Related papers: Computing the Distribution of a Tree Metric

We study the growth of a time-ordered rooted tree by probabilistic attachment of new vertices to leaves. We construct a likelihood function of the leaves based on the connectivity of the tree. We take such connectivity to be induced by the…

Random Forest (RF) is a widely used ensemble learning technique known for its robust classification performance across diverse domains. However, it often relies on hundreds of trees and all input features, leading to high inference cost and…

In this article we compare the known dynamical polynomial time algorithm for the game-over attack strategy, to that of the brute force approach; of checking all the ordered rooted subtrees of a given tree that represents a given computer…

Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…

We consider the number of common edges in two independent random spanning trees of a graph $G$. For complete graphs $K_n$, we give a new proof of the fact, originally obtained by Moon, that the distribution converges to a Poisson…

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…

Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…

Random forests are popular methods for regression and classification analysis, and many different variants have been proposed in recent years. One interesting example is the Mondrian random forest, in which the underlying constituent trees…

There is a sequence of random numbers x1,x2, ..., xn and so on. Numbers are independent of each other, but all numbers are from the same continuous distribution. If x1 < x2 > x3, then x2 is a local maximum. Here, we show that the…

We study the problem of approximating a discrete probability distribution, such as the next-token distribution of a large language model, by a dyadic distribution induced by a binary tree under encoding rate constraints. The objective is to…

For a tree Markov random field non-reconstruction is said to hold if as the depth of the tree goes to infinity the information that a typical configuration at the leaves gives about the value at the root goes to zero. The distribution of…

The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…

We propose a procedure to build a decision tree which approximates the performance of complex machine learning models. This single approximation tree can be used to interpret and simplify the predicting pattern of random forests (RFs) and…

We introduce and study the problem of posterior inference on tree-structured graphical models in the presence of a malicious adversary who can corrupt some observed nodes. In the well-studied broadcasting on trees model, corresponding to…

A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…

The search for similarity and dissimilarity measures on phylogenetic trees has been motivated by the computation of consensus trees, the search by similarity in phylogenetic databases, and the assessment of clustering results in…

We consider the model of random trees introduced by Devroye [SIAM J. Comput. 28 (1999) 409-432]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion…

Distance-based approaches in phylogenetics such as Neighbor-Joining are a fast and popular approach for building trees. These methods take pairs of sequences from them construct a value that, in expectation, is additive under a stochastic…

Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric…

We consider a random tree and introduce a metric in the space of trees to define the ``mean tree'' as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and…