Related papers: Stanley-Wilf Limits for Patterns in Rooted Labeled…
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.
Assume we are given a set of items from a general metric space, but we neither have access to the representation of the data nor to the distances between data points. Instead, suppose that we can actively choose a triplet of items (A,B,C)…
Jel\'inek, Mansour, and Shattuck studied Wilf-equivalence among pairs of patterns of the form $\{\sigma,\tau\}$ where $\sigma$ is a set partition of size $3$ with at least two blocks. They obtained an upper bound for the number of…
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…
Random Forests (RFs) are strong machine learning tools for classification and regression. However, they remain supervised algorithms, and no extension of RFs to the one-class setting has been proposed, except for techniques based on…
We develop a finite-sample, design-based theory for random forests in which each tree is a randomized conditional predictor acting on fixed covariates and the forest is their Monte Carlo average. An exact variance identity separates Monte…
We present a new method for inferring species trees from multi-copy gene trees. Our method is based on a generalization of the Robinson-Foulds (RF) distance to multi-labeled trees (mul-trees), i.e., gene trees in which multiple leaves can…
Random forests on the one hand, and neural networks on the other hand, have met great success in the machine learning community for their predictive performance. Combinations of both have been proposed in the literature, notably leading to…
We study the long-term behavior of weighted multi-type branching processes, focusing on extending classical laws of large numbers and martingale convergence to settings with infinitely many weighted particles, arbitrary type spaces and…
In this paper we consider $q$-state potential on general infinite trees with a nearest-neighbor $p$-adic interactions given by a stochastic matrix. {We show the uniqueness of the associated Markov chain ({\em splitting Gibbs measures})…
Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
We consider general Gaussian latent tree models in which the observed variables are not restricted to be leaves of the tree. Extending related recent work, we give a full semi-algebraic description of the set of covariance matrices of any…
We provide a uniform upper bound on the minimal drift so that the one-per-site frog model on a $d$-ary tree is recurrent. To do this, we introduce a subprocess that couples across trees with different degrees. Finding couplings for frog…
We present here a new and universal approach for the study of random and/or trees, unifying in one framework many different models, including some novel ones not yet understood in the literature. An and/or tree is a Boolean expression…
Random forests are widely used in regression. However, the decision trees used as base learners are poor approximators of linear relationships. To address this limitation we propose RaFFLE (Random Forest Featuring Linear Extensions), a…
Multi-target regression is useful in a plethora of applications. Although random forest models perform well in these tasks, they are often difficult to interpret. Interpretability is crucial in machine learning, especially when it can…
We propose Range and Roots which are two common patterns useful for specifying a wide range of counting and occurrence constraints. We design specialised propagation algorithms for these two patterns. Counting and occurrence constraints…
Stankova and West proved in 2002 that the patterns 231 and 312 are shape-Wilf-equivalent. Their proof was nonbijective and fairly complicated. We give a new characterization of 231 and 312 avoiding full rook placements and use this to give…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…