arXiv subjects

Mikhail Hayhoe

Publications and source records attributed to Mikhail Hayhoe.

9 recordsLinked to original sources

arXiv2022

Stable and Transferable Hyper-Graph Neural Networks

We introduce an architecture for processing signals supported on hypergraphs via graph neural networks (GNNs), which we call a Hyper-graph Expansion Neural Network (HENN), and provide the first bounds on the stability and transferability error of a hypergraph signal processing model. To do so, we provide a framework for bounding the stability and transferability error of GNNs across arbitrary graphs via spectral similarity. By bounding the difference between two graph shift operators (GSOs) in the positive semi-definite sense via their eigenvalue spectrum, we show that this error depends only on the properties of the GNN and the magnitude of spectral similarity of the GSOs. Moreover, we show that existing transferability results that assume the graphs are small perturbations of one another, or that the graphs are random and drawn from the same distribution or sampled from the same graphon can be recovered using our approach. Thus, both GNNs and our HENNs (trained using normalized Laplacians as graph shift operators) will be increasingly stable and transferable as the graphs become larger. Experimental results illustrate the importance of considering multiple graph representations in HENN, and show its superior performance when transferability is desired.

cs.LG↗

arXiv2021

AutoEKF: Scalable System Identification for COVID-19 Forecasting from Large-Scale GPS Data

We present an Extended Kalman Filter framework for system identification and control of a stochastic high-dimensional epidemic model. The scale and severity of the COVID-19 emergency have highlighted the need for accurate forecasts of the state of the pandemic at a high resolution. Mechanistic compartmental models are widely used to produce such forecasts and assist in the design of control and relief policies. Unfortunately, the scale and stochastic nature of many of these models often makes the estimation of their parameters difficult. With the goal of calibrating a high dimensional COVID-19 model using low-level mobility data, we introduce a method for tractable maximum likelihood estimation that combines tools from Bayesian inference with scalable optimization techniques from machine learning. The proposed approach uses automatic backward-differentiation to directly compute the gradient of the likelihood of COVID-19 incidence and death data. The likelihood of the observations is estimated recursively using an Extended Kalman Filter and can be easily optimized using gradient-based methods to compute maximum likelihood estimators. Our compartmental model is trained using GPS mobility data that measures the mobility patterns of millions of mobile phones across the United States. We show that, after calibrating against incidence and deaths data from the city of Philadelphia, our model is able to produce an accurate 30-day forecast of the evolution of the pandemic.

eess.SY↗

arXiv2020

Data-Driven Control of the COVID-19 Outbreak via Non-Pharmaceutical Interventions: A Geometric Programming Approach

In this paper we propose a data-driven model for the spread of SARS-CoV-2 and use it to design optimal control strategies of human-mobility restrictions that both curb the epidemic and minimize the economic costs associated with implementing non-pharmaceutical interventions. We develop an extension of the SEIR epidemic model that captures the effects of changes in human mobility on the spread of the disease. The parameters of our data-driven model are learned using a multitask learning approach that leverages both data on the number of deaths across a set of regions, and cellphone data on individuals' mobility patterns specific to each region. We propose an optimal control problem on this data-driven model with a tractable solution provided by geometric programming. The result of this framework is a mobility-based intervention strategy that curbs the spread of the epidemic while obeying a budget on the economic cost incurred. Furthermore, in the absence of a straightforward mapping from human mobility data to economic costs, we propose a practical method by which a budget on economic losses incurred may be chosen to eliminate excess deaths due to over-utilization of hospital resources. Our results are demonstrated with numerical simulations using real data from the Philadelphia metropolitan area.

math.OC↗

arXiv2020

A Dynamical Approach to Efficient Eigenvalue Estimation in General Multiagent Networks

We propose a method to efficiently estimate the eigenvalues of any arbitrary (potentially weighted and/or directed) network of interacting dynamical agents from dynamical observations. These observations are discrete, temporal measurements about the evolution of the outputs of a subset of agents (potentially one) during a finite time horizon; notably, we do not require knowledge of which agents are contributing to our measurements. We propose an efficient algorithm to exactly recover the (potentially complex) eigenvalues corresponding to network modes that are observable from the output measurements. The length of the sequence of measurements required by our method to generate a full reconstruction of the observable eigenvalue spectrum is, at most, twice the number of agents in the network, but smaller in practice. The proposed technique can be applied to networks of multiagent systems with arbitrary dynamics in both continuous- and discrete-time. Finally, we illustrate our results with numerical simulations.

math.OC↗

arXiv2020

New bounds on the spectral radius of graphs based on the moment problem

Let $\mathcal{G}$ be an undirected graph with adjacency matrix $A$ and spectral radius $ρ$. Let $w_k, ϕ_k$ and $ϕ_k^{(i)}$ be, respectively, the number walks of length $k$, closed walks of length $k$ and closed walks starting and ending at vertex $i$ after $k$ steps. In this paper, we propose a measure-theoretic framework which allows us to relate walks in a graph with its spectral properties. In particular, we show that $w_k, ϕ_k$ and $ϕ_k^{(i)}$ can be interpreted as the moments of three different measures, all of them supported on the spectrum of $A$. Building on this interpretation, we leverage results from the classical moment problem to formulate a hierarchy of new lower and upper bounds on $ρ$, as well as provide alternative proofs to several well-known bounds in the literature.

math.CO↗

arXiv2019

Sparse estimation of Laplacian eigenvalues in multiagent networks

We propose a method to efficiently estimate the Laplacian eigenvalues of an arbitrary, unknown network of interacting dynamical agents. The inputs to our estimation algorithm are measurements about the evolution of a collection of agents (potentially one) during a finite time horizon; notably, we do not require knowledge of which agents are contributing to our measurements. We propose a scalable algorithm to exactly recover a subset of the Laplacian eigenvalues from these measurements. These eigenvalues correspond directly to those Laplacian modes that are observable from our measurements. We show how our technique can be applied to networks of multiagent systems with arbitrary dynamics in both continuous- and discrete-time. Finally, we illustrate our results with numerical simulations.

math.SP↗

arXiv2019

SPECTRE: Seedless Network Alignment via Spectral Centralities

Network alignment consists of finding a structure-preserving correspondence between the nodes of two correlated, but not necessarily identical, networks. This problem finds applications in a wide variety of fields, from the alignment of proteins in computational biology, to the de-anonymization of social networks, as well as recognition tasks in computer vision. In this work we introduce SPECTRE, a scalable algorithm that uses spectral centrality measures and percolation techniques. Unlike most network alignment algorithms, SPECTRE requires no seeds (i.e., pairs of nodes identified beforehand), which in many cases are expensive, or impossible, to obtain. Instead, SPECTRE generates an initial noisy seed set via spectral centrality measures which is then used to robustly grow a network alignment via bootstrap percolation techniques. We show that, while this seed set may contain a majority of incorrect pairs, SPECTRE is still able to obtain a high-quality alignment. Through extensive numerical simulations, we show that SPECTRE allows for fast run times and high accuracy on large synthetic and real-world networks, even those which do not exhibit a high correlation.

cs.SI↗

arXiv2017

A Polya Contagion Model for Networks

A network epidemics model based on the classical Polya urn scheme is investigated. Temporal contagion processes are generated on the network nodes using a modified Polya sampling scheme that accounts for spatial infection among neighbouring nodes. The stochastic properties and the asymptotic behaviour of the resulting network contagion process are analyzed. Unlike the classical Polya process, the network process is noted to be non-stationary in general, although it is shown to be time-invariant in its first and some of its second-order statistics and to satisfy martingale convergence properties under certain conditions. Three classical Polya processes, one computational and two analytical, are proposed to statistically approximate the contagion process of each node, showing a good fit for a range of system parameters. Finally, empirical results compare and contrast our model with the well-known discrete time SIS model.

cs.SI↗

arXiv2017

Curing Epidemics on Networks using a Polya Contagion Model

We study the curing of epidemics of a network contagion, which is modelled using a variation of the classical Polya urn process that takes into account spatial infection among neighbouring nodes. We introduce several quantities for measuring the overall infection in the network and use them to formulate an optimal control problem for minimizing the average infection rate using limited curing resources. We prove the feasibility of this problem under high curing budgets by deriving conservative lower bounds on the amount of curing per node that turns our measures of network infection into supermartingales. We also provide a provably convergent gradient descent algorithm to find the allocation of curing under limited budgets. Motivated by the fact that this strategy is computationally expensive, we design a suit of heuristic methods that are locally implementable and nearly as effective. Extensive simulations run on largescale networks demonstrate the effectiveness of our proposed strategies.

math.OC↗