Related papers: Implicit Renewal Theory and Power Tails on Trees
We develop a theoretical framework for the analysis of oblique decision trees, where the splits at each decision node occur at linear combinations of the covariates (as opposed to conventional tree constructions that force axis-aligned…
This paper investigates Hawkes processes on the positive real line exhibiting both self-excitation and inhibition. Each point of this point process impacts its future intensity by the addition of a signed reproduction function. The case of…
Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol…
Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of…
We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large-z…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
There is a growing desire in the field of reinforcement learning (and machine learning in general) to move from black-box models toward more "interpretable AI." We improve interpretability of reinforcement learning by increasing the utility…
Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are…
Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes…
We formalize the tail redundancy of a collection of distributions over a countably infinite alphabet, and show that this fundamental quantity characterizes the asymptotic per-symbol redundancy of universally compressing sequences generated…
We consider the Brownian tree introduced by Aldous and the associated Q-process which consists in an infinite spine on which are grafted independent Brownian trees. We present a reversal procedure on these trees that consists in looking at…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…
In this article, we study concave recursions on trees, which appear widely in information theory through algorithms such as belief propagation, and in statistical mechanics through models on tree-like graphs, including the Ising model,…
We study a random walk $\mathbf{S}_n$ on $\mathbb{Z}^d$ ($d\geq 1$), in the domain of attraction of an operator-stable distribution with index $\boldsymbol{\alpha}=(\alpha_1,\ldots,\alpha_d) \in (0,2]^d$: in particular, we allow the…
Several terms in an asynptotic estimate for the renewal mass function ina discrete random walk which has positive mean and regularly varying right-hand tail are given. Similar results are given for the renewal density function in the…
We propose a new modification of the coupling method for renewal process in continuous time. We call this modification "the stationary coupling method", and construct it primarily to obtain the bounds for convergence rate of the…
We study $I(T)$, the number of inversions in a tree $T$ with its vertices labeled uniformly at random, which is a generalization of inversions in permutations. We first show that the cumulants of $I(T)$ have explicit formulas involving the…
Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the utilization of a modified group of moments for estimating a…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
We study (plane) tree-valued Markov chains $(T_n,n \geq 1)$ with uniform backward dynamics and show that they can be obtained by sampling from a real tree. As non--plane trees, every such Markov chain is represented by a weighted real tree.…