14 research outputs found
The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systems
Generative Autoregressive Neural Networks (ARNN) have recently demonstrated
exceptional results in image and language generation tasks, contributing to the
growing popularity of generative models in both scientific and commercial
applications. This work presents a physical interpretation of the ARNNs by
reformulating the Boltzmann distribution of binary pairwise interacting systems
into autoregressive form. The resulting ARNN architecture has weights and
biases of its first layer corresponding to the Hamiltonian's couplings and
external fields, featuring widely used structures like the residual connections
and a recurrent architecture with clear physical meanings. However, the
exponential growth, with system size, of the number of parameters of the hidden
layers makes its direct application unfeasible. Nevertheless, its
architecture's explicit formulation allows using statistical physics techniques
to derive new ARNNs for specific systems. As examples, new effective ARNN
architectures are derived from two well-known mean-field systems, the
Curie-Weiss and Sherrington-Kirkpatrick models, showing superior performances
in approximating the Boltzmann distributions of the corresponding physics model
than other commonly used ARNNs architectures. The connection established
between the physics of the system and the ARNN architecture provides a way to
derive new neural network architectures for different interacting systems and
interpret existing ones from a physical perspective.Comment: 10 pages, 6 figure plus the Supplementary Informatio
On the performance of a cavity method based algorithm for the Prize-Collecting Steiner Tree Problem on graphs
We study the behavior of an algorithm derived from the cavity method for the
Prize-Collecting Steiner Tree (PCST) problem on graphs. The algorithm is based
on the zero temperature limit of the cavity equations and as such is formally
simple (a fixed point equation resolved by iteration) and distributed
(parallelizable). We provide a detailed comparison with state-of-the-art
algorithms on a wide range of existing benchmarks networks and random graphs.
Specifically, we consider an enhanced derivative of the Goemans-Williamson
heuristics and the DHEA solver, a Branch and Cut Linear/Integer Programming
based approach. The comparison shows that the cavity algorithm outperforms the
two algorithms in most large instances both in running time and quality of the
solution. Finally we prove a few optimality properties of the solutions
provided by our algorithm, including optimality under the two post-processing
procedures defined in the Goemans-Williamson derivative and global optimality
in some limit cases
General scores for accessibility and inequality measures in urban areas
In the last decades, the acceleration of urban growth has led to an
unprecedented level of urban interactions and interdependence. This situation
calls for a significant effort among the scientific community to come up with
engaging and meaningful visualizations and accessible scenario simulation
engines. The present paper gives a contribution in this direction by providing
general methods to evaluate accessibility in cities based on public
transportation data. Through the notion of isochrones, the accessibility
quantities proposed measure the performance of transport systems at connecting
places and people in urban systems. Then we introduce scores rank cities
according to their overall accessibility. We highlight significant inequalities
in the distribution of these measures across the population, which are found to
be strikingly similar across various urban environments. Our results are
released through the interactive platform: www.citychrone.org, aimed at
providing the community at large with a useful tool for awareness and
decision-making
Cavity algorithms under global constraints: classical and quantum problems
The starting point of my thesis work was the study of optimization algorithms based on cavity method. These algorithms have been developed to a high degree of complexity in the last decade and they are also known as message passing algorithms (MPAs). My work has started by a question posed by my supervisor: what links can be found between those different approaches to the same problems? The starting aim of the PhD project was to explore the new ideas and algorithms that could result from a cross-fertilization between different approaches. During the first years we made a long and accurate comparison between different algorithms on a specific COP: the prize collecting Steiner tree problem. Looking to MPAs as an evolution of probability distributions of discrete variables led me to find some possible links with many body quantum physics, where typically we deal with probability amplitudes over discrete variables. In the recent years several results have appeared concerning the extension of the cavity method and message passing technics to quantum context. In 2012 Ramezanpour proposed a method, the variational quantum cavity method (VQCM), for finding approximate ground state wave functions based on a new messages passing algorithm used in stochastic optimization. Ramezanpour and I have extended this approach to find low excited states. In the last year of my Ph.D. I simplify the VQCM using imaginary time evolution operator. Moreover I extend this approach to find finite temperature density matri
A Bayesian generative neural network framework for epidemic inference problems
The reconstruction of missing information in epidemic spreading on contact networks can be essential in the prevention and containment strategies. The identification and warning of infectious but asymptomatic individuals (i.e., contact tracing), the well-known patient-zero problem, or the inference of the infectivity values in structured populations are examples of significant epidemic inference problems. As the number of possible epidemic cascades grows exponentially with the number of individuals involved and only an almost negligible subset of them is compatible with the observations (e.g., medical tests), epidemic inference in contact networks poses incredible computational challenges. We present a new generative neural networks framework that learns to generate the most probable infection cascades compatible with observations. The proposed method achieves better (in some cases, significantly better) or comparable results with existing methods in all problems considered both in synthetic and real contact networks. Given its generality, clear Bayesian and variational nature, the presented framework paves the way to solve fundamental inference epidemic problems with high precision in small and medium-sized real case scenarios such as the spread of infections in workplaces and hospitals
Epidemic mitigation by statistical inference from contact tracing data
Contact-tracing is an essential tool in order to mitigate the impact of
pandemic such as the COVID-19. In order to achieve efficient and scalable
contact-tracing in real time, digital devices can play an important role. While
a lot of attention has been paid to analyzing the privacy and ethical risks of
the associated mobile applications, so far much less research has been devoted
to optimizing their performance and assessing their impact on the mitigation of
the epidemic. We develop Bayesian inference methods to estimate the risk that
an individual is infected. This inference is based on the list of his recent
contacts and their own risk levels, as well as personal information such as
results of tests or presence of syndromes. We propose to use probabilistic risk
estimation in order to optimize testing and quarantining strategies for the
control of an epidemic. Our results show that in some range of epidemic
spreading (typically when the manual tracing of all contacts of infected people
becomes practically impossible, but before the fraction of infected people
reaches the scale where a lock-down becomes unavoidable), this inference of
individuals at risk could be an efficient way to mitigate the epidemic. Our
approaches translate into fully distributed algorithms that only require
communication between individuals who have recently been in contact. Such
communication may be encrypted and anonymized and thus compatible with privacy
preserving standards. We conclude that probabilistic risk estimation is capable
to enhance performance of digital contact tracing and should be considered in
the currently developed mobile applications.Comment: 21 pages, 7 figure
CityChrone: an Interactive Platform for Transport Network Analysis and Planning in Urban Systems
Urban systems studies in the last decades have greatly benefited from the digital revolution and the accumulation of a massive amount of data. Extracting useful information from these data calls for new and innovative theoretical and computational approaches. This work presents an open-source, modular, and scalable platform for urban planning and transports network analysis, the CityChrone [citychrone.org]. The platform shows, on interactive maps, measures of performances of public transport in cities. The measures are based on the computation of the travel time distance between a large set of points. Thanks to the high efficiency of the routing algorithm developed, the platform allows users to create new public transports networks and showing the effect on mobility in a small amount of time. A preliminary analysis of the user-generated scenarios is presented. All the source code of the CityChrone platform is open-source, and we employ only open data to ensure the reproducibility of results