population genealogy in the classic neutral Moran Model of finite size and in discrete time. The stochastic transformations that shape a Moran population can be realized directly on its genealogy and give rise…

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…

This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of…

We study a discrete-time stochastic process that can also be interpreted as a model for a viral evolution. A distinguishing feature of our process is power-law tails due to dynamics that resembles preferential attachment models. In the…

The paper written in 1925 by G. Udny Yule that we celebrate in this special issue introduces several novelties and results that we recall in detail. First, we discuss Yule (1925)'s main legacies over the past century, focusing on empirical…

We propose a framework for fitting fractional polynomials models as special cases of Bayesian Generalized Nonlinear Models, applying an adapted version of the Genetically Modified Mode Jumping Markov Chain Monte Carlo algorithm. The…

Learning causal relationships between variables is a well-studied problem in statistics, with many important applications in science. However, modeling real-world systems remain challenging, as most existing algorithms assume that the…

Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…

We propose the introduction of nonlinear operation into the feature generation process in convolutional neural networks. This nonlinearity can be implemented in various ways. First we discuss the use of nonlinearities in the process of data…

We revisit granular models that represent the size of a firm as the sum of the sizes of multiple constituents or sub-units. Originally developed to address the unexpectedly slow reduction in volatility as firm size increases, these models…

Modern generative machine learning models demonstrate surprising ability to create realistic outputs far beyond their training data, such as photorealistic artwork, accurate protein structures, or conversational text. These successes…

For two decades, the Colless index has been the most frequently used statistic for assessing the balance of phylogenetic trees. In this article, this statistic is studied under the Yule and uniform model of phylogenetic trees. The main tool…

There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…

In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…

This article introduces a causal discovery method to learn nonlinear relationships in a directed acyclic graph with correlated Gaussian errors due to confounding. First, we derive model identifiability under the sublinear growth assumption.…

Stochastic models, based on random processes, may lead to power law distributions, which provide long range correlations. The observation of power law behavior and the presence of long range correlations in biological systems has been…