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Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…
Consider a tree network T, where each edge acts as an independent copy of a given channel M, and information is propagated from the root. For which T and M does the configuration obtained at level n of T typically contain significant…
R\'emy's algorithm is a Markov chain that iteratively generates a sequence of random trees in such a way that the $n^{\mathrm{th}}$ tree is uniformly distributed over the set of rooted, planar, binary trees with $2n+1$ vertices. We obtain a…
We introduce two models for multi-type random trees motivated by studies of trait dependence in the evolution of species. Our discrete time model, the multi-type ERM tree, is a generalization of Markov propagation models on a random tree…
Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of…
For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem…
Decision trees are commonly used predictive models due to their flexibility and interpretability. This paper is directed at quantifying the uncertainty of decision tree predictions by employing a Bayesian inference approach. This is…
Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…
We propose Markov two-components processes (M2CP) as a probabilistic model of asynchronous systems based on the trace semantics for concurrency. Considering an asynchronous system distributed over two sites, we introduce concepts and tools…
Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…
We learn the structure of a Markov Network between two groups of random variables from joint observations. Since modelling and learning the full MN structure may be hard, learning the links between two groups directly may be a preferable…
The output of a discrete Markov source is to be encoded instantaneously by a variable-rate encoder and decoded by a finite-state decoder. Our performance measure is a linear combination of the distortion and the instantaneous rate.…
The evolution of aligned DNA sequence sites is generally modeled by a Markov process operating along the edges of a phylogenetic tree. It is well known that the probability distribution on the site patterns at the tips of the tree…
Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic…
It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provide sharp sufficient conditions for the regular variation…
We study the size properties of a general model of fractal sets that are based on a tree-indexed family of random compacts and a tree-indexed Markov chain. These fractals may be regarded as a generalization of those resulting from the…
In binary and ordinal regression one can distinguish between a location component and a scaling component. While the former determines the location within the range of the response categories, the scaling indicates variance heterogeneity.…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
The mother-dependent neutral mutations model describes the evolution of a population across discrete generations, where neutral mutations occur among a finite set of possible alleles. In this model, each mutant child acquires a type…
A recursive function on a tree is a function in which each leaf has a given value, and each internal node has a value equal to a function of the number of children, the values of the children, and possibly an explicitly specified random…