Related papers: Spectral Inference Methods on Sparse Graphs: Theor…
This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…
We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the…
We estimate fair graphs from graph-stationary nodal observations such that connections are not biased with respect to sensitive attributes. Edges in real-world graphs often exhibit preferences for connecting certain pairs of groups. Biased…
This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…
Graphs are central to modeling complex systems in domains such as social networks, molecular chemistry, and neuroscience. While Graph Neural Networks, particularly Graph Convolutional Networks, have become standard tools for graph learning,…
This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…
Characterizing motif (i.e., locally connected subgraph patterns) statistics is important for understanding complex networks such as online social networks and communication networks. Previous work made the strong assumption that the graph…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…
Theoretical analysis of biological and artificial neural networks e.g. modelling of synaptic or weight matrices necessitate consideration of the generic real-asymmetric matrix ensembles, those with varying order of matrix elements e.g. a…
Graphical modelling techniques based on sparse selection have been applied to infer complex networks in many fields, including biology and medicine, engineering, finance, and social sciences. One structural feature of some of the networks…
Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…
Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…
Community detection is one of the most important problems in network analysis. Among many algorithms proposed for this task, methods based on statistical inference are of particular interest: they are mathematically sound and were shown to…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
A wide variety of application domains are concerned with data consisting of entities and their relationships or connections, formally represented as graphs. Within these diverse application areas, a common problem of interest is the…
We compute spectra of large stochastic matrices $W$, defined on sparse random graphs, where edges $(i,j)$ of the graph are given positive random weights $W_{ij}>0$ in such a fashion that column sums are normalized to one. We compute spectra…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
Classical results in sparse recovery guarantee the exact reconstruction of $s$-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since…