Related papers: Universally Consistent Latent Position Estimation …
We consider the ensemble of adjacency matrices of Erd{\H o}s-R\'enyi random graphs, i.e.\ graphs on $N$ vertices where every edge is chosen independently and with probability $p \equiv p(N)$. We rescale the matrix so that its bulk…
This paper proposes a multi-label classification algorithm capable of continual learning by applying an Adaptive Resonance Theory (ART)-based clustering algorithm and the Bayesian approach for label probability computation. The ART-based…
Consider any random graph model where potential edges appear independently, with possibly different probabilities, and assume that the minimum expected degree is omega(ln n). We prove that the adjacency matrix and the Laplacian of that…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
Consider the normalized adjacency matrices of random $d$-regular graphs on $N$ vertices with fixed degree $d\geq3$. We prove that, with probability $1-N^{-1+{\varepsilon}}$ for any ${\varepsilon} >0$, the following two properties hold as $N…
The vertex-random graphs called proximity catch digraphs (PCDs) have been introduced recently and have applications in pattern recognition and spatial pattern analysis. A PCD is a random directed graph (i.e., digraph) which is constructed…
We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…
This work provides a theoretical analysis for optimally solving the pose estimation problem using total least squares for vector observations from landmark features, which is central to applications involving simultaneous localization and…
Graph-based causal discovery methods aim to capture conditional independencies consistent with the observed data and differentiate causal relationships from indirect or induced ones. Successful construction of graphical models of data…
We consider Bayesian estimation of a $p\times p$ precision matrix, when $p$ can be much larger than the available sample size $n$. It is well known that consistent estimation in such ultra-high dimensional situations requires regularization…
We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of random matrices that includes the normalized adjacency matrices of the Erd{\H o}s-R{\'e}nyi graph $G(N,p)$. Recently, it was shown by Lee, up to an…
This paper studies a stylized, yet natural, learning-to-rank problem and points out the critical incorrectness of a widely used nearest neighbor algorithm. We consider a model with $n$ agents (users) $\{x_i\}_{i \in [n]}$ and $m$…
We study the blind centrality ranking problem, where our goal is to infer the eigenvector centrality ranking of nodes solely from nodal observations, i.e., without information about the topology of the network. We formalize these nodal…
We propose a new representation of visual data that disentangles object position from appearance. Our method, termed Deep Latent Particles (DLP), decomposes the visual input into low-dimensional latent ``particles'', where each particle is…
We present a factor graph formulation and particle-based sum-product algorithm for robust localization and tracking in multipath-prone environments. The proposed sequential algorithm jointly estimates the mobile agent's position together…
In this paper we study the local law for eigenvalues of large random regular bipartite graphs with degree growing arbitrarily fast. We prove that the empirical spectral distribution of the adjacency matrix converges to a scaled down copy of…
For a multi-agent system state estimation resting upon noisy measurements constitutes a problem related to several application scenarios. Adopting the standard least-squares approach, in this work we derive both the (centralized) analytic…
Community detection is one of the fundamental problems of network analysis, for which a number of methods have been proposed. Most model-based or criteria-based methods have to solve an optimization problem over a discrete set of labels to…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…
Neural networks are often regarded as universal equations that can estimate any function. This flexibility, however, comes with the drawback of high complexity, rendering these networks into black box models, which is especially relevant in…