Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the temporal dependence structure of Hawkes processes is generally a computationally expensive task, all the more with Bayesian estimation methods. In particular, for generalised nonlinear Hawkes processes, Monte-Carlo Markov Chain methods applied to compute the doubly intractable posterior distribution are not scalable to high-dimensional processes in practice. Recently, efficient algorithms targeting a mean-field variational approximation of the posterior distribution have been proposed. In this work, we first unify existing variational Bayes approaches under a general nonparametric inference framework, and analyse the asymptotic properties of these methods under easily verifiable conditions on the prior, the variational class, and the nonlinear model. Secondly, we propose a novel sparsity-inducing procedure, and derive an adaptive mean-field variational algorithm for the popular sigmoid Hawkes processes. Our algorithm is parallelisable and therefore computationally efficient in high-dimensional setting. Through an extensive set of numerical simulations, we also demonstrate that our procedure is able to adapt to the dimensionality of the parameter of the Hawkes process, and is partially robust to some type of model mis-specification. Keywords: temporal point processes, bayesian nonparametrics, connectivity graph, variational approximation.

Pearl and Verma developed d-separation as a widely used graphical criterion to reason about the conditional independencies that are implied by the causal structure of a Bayesian network. As acyclic ground probabilistic logic programs correspond to Bayesian networks on their dependency graph, we can compute conditional independencies from d-separation in the latter. In the present paper, we generalize the reasoning above to the non-ground case. First, we abstract the notion of a probabilistic logic program away from external databases and probabilities to obtain so-called program structures. We then present a correct meta-interpreter that decides whether a certain conditional independence statement is implied by a program structure on a given external database. Finally, we give a fragment of program structures for which we obtain a completeness statement of our conditional independence oracle. We close with an experimental evaluation of our approach revealing that our meta-interpreter performs significantly faster than checking the definition of independence using exact inference in ProbLog 2.

Retrosynthesis planning is a fundamental challenge in chemistry which aims at designing reaction pathways from commercially available starting materials to a target molecule. Each step in multi-step retrosynthesis planning requires accurate prediction of possible precursor molecules given the target molecule and confidence estimates to guide heuristic search algorithms. We model single-step retrosynthesis planning as a distribution learning problem in a discrete state space. First, we introduce the Markov Bridge Model, a generative framework aimed to approximate the dependency between two intractable discrete distributions accessible via a finite sample of coupled data points. Our framework is based on the concept of a Markov bridge, a Markov process pinned at its endpoints. Unlike diffusion-based methods, our Markov Bridge Model does not need a tractable noise distribution as a sampling proxy and directly operates on the input product molecules as samples from the intractable prior distribution. We then address the retrosynthesis planning problem with our novel framework and introduce RetroBridge, a template-free retrosynthesis modeling approach that achieves state-of-the-art results on standard evaluation benchmarks.

The main goal of Few-Shot learning algorithms is to enable learning from small amounts of data. One of the most popular and elegant Few-Shot learning approaches is Model-Agnostic Meta-Learning (MAML). The main idea behind this method is to learn the shared universal weights of a meta-model, which are then adapted for specific tasks. However, the method suffers from over-fitting and poorly quantifies uncertainty due to limited data size. Bayesian approaches could, in principle, alleviate these shortcomings by learning weight distributions in place of point-wise weights. Unfortunately, previous modifications of MAML are limited due to the simplicity of Gaussian posteriors, MAML-like gradient-based weight updates, or by the same structure enforced for universal and adapted weights. In this paper, we propose a novel framework for Bayesian MAML called BayesianHMAML, which employs Hypernetworks for weight updates. It learns the universal weights point-wise, but a probabilistic structure is added when adapted for specific tasks. In such a framework, we can use simple Gaussian distributions or more complicated posteriors induced by Continuous Normalizing Flows.

Minimizing error in prevalence estimates and diagnostic classifiers remains a challenging task in serology. In theory, these problems can be reduced to modeling class-conditional probability densities (PDFs) of measurement outcomes, which control all downstream analyses. However, this task quickly succumbs to the curse of dimensionality, even for assay outputs with only a few dimensions (e.g. target antigens). To address this problem, we propose a technique that uses empirical training data to classify samples and estimate prevalence in arbitrary dimension without direct access to the conditional PDFs. We motivate this method via a lemma that relates relative conditional probabilities to minimum-error classification boundaries. This leads us to formulate an optimization problem that: (i) embeds the data in a parameterized, curved space; (ii) classifies samples based on their position relative to a coordinate axis; and (iii) subsequently optimizes the space by minimizing the empirical classification error of pure training data, for which the classes are known. Interestingly, the solution to this problem requires use of a homotopy-type method to stabilize the optimization. We then extend the analysis to the case of impure training data, for which the classes are unknown. We find that two impure datasets suffice for both prevalence estimation and classification, provided they satisfy a linear independence property. Lastly, we discuss how our analysis unifies discriminative and generative learning techniques in a common framework based on ideas from set and measure theory. Throughout, we validate our methods in the context of synthetic data and a research-use SARS-CoV-2 enzyme-linked immunosorbent (ELISA) assay.

Given observed data and a probabilistic generative model, Bayesian inference searches for the distribution of the model's parameters that could have yielded the data. Inference is challenging for large population studies where millions of measurements are performed over a cohort of hundreds of subjects, resulting in a massive parameter space. This large cardinality renders off-the-shelf Variational Inference (VI) computationally impractical. In this work, we design structured VI families that efficiently tackle large population studies. Our main idea is to share the parameterization and learning across the different i.i.d. variables in a generative model, symbolized by the model's \textit{plates}. We name this concept \textit{plate amortization}. Contrary to off-the-shelf stochastic VI, which slows down inference, plate amortization results in orders of magnitude faster to train variational distributions. Applied to large-scale hierarchical problems, PAVI yields expressive, parsimoniously parameterized VI with an affordable training time. This faster convergence effectively unlocks inference in those large regimes. We illustrate the practical utility of PAVI through a challenging Neuroimaging example featuring 400 million latent parameters, demonstrating a significant step towards scalable and expressive Variational Inference.

Real-world software applications must constantly evolve to remain relevant. This evolution occurs when developing new applications or adapting existing ones to meet new requirements, make corrections, or incorporate future functionality. Traditional methods of software quality control involve software quality models and continuous code inspection tools. These measures focus on directly assessing the quality of the software. However, there is a strong correlation and causation between the quality of the development process and the resulting software product. Therefore, improving the development process indirectly improves the software product, too. To achieve this, effective learning from past processes is necessary, often embraced through post mortem organizational learning. While qualitative evaluation of large artifacts is common, smaller quantitative changes captured by application lifecycle management are often overlooked. In addition to software metrics, these smaller changes can reveal complex phenomena related to project culture and management. Leveraging these changes can help detect and address such complex issues. Software evolution was previously measured by the size of changes, but the lack of consensus on a reliable and versatile quantification method prevents its use as a dependable metric. Different size classifications fail to reliably describe the nature of evolution. While application lifecycle management data is rich, identifying which artifacts can model detrimental managerial practices remains uncertain. Approaches such as simulation modeling, discrete events simulation, or Bayesian networks have only limited ability to exploit continuous-time process models of such phenomena. Even worse, the accessibility and mechanistic insight into such gray- or black-box models are typically very low. To address these challenges, we suggest leveraging objectively [...]

Commonly adopted in the manufacturing and aerospace sectors, digital twin (DT) platforms are increasingly seen as a promising paradigm to control, monitor, and analyze software-based, "open", communication systems. Notably, DT platforms provide a sandbox in which to test artificial intelligence (AI) solutions for communication systems, potentially reducing the need to collect data and test algorithms in the field, i.e., on the physical twin (PT). A key challenge in the deployment of DT systems is to ensure that virtual control optimization, monitoring, and analysis at the DT are safe and reliable, avoiding incorrect decisions caused by "model exploitation". To address this challenge, this paper presents a general Bayesian framework with the aim of quantifying and accounting for model uncertainty at the DT that is caused by limitations in the amount and quality of data available at the DT from the PT. In the proposed framework, the DT builds a Bayesian model of the communication system, which is leveraged to enable core DT functionalities such as control via multi-agent reinforcement learning (MARL), monitoring of the PT for anomaly detection, prediction, data-collection optimization, and counterfactual analysis. To exemplify the application of the proposed framework, we specifically investigate a case-study system encompassing multiple sensing devices that report to a common receiver. Experimental results validate the effectiveness of the proposed Bayesian framework as compared to standard frequentist model-based solutions.

Identifying causality is a challenging task in many data-intensive scenarios. Many algorithms have been proposed for this critical task. However, most of them consider the learning algorithms for directed acyclic graph (DAG) of Bayesian network (BN). These BN-based models only have limited causal explainability because of the issue of Markov equivalence class. Moreover, they are dependent on the assumption of stationarity, whereas many sampling time series from complex system are nonstationary. The nonstationary time series bring dataset shift problem, which leads to the unsatisfactory performances of these algorithms. To fill these gaps, a novel causation model named Unique Causal Network (UCN) is proposed in this paper. Different from the previous BN-based models, UCN considers the influence of time delay, and proves the uniqueness of obtained network structure, which addresses the issue of Markov equivalence class. Furthermore, based on the decomposability property of UCN, a higher-order causal entropy (HCE) algorithm is designed to identify the structure of UCN in a distributed way. HCE algorithm measures the strength of causality by using nearest-neighbors entropy estimator, which works well on nonstationary time series. Finally, lots of experiments validate that HCE algorithm achieves state-of-the-art accuracy when time series are nonstationary, compared to the other baseline algorithms.

Inhomogeneous Poisson process data defined on a continuous spatio-temporal domain has attracted immense attention recently in a wide variety of applications, including reliability analysis in manufacturing systems (Soleimani et al, 2017), event capture in sensing regions (Mutny and Krause, 2021), crime prediction in urban area (Shirota and Gelfand, 2017) and disease diagnosis based on medical records (Lasko, 2014). The reliable training of an inhomogeneous Poisson process model critically relies on a large amount of data to avoid overfitting, especially when modeling high-dimensional point processes. However, one challenge is that the available training data is routinely sparse or even partially missing in specific applications. Taking manufacturing failure and healthcare analysis as motivating examples: the modern manufacturing machines are reliable and sparsely fail; the individuals with healthy constitution will not visit hospital very often. The data missing problems also arise, e.g., the event location capture is intermittent for sensing systems because of weather or other related barriers.