Many areas of research are characterised by the deluge of large-scale highly-dimensional time-series data. However, using the data available for prediction and decision making is hampered by the current lag in our ability to uncover and quantify true interactions that explain the outcomes.We are interested in areas such as intensive care medicine, which are characterised by i) continuous monitoring of multivariate variables and non-uniform sampling of data streams, ii) the outcomes are generally governed by interactions between a small set of rare events, iii) these interactions are not necessarily definable by specific values (or value ranges) of a given group of variables, but rather, by the deviations of these values from the normal state recorded over time, iv) the need to explain the predictions made by the model. Here, while numerous data mining models have been formulated for outcome prediction, they are unable to explain their predictions. We present a model for uncovering interactions with the highest likelihood of generating the outcomes seen from highly-dimensional time series data. Interactions among variables are represented by a relational graph structure, which relies on qualitative abstractions to overcome non-uniform sampling and to capture the semantics of the interactions corresponding to the changes and deviations from normality of variables of interest over time. Using the assumption that similar templates of small interactions are responsible for the outcomes (as prevalent in the medical domains), we reformulate the discovery task to retrieve the most-likely templates from the data.

Cardiovascular Diseases (CVD) and strokes produce immense health and economic burdens globally. Coronary Artery Disease (CAD) is the most common type of cardiovascular disease. Coronary Angiography, which is an invasive treatment, is also the standard procedure for diagnosing CAD. In this work, we illustrate a Medical Decision Support System for the prediction of Coronary Artery Disease (CAD) utilizing Fuzzy Cognitive Maps (FCMs). FCMs are a promising modeling methodology, based on human knowledge, capable of dealing with ambiguity and uncertainty, and learning how to adapt to the unknown or changing environment. The newly proposed MDSS is developed using the basic notions of Fuzzy Logic and Fuzzy Cognitive Maps, with some adjustments to improve the results. The proposed model, tested on a labelled CAD dataset of 303 patients, obtains an accuracy of 78.2% outmatching several state-of-the-art classification algorithms.

A sum-product network (SPN) is a probabilistic model, based on a rooted acyclic directed graph, in which terminal nodes represent univariate probability distributions and non-terminal nodes represent convex combinations (weighted sums) and products of probability functions. They are closely related to probabilistic graphical models, in particular to Bayesian networks with multiple context-specific independencies. Their main advantage is the possibility of building tractable models from data, i.e., models that can perform several inference tasks in time proportional to the number of links in the graph. They are somewhat similar to neural networks and can address the same kinds of problems, such as image processing and natural language understanding. This paper offers a survey of SPNs, including their definition, the main algorithms for inference and learning from data, the main applications, a brief review of software libraries, and a comparison with related models

We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This ignores the non-deterministic character of most tasks. Especially if crucial decisions are based on the predictions, like in medical applications, it is essential to quantify the prediction uncertainty. The presented deep learning transformation model estimates the whole conditional probability distribution, which is the most thorough way to capture uncertainty about the outcome. We combine ideas from a statistical transformation model (most likely transformation) with recent transformation models from deep learning (normalizing flows) to predict complex outcome distributions. The core of the method is a parameterized transformation function which can be trained with the usual maximum likelihood framework using gradient descent. The method can be combined with existing deep learning architectures. For small machine learning benchmark datasets, we report state of the art performance for most dataset and partly even outperform it. Our method works for complex input data, which we demonstrate by employing a CNN architecture on image data.

It has recently been established that the numerical solution of ordinary differential equations can be posed as a nonlinear Bayesian inference problem, which can be approximately solved via Gaussian filtering and smoothing, whenever a Gauss--Markov prior is used. In this paper the class of $\nu$ times differentiable linear time invariant Gauss--Markov priors is considered. A taxonomy of Gaussian estimators is established, with the maximum a posteriori estimate at the top of the hierarchy, which can be computed with the iterated extended Kalman smoother. The remaining three classes are termed explicit, semi-implicit, and implicit, which are in similarity with the classical notions corresponding to conditions on the vector field, under which the filter update produces a local maximum a posteriori estimate. The maximum a posteriori estimate corresponds to an optimal interpolant in the reproducing Hilbert space associated with the prior, which in the present case is equivalent to a Sobolev space of smoothness $\nu+1$. Consequently, using methods from scattered data approximation and nonlinear analysis in Sobolev spaces, it is shown that the maximum a posteriori estimate converges to the true solution at a polynomial rate in the fill-distance (maximum step size) subject to mild conditions on the vector field. The methodology developed provides a novel and more natural approach to study the convergence of these estimators than classical methods of convergence analysis. The methods and theoretical results are demonstrated in numerical examples.

Predictive process monitoring aims to predict future characteristics of an ongoing process case, such as case outcome or remaining timestamp. Recently, several predictive process monitoring methods based on deep learning such as Long Short-Term Memory or Convolutional Neural Network have been proposed to address the problem of next event prediction. However, due to insufficient training data or sub-optimal network configuration and architecture, these approaches do not generalize well the problem at hand. This paper proposes a novel adversarial training framework to address this shortcoming, based on an adaptation of Generative Adversarial Networks (GANs) to the realm of sequential temporal data. The training works by putting one neural network against the other in a two-player game (hence the "adversarial" nature) which leads to predictions that are indistinguishable from the ground truth. We formally show that the worst-case accuracy of the proposed approach is at least equal to the accuracy achieved in non-adversarial settings. From the experimental evaluation it emerges that the approach systematically outperforms all baselines both in terms of accuracy and earliness of the prediction, despite using a simple network architecture and a naive feature encoding. Moreover, the approach is more robust, as its accuracy is not affected by fluctuations over the case length.

Researchers have long been interested in the role that norms can play in governing agent actions in multi-agent systems. Much work has been done on formalising normative concepts from human society and adapting them for the government of open software systems, and on the simulation of normative processes in human and artificial societies. However, there has been comparatively little work on applying normative MAS mechanisms to understanding the norms in human society. This work investigates this issue in the context of international politics. Using the GDELT dataset, containing machine-encoded records of international events extracted from news reports, we extracted bilateral sequences of inter-country events and applied a Bayesian norm mining mechanism to identify norms that best explained the observed behaviour. A statistical evaluation showed that the normative model fitted the data significantly better than a probabilistic discrete event model.

Assume we have potential "causes" $z\in Z$, which produce "events" $w$ with known probabilities $\beta(w|z)$. We observe $w_1,w_2,...,w_n$, what can we say about the distribution of the causes? A Bayesian estimate will assume a prior on distributions on $Z$ (we assume a Dirichlet prior) and calculate a posterior. An average over that posterior then gives a distribution on $Z$, which estimates how much each cause $z$ contributed to our observations. This is the setting of Latent Dirichlet Allocation, which can be applied e.g. to topics "producing" words in a document. In this setting usually the number of observed words is large, but the number of potential topics is small. We are here interested in applications with many potential "causes" (e.g. locations on the globe), but only a few observations. We show that the exact Bayesian estimate can be computed in linear time (and constant space) in $|Z|$ for a given upper bound on $n$ with a surprisingly simple formula. We generalize this algorithm to the case of sparse probabilities $\beta(w|z)$, in which we only need to assume that the tree width of an "interaction graph" on the observations is limited. On the other hand we also show that without such limitation the problem is NP-hard.

We introduce manifold-modeling flows (MFMFs), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs, autoencoders, and energy-based models, they have the potential to represent data sets with a manifold structure more faithfully and provide handles on dimensionality reduction, denoising, and out-of-distribution detection. We argue why such models should not be trained by maximum likelihood alone and present a new training algorithm that separates manifold and density updates. With two pedagogical examples we demonstrate how manifold-modeling flows let us learn the data manifold and allow for better inference than standard flows in the ambient data space.

In linear regression models, a fusion of the coefficients is used to identify the predictors having similar relationships with the response. This is called variable fusion. This paper presents a novel variable fusion method in terms of Bayesian linear regression models. We focus on hierarchical Bayesian models based on a spike-and-slab prior approach. A spike-and-slab prior is designed to perform variable fusion. To obtain estimates of parameters, we develop a Gibbs sampler for the parameters. Simulation studies and a real data analysis show that our proposed method has better performances than previous methods.