Related papers: Error Probability Bounds for M-ary Relay Trees
We consider the problem of detecting the source of a rumor which has spread in a network using only observations about which set of nodes are infected with the rumor and with no information as to \emph{when} these nodes became infected. In…
In classification and forecasting with tabular data, one often utilizes tree-based models. Those can be competitive with deep neural networks on tabular data and, under some conditions, explainable. The explainability depends on the depth…
In the present paper, we derive an upper bound of the average network breakdown probability of packet networks with unreliable relay nodes. We here assume that relay nodes get independently broken with a given node breakdown probability. A…
We study the average height of random trees generated by leaf-centric binary tree sources as introduced by Zhang, Yang and Kieffer. A leaf-centric binary tree source induces for every $n \geq 2$ a probability distribution on the set of…
In this work, we investigate a slotted-time relay assisted cooperative random access wireless network with multipacket (MPR) reception capabilities. MPR refers to the capability of a wireless node to successfully receive packets from more…
Let $\Omega_n$ be the family of binary trees on $n$ vertices obtained by identifying the root of an rgood binary tree with a vertex of maximum eccentricity of a binary caterpillar. In the paper titled "On different middle parts of a tree…
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 prove risk bounds for binary classification in high-dimensional settings when the sample size is allowed to be smaller than the dimensionality of the training set observations. In particular, we prove upper bounds for both 'compressive…
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 particular continuous-time multitype branching process is considered, it is the continuous-time embedding of a discrete-time process which is very popular in theoretical computer science: the m-ary search tree (m is an integer). There is…
Consider a distributed detection problem in which the underlying distributions of the observations are unknown; instead of these distributions, noisy versions of empirically observed statistics are available to the fusion center. These…
We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are…
We show that MLP layers in transformer language models perform binary routing of continuous signals: the decision of whether a token needs nonlinear processing is well-captured by binary neuron activations, even though the signals being…
Maximum A Posteriori inference in graphical models is often solved via message-passing algorithms, such as the junction-tree algorithm, or loopy belief-propagation. The exact solution to this problem is well known to be exponential in the…
The size of the largest common subtree (maximum agreement subtree) of two independent uniform random binary trees on $n$ leaves is known to be between orders $n^{1/8}$ and $n^{1/2}$. By a construction based on recursive splitting and…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
This paper presents a novel theoretical study of the general problem of multiple source adaptation using the notion of Renyi divergence. Our results build on our previous work [12], but significantly broaden the scope of that work in…
In evolutionary biology, networks are becoming increasingly used to represent evolutionary histories for species that have undergone non-treelike or reticulate evolution. Such networks are essentially directed acyclic graphs with a leaf set…
We consider the problem of learning co-occurrence information between two word categories, or more in general between two discrete random variables taking values in a hierarchically classified domain. In particular, we consider the problem…
In the broadcasting problem on trees, a $\{-1,1\}$-message originating in an unknown node is passed along the tree with a certain error probability $q$. The goal is to estimate the original message without knowing the order in which the…