arXiv subjects

Matteo Mariani

Publications and source records attributed to Matteo Mariani.

5 recordsLinked to original sources

arXiv2025

Evidence of Replica Symmetry Breaking under the Nishimori conditions in epidemic inference on graphs

In Bayesian inference, computing the posterior distribution from the data is typically a non-trivial problem, which usually requires approximations such as mean-field approaches or numerical methods, like the Monte Carlo Markov Chain. Being a high-dimensional distribution over a set of correlated variables, the posterior distribution can undergo the notorious replica symmetry breaking transition. When it happens, several mean-field methods and virtually every Monte Carlo scheme can not provide a reasonable approximation to the posterior and its marginals. Replica symmetry is believed to be guaranteed whenever the data is generated with known prior and likelihood distributions, namely under the so-called Nishimori conditions. In this paper, we break this belief, by providing a counter-example showing that, under the Nishimori conditions, replica symmetry breaking arises. Introducing a simple, geometrical model that can be thought of as a patient zero retrieval problem in a highly infectious regime of the epidemic Susceptible-Infectious model, we show that under the Nishimori conditions, there is evidence of replica symmetry breaking. We achieve this result by computing the instability of the replica symmetric cavity method toward the one step replica symmetry broken phase. The origin of this phenomenon -- replica symmetry breaking under the Nishimori conditions -- is likely due to the correlated disorder appearing in the epidemic models.

cond-mat.dis-nn↗

arXiv2023

Small-Coupling Dynamic Cavity: a Bayesian mean-field framework for epidemic inference

We present the Small-Coupling Dynamic Cavity (SCDC) method, a novel generalized mean-field approximation for epidemic inference and risk assessment within a fully Bayesian framework. SCDC accounts for non-causal effects of observations and uses a graphical model representation of epidemic processes to derive self-consistent equations for edge probability marginals. A small-coupling expansion yields time-dependent cavity messages capturing individual infection probabilities and observational conditioning. With linear computational cost per iteration in the epidemic duration, SCDC is particularly efficient and valid even for recurrent epidemic processes, where standard methods are exponentially complex. Tested on synthetic networks, it matches Belief Propagation in accuracy and outperforms individual-based mean-field methods. Notably, despite being derived as a small-infectiousness expansion, SCDC maintains good accuracy even for relatively large infection probabilities. While convergence issues may arise on graphs with long-range correlations, SCDC reliably estimates risk. Future extensions include non-Markovian models and higher-order terms in the dynamic cavity framework.

cond-mat.dis-nn↗

arXiv2023

Statistical Mechanics of Inference in Epidemic Spreading

We investigate the information-theoretical limits of inference tasks in epidemic spreading on graphs in the thermodynamic limit. The typical inference tasks consist in computing observables of the posterior distribution of the epidemic model given observations taken from a ground truth (sometimes called planted) random trajectory. We can identify two main sources of quenched disorder: the graph ensemble and the planted trajectory. The epidemic dynamics however induces non-trivial long-range correlations among individuals' states on the latter. This results in non-local correlated quenched disorder which unfortunately is typically hard to handle. To overcome this difficulty, we divide the dynamical process into two sets of variables: a set of stochastic independent variables (representing transmission delays), plus a set of correlated variables (the infection times) that depend deterministically on the first. Treating the former as quenched variables and the latter as dynamic ones, computing disorder average becomes feasible by means of the Replica Symmetric cavity method. We give theoretical predictions on the posterior probability distribution of the trajectory of each individual, conditioned to observations on the state of individuals at given times, focusing on the Susceptible Infectious (SI) model. In the Bayes-optimal condition, i.e. when true dynamic parameters are known, the inference task is expected to fall in the Replica Symmetric regime. We indeed provide predictions for the information theoretic limits of various inference tasks, in form of phase diagrams. We also identify a region, in the Bayes-Optimal setting, with strong hints of Replica Symmetry Breaking. When true parameters are unknown, we show how a maximum-likelihood procedure is able to recover them with mostly unaffected performance.

physics.soc-ph↗

arXiv2022

Inference in conditioned dynamics through causality restoration

Computing observables from conditioned dynamics is typically computationally hard, because, although obtaining independent samples efficiently from the unconditioned dynamics is usually feasible, generally most of the samples must be discarded (in a form of importance sampling) because they do not satisfy the imposed conditions. Sampling directly from the conditioned distribution is non-trivial, as conditioning breaks the causal properties of the dynamics which ultimately renders the sampling procedure efficient. One standard way of achieving it is through a Metropolis Monte-Carlo procedure, but this procedure is normally slow and a very large number of Monte-Carlo steps is needed to obtain a small number of statistically independent samples. In this work, we propose an alternative method to produce independent samples from a conditioned distribution. The method learns the parameters of a generalized dynamical model that optimally describe the conditioned distribution in a variational sense. The outcome is an effective, unconditioned, dynamical model, from which one can trivially obtain independent samples, effectively restoring causality of the conditioned distribution. The consequences are twofold: on the one hand, it allows us to efficiently compute observables from the conditioned dynamics by simply averaging over independent samples. On the other hand, the method gives an effective unconditioned distribution which is easier to interpret. The method is flexible and can be applied virtually to any dynamics. We discuss an important application of the method, namely the problem of epidemic risk assessment from (imperfect) clinical tests, for a large family of time-continuous epidemic models endowed with a Gillespie-like sampler. We show that the method compares favorably against the state of the art, including the soft-margin approach and mean-field methods.

physics.data-an↗

arXiv2020

Designing Robust API Monitoring Solutions

Tracing the sequence of library and system calls that a program makes is very helpful in the characterization of its interactions with the surrounding environment and ultimately of its semantics. Due to entanglements of real-world software stacks, accomplishing this task can be surprisingly challenging as we take accuracy, reliability, and transparency into the equation. To manage these dimensions effectively, we identify six challenges that API monitoring solutions should overcome and outline actionable design points for them, reporting insights from our experience in building API tracers for software security research. We detail two implementation variants, based on hardware-assisted virtualization (realizing the first general-purpose user-space tracer of this kind) and on dynamic binary translation, that achieve API monitoring robustly. We share our SNIPER system as open source.

cs.CR↗