Related papers: Information Ranking and Power Laws on Trees

We study the emergence of a power law distribution in the systems which can be characterized by a hierarchically organized supplying network. It is shown that conservation laws on the branches of the network can, at some approximation,…

We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the…

Consider the linear nonhomogeneous fixed point equation R =_d sum_{i=1}^N C_i R_i + Q, where (Q,N,C_1,...,C_N) is a random vector with N in{0,1,2,3,...}U{infty}, {C_i}_{i=1}^N >= 0, P(|Q|>0) > 0, and {R_i}_{i=1}^N is a sequence of i.i.d.…

We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of…

The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…

This paper investigates the information encoded in the embeddings of large language models (LLMs). We conduct simulations to analyze the representation entropy and discover a power law relationship with model sizes. Building upon this…

We consider linear preferential attachment trees, and show that they can be regarded as random split trees in the sense of Devroye (1999), although with infinite potential branching. In particular, this applies to the random recursive tree…

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…

Precision medicine provides customized treatments to patients based on their characteristics and is a promising approach to improving treatment efficiency. Large scale omics data are useful for patient characterization, but often their…

We study the broadcasting problem when the underlying tree is a random recursive tree. The root of the tree has a random bit value assigned. Every other vertex has the same bit value as its parent with probability $1-q$ and the opposite…

We consider the following recurrence relation with random i.i.d. coefficients $(a_n,b_n)$: $$ x_{n+1}=a_{n+1} x_n+b_{n+1} $$ where $a_n\in GL(d,\mathbb{R}),b_n\in \mathbb{R}^d$. Under natural conditions on $(a_n,b_n)$ this equation has a…

Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and…

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…

Estimating individualized treatment rules is a central task for personalized medicine. [zhao2012estimating] and [zhang2012robust] proposed outcome weighted learning to estimate individualized treatment rules directly through maximizing the…

We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…

In the last years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipf's systems, due to the discreteness of the variables and to the existence of two representations…

Tree-based ensemble methods, as Random Forests and Gradient Boosted Trees, have been successfully used for regression in many applications and research studies. Furthermore, these methods have been extended in order to deal with uncertainty…

In this thesis the properties of two kinds of non-uniform random recursive trees are studied. In the first model weights are assigned to each node, thus altering the attachment probabilities. We will call these trees weighted recursive…

We prove a strong form of the invariance under re-rooting of the distribution of the continuous random trees called Levy trees. This extends previous results due to several authors.

Online decision tree learning algorithms typically examine all features of a new data point to update model parameters. We propose a novel alternative, Reinforcement Learning- based Decision Trees (RLDT), that uses Reinforcement Learning…