While mathematically elegant, a fundamental issue with AIXI is that it is only asymptotically computable.

This paper introduces factored conditional filters, new filtering algorithms for simultaneously tracking states and estimating parameters in high-dimensional state spaces. The conditional nature of the algorithms is used to estimate parameters and the factored nature is used to decompose the state space into low-dimensional subspaces in such a way that filtering on these subspaces gives distributions whose product is a good approximation to the distribution on the entire state space. The conditions for successful application of the algorithms are that observations be available at the subspace level and that the transition model can be factored into local transition models that are approximately confined to the subspaces; these conditions are widely satisfied in computer science, engineering, and geophysical filtering applications. We give experimental results on tracking epidemics and estimating parameters in large contact networks that show the effectiveness of our approach.

Synthetic contact networks are useful for modeling epidemic spread and social transmission, but data to infer realistic contact patterns that take account of assortative connections at the geographic and economic levels is limited. We developed a method to generate synthetic contact networks for any region of the United States based on publicly available data. First, we generate a synthetic population of individuals within households from US census data using combinatorial optimization. Then, individuals are assigned to workplaces and schools using commute data, employment statistics, and school enrollment data. The resulting population is then connected into a realistic contact network using graph generation algorithms. We test the method on two census regions and show that the synthetic populations accurately reflect the source data. We further show that the contact networks have distinct properties compared to networks generated without a synthetic population, and that those differences affect the rate of disease transmission in an epidemiological simulation. We provide open-source software to generate a synthetic population and contact network for any area within the US.

We employ an agent-based contact network model to study the relationship between vaccine uptake and disease dynamics in a hypothetical country town from New South Wales, Australia, undergoing a COVID-19 epidemic, over a period of three years. We model the contact network in this hypothetical township of N = 10000 people as a scale-free network, and simulate the spread of COVID-19 and vaccination program using disease and vaccination uptake parameters typically observed in such a NSW town. We simulate the spread of the ancestral variant of COVID-19 in this town, and study the disease dynamics while the town maintains limited but non-negligible contact with the rest of the country which is assumed to be undergoing a severe COVID-19 epidemic. We also simulate a maximum three doses of Pfizer Comirnaty vaccine being administered in this town, with limited vaccine supply at first which gradually increases, and analyse how the vaccination uptake affects the disease dynamics in this town, which is captured using an extended compartmental model with epidemic parameters typical for a COVID-19 epidemic in Australia. Our results show that, in such a township, three vaccination doses are sufficient to contain but not eradicate COVID-19, and the disease essentially becomes endemic. We also show that the average degree of infected nodes (the average number of contacts for infected people) predicts the proportion of infected people. Therefore, if the hubs (people with a relatively high number of contacts) are disproportionately infected, this indicates an oncoming peak of the infection, though the lag time thereof depends on the maximum number of vaccines administered to the populace. Overall, our analysis provides interesting insights in understanding the interplay between network topology, vaccination levels, and COVID-19 disease dynamics in a typical remote NSW country town.

The recent COVID-19 pandemic underscores the significance of early-stage non-pharmacological intervention strategies. The widespread use of masks and the systematic implementation of contact tracing strategies provide a potentially equally effective and socially less impactful alternative to more conventional approaches, such as large-scale mobility restrictions. However, manual contact tracing faces strong limitations in accessing the network of contacts, and the scalability of currently implemented protocols for smartphone-based digital contact tracing becomes impractical during the rapid expansion phases of the outbreaks, due to the surge in exposure notifications and associated tests. A substantial improvement in digital contact tracing can be obtained through the integration of probabilistic techniques for risk assessment that can more effectively guide the allocation of new diagnostic tests. In this study, we first quantitatively analyze the diagnostic and social costs associated with these containment measures based on contact tracing, employing three state-of-the-art models of SARS-CoV-2 spreading. Our results suggest that probabilistic techniques allow for more effective mitigation at a lower cost. Secondly, our findings reveal a remarkable efficacy of probabilistic contact-tracing techniques in capturing backward propagations and super-spreading events, relevant features of the diffusion of many pathogens, including SARS-CoV-2.

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.

The spread of an undesirable contact process, such as an infectious disease (e.g. COVID-19), is contained through testing and isolation of infected nodes. The temporal and spatial evolution of the process (along with containment through isolation) render such detection as fundamentally different from active search detection strategies. In this work, through an active learning approach, we design testing and isolation strategies to contain the spread and minimize the cumulative infections under a given test budget. We prove that the objective can be optimized, with performance guarantees, by greedily selecting the nodes to test. We further design reward-based methodologies that effectively minimize an upper bound on the cumulative infections and are computationally more tractable in large networks. These policies, however, need knowledge about the nodes' infection probabilities which are dynamically changing and have to be learned by sequential testing. We develop a message-passing framework for this purpose and, building on that, show novel tradeoffs between exploitation of knowledge through reward-based heuristics and exploration of the unknown through a carefully designed probabilistic testing. The tradeoffs are fundamentally distinct from the classical counterparts under active search or multi-armed bandit problems (MABs). We provably show the necessity of exploration in a stylized network and show through simulations that exploration can outperform exploitation in various synthetic and real-data networks depending on the parameters of the network and the spread.

We propose a practical integration of logical state abstraction with AIXI, a Bayesian optimality notion for reinforcement learning agents, to significantly expand the model class that AIXI agents can be approximated over to complex history-dependent and structured environments. The state representation and reasoning framework is based on higher-order logic, which can be used to define and enumerate complex features on non-Markovian and structured environments. We address the problem of selecting the right subset of features to form state abstractions by adapting the $\Phi$-MDP optimisation criterion from state abstraction theory. Exact Bayesian model learning is then achieved using a suitable generalisation of Context Tree Weighting over abstract state sequences. The resultant architecture can be integrated with different planning algorithms. Experimental results on controlling epidemics on large-scale contact networks validates the agent's performance.

Reconstructing missing information in epidemic spreading on contact networks can be essential in prevention and containment strategies. For instance, identifying and warning infective but asymptomatic individuals (e.g., manual contact tracing) helped contain outbreaks in the COVID-19 pandemic. The number of possible epidemic cascades typically grows exponentially with the number of individuals involved. The challenge posed by inference problems in the epidemics processes originates from the difficulty of identifying the almost negligible subset of those compatible with the evidence (for instance, medical tests). Here we present a new generative neural networks framework that can sample the most probable infection cascades compatible with observations. Moreover, the framework can infer the parameters governing the spreading of infections. The proposed method obtains better or comparable results with existing methods on the patient zero problem, risk assessment, and inference of infectious parameters in synthetic and real case scenarios like spreading infections in workplaces and hospitals.

Accurate and real-time disease prediction is vital for the prevention and control of healthcare-related infections. Although contacts between individuals are primarily responsible for infection chains, most prediction frameworks do not capture the contact dynamics. Researchers from the UK recently developed a real-time machine learning framework that uses dynamic patient contact networks to predict hospital-onset COVID-19 infections (HOCIs) at the patient level. They then tested and validated the framework on international multi-site datasets across various epidemic and endemic periods. This study can be found on the medRxiv* preprint server.