Related papers: Information Ranking and Power Laws on Trees
The aim of the current work is to prove a law of large numbers for the range size of recurrent rotor walks with random initial configuration on a general class of trees, called periodic trees or directed covers of graphs.
A step-reinforced random walk is a discrete-time stochastic process with long-range dependence. At each step, with a fixed probability $\alpha$, the so-called positively step-reinforced random walk repeats one of its previous steps, chosen…
Given an edge-weighted tree $T$ with $n$ leaves, sample the leaves uniformly at random without replacement and let $W_k$, $2 \le k \le n$, be the length of the subtree spanned by the first $k$ leaves. We consider the question, "Can $T$ be…
A new version of a Strong Law of Large Numbers is proposed in this note for pairwise independent random variables. The main goal is to relax the assumption on a finite expectation for each term.
Via a coupling argument, it is proved that the solution to a renewal equation has a power law decay rate in the case of a spread out interarrival distribution. By the regenerative property, the convergence in distribution for the recurrence…
Science in the 21st century seems to be governed by novel approaches involving interdisciplinary work, systemic perspectives and complexity theory concepts. These new paradigms force us to leave aside our elder mechanistic approaches and…
Decision trees and their ensembles are popular in machine learning as easy-to-understand models. Several techniques have been proposed in the literature for learning tree-based classifiers, with different techniques working well for data…
Decision trees and decision rule systems play important roles as classifiers, knowledge representation tools, and algorithms. They are easily interpretable models for data analysis, making them widely used and studied in computer science.…
Many man-made and natural phenomena, including the intensity of earthquakes, population of cities and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has…
Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment…
We introduce a Green function and analogues of other related kernels for finite and infinite networks whose edge weights are complex-valued admittances with positive real part. We provide comparison results with the same kernels associated…
In real practice, questions are typically complex and knowledge-intensive, requiring Large Language Models (LLMs) to recognize the multifaceted nature of the question and reason across multiple information sources. Iterative and adaptive…
Variable selection for high-dimensional linear models has received a lot of attention lately, mostly in the context of l1-regularization. Part of the attraction is the variable selection effect: parsimonious models are obtained, which are…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
In real-world scenarios, where knowledge distributions exhibit long-tail. Humans manage to master knowledge uniformly across imbalanced distributions, a feat attributed to their diligent practices of reviewing, summarizing, and correcting…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
We derive two formulas for the weighted sums of rooted spanning forests of particular sequence of graphs by using the matrix tree theorem. We consider cycle graphs with edges so called the pendant edges. One of our formula can be described…
Decision trees are well-known due to their ease of interpretability. To improve accuracy, we need to grow deep trees or ensembles of trees. These are hard to interpret, offsetting their original benefits. Shapley values have recently become…
This paper concerns the recursive utility maximization problem under partial information. We first transform our problem under partial information into the one under full information. When the generator of the recursive utility is concave,…
We establish the large deviation probabilities for the height of random recursive trees, revealing polynomial upper-tail decay and stretched-exponential lower-tail decay. Remarkably, the lower tail features an atypical prefactor that grows…