Networks can describe the structure of a wide variety of complex systems by specifying how pairs of nodes interact. This choice of representation is flexible, but not necessarily appropriate when joint interactions between groups of nodes are needed to explain empirical phenomena. Networks remain the de facto standard, however, as relational datasets often fail to include higher-order interactions. Here, we introduce a Bayesian approach to reconstruct these missing higher-order interactions, from pairwise network data. Our method is based on the principle of parsimony and only includes higher-order structures when there is sufficient statistical evidence for them.

Quantum computing-based machine learning mainly focuses on quantum computing hardware that is experimentally challenging to realize due to requiring quantum gates that operate at very low temperature. Instead, we demonstrate the existence of a lower performance and much lower effort island on the accuracy-vs-qubits graph that may well be experimentally accessible with room temperature optics. This high temperature "quantum computing toy model" is nevertheless interesting to study as it allows rather accessible explanations of key concepts in quantum computing, in particular interference, entanglement, and the measurement process. We specifically study the problem of classifying an example from the MNIST and Fashion-MNIST datasets, subject to the constraint that we have to make a prediction after the detection of the very first photon that passed a coherently illuminated filter showing the example. Whereas a classical setup in which a photon is detected after falling on one of the 28 28 image pixels is limited to a (maximum likelihood estimation) accuracy of 21.27% for MNIST, respectively 18.27% for Fashion-MNIST, we show that the theoretically achievable accuracy when exploiting inference by optically transforming the quantum state of the photon is at least 41.27% for MNIST, respectively 36.14% for Fashion-MNIST. We show in detail how to train the corresponding transformation with TensorFlow and also explain how this example can serve as a teaching tool for the measurement process in quantum mechanics.

This paper presents an empirical study regarding training probabilistic neural networks using training objectives derived from PAC-Bayes bounds. In the context of probabilistic neural networks, the output of training is a probability distribution over network weights. We present two training objectives, used here for the first time in connection with training neural networks. These two training objectives are derived from tight PAC-Bayes bounds. We also re-implement a previously used training objective based on a classical PAC-Bayes bound, to compare the properties of the predictors learned using the different training objectives. We compute risk certificates that are valid on any unseen examples for the learnt predictors. We further experiment with different types of priors on the weights (both data-free and data-dependent priors) and neural network architectures. Our experiments on MNIST and CIFAR-10 show that our training methods produce competitive test set errors and non-vacuous risk bounds with much tighter values than previous results in the literature, showing promise not only to guide the learning algorithm through bounding the risk but also for model selection. These observations suggest that the methods studied here might be good candidates for self-certified learning, in the sense of certifying the risk on any unseen data without the need for data-splitting protocols.

This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of Gaussian processes in the hierarchy. The idea of the state-space approach is to represent the DGP as a non-linear hierarchical system of linear stochastic differential equations (SDEs), where each SDE corresponds to a conditional GP. The DGP regression problem then becomes a state estimation problem, and we can estimate the state efficiently with sequential methods by using the Markov property of the state-space DGP. The computational complexity scales linearly with respect to the number of measurements. Based on this, we formulate state-space MAP as well as Bayesian filtering and smoothing solutions to the DGP regression problem. We demonstrate the performance of the proposed models and methods on synthetic non-stationary signals and apply the state-space DGP to detection of the gravitational waves from LIGO measurements.

This paper proposes a careful separation between an entity's epistemic system and their decision system. Crucially, Bayesian counterfactuals are estimated by the epistemic system; not by the decision system. Based on this remark, I prove the existence of Newcomb-like problems for which an epistemic system necessarily expects the entity to make a counterfactually bad decision. I then address (a slight generalization of) Newcomb's paradox. I solve the specific case where the player believes that the predictor applies Bayes rule with a supset of all the data available to the player. I prove that the counterfactual optimality of the 1-Box strategy depends on the player's prior on the predictor's additional data. If these additional data are not expected to reduce sufficiently the predictor's uncertainty on the player's decision, then the player's epistemic system will counterfactually prefer to 2-Box. But if the predictor's data is believed to make them quasi-omniscient, then 1-Box will be counterfactually preferred. Implications of the analysis are then discussed. More generally, I argue that, to better understand or design an entity, it is useful to clearly separate the entity's epistemic, decision, but also data collection, reward and maintenance systems, whether the entity is human, algorithmic or institutional.

Whether the goal is to estimate the number of people that live in a congressional district, to estimate the number of individuals that have died in an armed conflict, or to disambiguate individual authors using bibliographic data, all these applications have a common theme - integrating information from multiple sources. Before such questions can be answered, databases must be cleaned and integrated in a systematic and accurate way, commonly known as record linkage, de-duplication, or entity resolution. In this article, we review motivational applications and seminal papers that have led to the growth of this area. Specifically, we review the foundational work that began in the 1940's and 50's that have led to modern probabilistic record linkage. We review clustering approaches to entity resolution, semi- and fully supervised methods, and canonicalization, which are being used throughout industry and academia in applications such as human rights, official statistics, medicine, citation networks, among others. Finally, we discuss current research topics of practical importance.

Data dimensionality informs us about data complexity and sets limit on the structure of successful signal processing pipelines. In this work we revisit and improve the manifold-adaptive Farahmand-Szepesv\'ari-Audibert (FSA) dimension estimator, making it one of the best nearest neighbor-based dimension estimators available. We compute the probability density function of local FSA estimates, if the local manifold density is uniform. Based on the probability density function, we propose to use the median of local estimates as a basic global measure of intrinsic dimensionality, and we demonstrate the advantages of this asymptotically unbiased estimator over the previously proposed statistics: the mode and the mean. Additionally, from the probability density function, we derive the maximum likelihood formula for global intrinsic dimensionality, if i.i.d. holds. We tackle edge and finite-sample effects with an exponential correction formula, calibrated on hypercube datasets. We compare the performance of the corrected-median-FSA estimator with kNN estimators: maximum likelihood (ML, Levina-Bickel) and two implementations of DANCo (R and matlab). We show that corrected-median-FSA estimator beats the ML estimator and it is on equal footing with DANCo for standard synthetic benchmarks according to mean percentage error and error rate metrics. With the median-FSA algorithm, we reveal diverse changes in the neural dynamics while resting state and during epileptic seizures. We identify brain areas with lower-dimensional dynamics that are possible causal sources and candidates for being seizure onset zones.

Contemporary Epidemiological Surveillance (ES) relies heavily on data analytics. These analytics are critical input for pandemics preparedness networks; however, this input is not integrated into a form suitable for decision makers or experts in preparedness. A decision support system (DSS) with Computational Intelligence (CI) tools is required to bridge the gap between epidemiological model of evidence and expert group decision. We argue that such DSS shall be a cognitive dynamic system enabling the CI and human expert to work together. The core of such DSS must be based on machine reasoning techniques such as probabilistic inference, and shall be capable of estimating risks, reliability and biases in decision making.

Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process in a laboratory, ensuring high precision while being costly in materials and logistics. In both scenarios, only limited amount of data can be generated by querying the expensive information source at a finite number of inputs or designs. This problem is compounded further in the presence of a high-dimensional input space. State-of-the-art parameter space dimension reduction methods, such as active subspace, aim to identify a subspace of the original input space that is sufficient to explain the output response. These methods are restricted by their reliance on gradient evaluations or copious data, making them inadequate to expensive problems without direct access to gradients. The proposed methodology is gradient-free and fully Bayesian, as it quantifies uncertainty in both the low-dimensional subspace and the surrogate model parameters. This enables a full quantification of epistemic uncertainty and robustness to limited data availability. It is validated on multiple datasets from engineering and science and compared to two other state-of-the-art methods based on four aspects: a) recovery of the active subspace, b) deterministic prediction accuracy, c) probabilistic prediction accuracy, and d) training time. The comparison shows that the proposed method improves the active subspace recovery and predictive accuracy, in both the deterministic and probabilistic sense, when only few model observations are available for training, at the cost of increased training time.

Data cleaning is naturally framed as probabilistic inference in a generative model, combining a prior distribution over ground-truth databases with a likelihood that models the noisy channel by which the data are filtered, corrupted, and joined to yield incomplete, dirty, and denormalized datasets. Based on this view, we present PClean, a unified generative modeling architecture for cleaning and normalizing dirty data in diverse domains. Given an unclean dataset and a probabilistic program encoding relevant domain knowledge, PClean learns a structured representation of the data as a relational database of interrelated objects, and uses this latent structure to impute missing values, identify duplicates, detect errors, and propose corrections in the original data table. PClean makes three modeling and inference contributions: (i) a domain-general non-parametric generative model of relational data, for inferring latent objects and their network of latent connections; (ii) a domain-specific probabilistic programming language, for encoding domain knowledge specific to each dataset being cleaned; and (iii) a domain-general inference engine that adapts to each PClean program by constructing data-driven proposals used in sequential Monte Carlo and particle Gibbs. We show empirically that short (< 50-line) PClean programs deliver higher accuracy than state-of-the-art data cleaning systems based on machine learning and weighted logic; that PClean's inference algorithm is faster than generic particle Gibbs inference for probabilistic programs; and that PClean scales to large real-world datasets with millions of rows.