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Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
One of the most fundamental concepts of evolutionary dynamics is the "fixation" probability, i.e. the probability that a mutant spreads through the whole population. Most natural communities are geographically structured into habitats…
In this paper, we develop a node-based approximate model for Markovian contagion dynamics on networks. We prove that our approximate model is exact for SIR (susceptible-infectious-recovered) and SEIR…
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…
We study the Susceptible-Infected-Recovered (SIR) and the Susceptible-Exposed-Infected-Recovered (SEIR) models of epidemics, with possibly time-varying rates, on a class of networks that are locally tree-like, which includes sparse…
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…
We study the SIR ("susceptible, infected, removed/recovered") model on directed graphs with heterogeneous transmission probabilities within the message-passing approximation. We characterize the percolation transition, predict cluster size…
Phylogenetic trees describe the relationships between species in the evolutionary process, and provide information about the rates of diversification. To understand the mechanisms behind macroevolution, we consider a class of multitype…
We study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral…
The branching structure of biological evolution confers statistical dependencies on phenotypic trait values in related organisms. For this reason, comparative macroevolutionary studies usually begin with an inferred phylogeny that describes…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
It is well known that the Cox-Ingersoll-Ross (CIR) stochastic model to study the term structure of interest rates, as introduced in 1985, is inadequate for modelling the current market environment with negative short interest rates.…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
We adopt a maximum-likelihood framework to estimate parameters of a stochastic susceptible-infected-recovered (SIR) model with contact tracing on a rooted random tree. Given the number of detectees per index case, our estimator allows to…
Forward-time models of diversification (i.e., speciation and extinction) produce phylogenetic trees that grow "vertically" as time goes by. Pruning the extinct lineages out of such trees leads to natural models for reconstructed trees…
Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from training to testing stages while the…
Three types of explicit estimators are proposed here to estimate the loss rates of the links in a network of the tree topology. All of them are derived by the maximum likelihood principle and proved to be either asymptotic unbiased or…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
A Profile Mixture Model is a model of protein evolution, describing sequence data in which sites are assumed to follow many related substitution processes on a single evolutionary tree. The processes depend in part on different amino acid…