Related papers: Cycling in the forest with Wilson's algorithm
The matrices of spanning rooted forests are studied as a tool for analysing the structure of digraphs and measuring their characteristics. The problems of revealing the basis bicomponents, measuring vertex proximity, and ranking from…
Random forests are a statistical learning technique that use bootstrap aggregation to average high-variance and low-bias trees. Improvements to random forests, such as applying Lasso regression to the tree predictions, have been proposed in…
I develop Macroeconomic Random Forest (MRF), an algorithm adapting the canonical Machine Learning (ML) tool to flexibly model evolving parameters in a linear macro equation. Its main output, Generalized Time-Varying Parameters (GTVPs), is a…
The structure of an evolving network contains information about its past. Extracting this information efficiently, however, is, in general, a difficult challenge. We formulate a fast and efficient method to estimate the most likely history…
The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
The wealth of data being gathered about humans and their surroundings drives new machine learning applications in various fields. Consequently, more and more often, classifiers are trained using not only numerical data but also complex data…
In materials science, data-driven methods accelerate material discovery and optimization while reducing costs and improving success rates. Symbolic regression is a key to extracting material descriptors from large datasets, in particular…
We prove a new formula for the generating function of multitype Cayley trees counted according to their degree distribution. Using this formula we recover and extend several enumerative results about trees. In particular, we extend some…
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…
Random survival forest and survival trees are popular models in statistics and machine learning. However, there is a lack of general understanding regarding consistency, splitting rules and influence of the censoring mechanism. In this…
This paper considers the problem of matching fragment to organism using its complete genome. Our method is based on the probability measure representation of a genome. We first demonstrate that these probability measures can be modelled as…
The goal of this note is twofold: first, we explain the relation between the isomorphism theorems in the context of vertex reinforced jump process discovered in [BHS19, BHS21] and the standard Markovian isomorphism theorems for Markovian…
Spatially Coherent Random Forest (SCRF) extends Random Forest to create spatially coherent labeling. Each split function in SCRF is evaluated based on a traditional information gain measure that is regularized by a spatial coherency term.…
Throughout the last decade, random forests have established themselves as among the most accurate and popular supervised learning methods. While their black-box nature has made their mathematical analysis difficult, recent work has…
This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability spaces. We establish a "broken exponential martingale" expansion that generalizes and unifies the exponentiation result of…
Random Forest (RFs) are among the most widely used Machine Learning (ML) classifiers. Even though RFs are not interpretable, there are no dedicated non-heuristic approaches for computing explanations of RFs. Moreover, there is recent work…
Random forests construct each tree with a different, randomised representation of the feature space. Their uniform voting cannot correct errors in regions where trees with incorrect representations probabilistically outnumber correct ones,…
Random forests are a very effective and commonly used statistical method, but their full theoretical analysis is still an open problem. As a first step, simplified models such as purely random forests have been introduced, in order to shed…
It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such Sample Space Reducing processes…