Related papers: Error Probability Bounds for M-ary Relay Trees

Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…

When using machine learning for imbalanced binary classification problems, it is common to subsample the majority class to create a (more) balanced training dataset. This biases the model's predictions because the model learns from data…

We explore the fundamental limits of heterogeneous distributed detection in an anonymous sensor network with n sensors and a single fusion center. The fusion center collects the single observation from each of the n sensors to detect a…

Rotation distance between rooted binary trees is the minimum number of simple rotations needed to transform one tree into the other. Computing the rotation distance between a pair of rooted trees can be quickly reduced in cases where there…

Let's denote a complete $m$-ary rooted tree graph of height $n$ as $G$. In scope of this paper we prove the certain relations between the properties of $G$ and the expectation and variance of the distribution of lengths of strings,…

Many machine learning tasks admit multiple models that perform almost equally well, a phenomenon known as predictive multiplicity. A fundamental source of this multiplicity is observational multiplicity, which arises from the stochastic…

The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the sum of ranks over all vertices (known as the security) in…

Trees with many leaves have applications on broadcasting, which is a method in networks for transferring a message to all recipients simultaneously. Internal nodes of a broadcasting tree require more expensive technology, because they have…

A single-sensor two-detectors system is considered where the sensor communicates with both detectors and Detector 1 communicates with Detector 2, all over noise-free rate-limited links. The sensor and both detectors observe discrete…

In many modern applications, large-scale sensor networks are used to perform statistical inference tasks. In this paper, we propose Bayesian methods for multiple change-point detection using a sensor network in which a fusion center (FC)…

Agricultural weed detection on edge devices is subject to strict constraints on model capacity, computational resources, and real-time inference latency, which prevent performance improvements through model scaling or ensembling. This paper…

We present a simple, efficient model for learning boundary detection based on a random forest classifier. Our approach combines (1) efficient clustering of training examples based on simple partitioning of the space of local edge…

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…

We study the fundamental problem of distributed network formation among mobile agents of limited computational power that aim to achieve energy balance by wirelessly transmitting and receiving energy in a peer-to-peer manner. Specifically,…

The inverse relation between mutual information (MI) and Bayesian error is sharpened by deriving finite sequences of upper and lower bounds on MI in terms of the minimum probability of error (MPE) and related Bayesian quantities. The well…

We study preferential attachment models where vertices enter the network with i.i.d. random numbers of edges that we call the out-degree. We identify the local limit of such models, substantially extending the work of Berger et al.(2014).…

Let $M$ be a random $m \times n$ matrix with binary entries and i.i.d. rows. The weight (i.e., number of ones) of a row has a specified probability distribution, with the row chosen uniformly at random given its weight. Let $N(n,m)$ denote…

We consider a single-source, multiple-relay, single-destination lossy network employing Random Linear Network coding at all transmitting nodes. We address the problem of calculating the probability of successful decoding at the destination…

We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices…

In the influence maximization (IM) problem, we are given a social network and a budget $k$, and we look for a set of $k$ nodes in the network, called seeds, that maximize the expected number of nodes that are reached by an influence cascade…