The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability --- via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

Formal Verification (Fv) and Machine Learning (Ml) can seem incompatible due to their opposite mathematical foundations and their use in real-life problems: Fv mostly relies on discrete mathematics and aims at ensuring correctness; Ml often relies on probabilistic models and consists of learning patterns from training data. In this paper, we postulate that they are complementary in practice, and explore how Ml helps Fv in its classical approaches: static analysis, model-checking, theorem-proving, and Sat solving. We draw a landscape of the current practice and catalog some of the most prominent uses of Ml inside Fv tools, thus offering a new perspective on Fv techniques that can help researchers and practitioners to better locate the possible synergies. We discuss lessons learned from our work, point to possible improvements and offer visions for the future of the domain in the light of the science of software and systems modeling.

A staggering amount of data is created everyday; analyzing and organizing this enormous amount of data can be quite a complex task. Haskell is a powerful and well-designed functional programming language that is designed to work with complex data. It is trending in the field of data science as it provides a powerful platform for robust data science practices. This course will introduce the basic concepts of Haskell and move on to discuss how Haskell can be used to solve the issues by using the real-world data. The course will guide you through the installation procedure, after you have all the tools that you require in place, you will explore the basic concepts of Haskell including the functions, and the data structures.

We present an application of deep generative models in the context of partial-differential equation (PDE) constrained inverse problems. We combine a generative adversarial network (GAN) representing an a priori model that creates subsurface geological structures and their petrophysical properties, with the numerical solution of the PDE governing the propagation of acoustic waves within the earth's interior. We perform Bayesian inversion using an approximate Metropolis-adjusted Langevin algorithm (MALA) to sample from the posterior given seismic observations. Gradients with respect to the model parameters governing the forward problem are obtained by solving the adjoint of the acoustic wave equation. Gradients of the mismatch with respect to the latent variables are obtained by leveraging the differentiable nature of the deep neural network used to represent the generative model. We show that approximate MALA sampling allows efficient Bayesian inversion of model parameters obtained from a prior represented by a deep generative model, obtaining a diverse set of realizations that reflect the observed seismic response.

We introduce a method for embedding words as probability densities in a low-dimensional space. Rather than assuming that a word embedding is fixed across the entire text collection, as in standard word embedding methods, in our Bayesian model we generate it from a word-specific prior density for each occurrence of a given word. Intuitively, for each word, the prior density encodes the distribution of its potential 'meanings'. These prior densities are conceptually similar to Gaussian embeddings. Interestingly, unlike the Gaussian embeddings, we can also obtain context-specific densities: they encode uncertainty about the sense of a word given its context and correspond to posterior distributions within our model. The context-dependent densities have many potential applications: for example, we show that they can be directly used in the lexical substitution task. We describe an effective estimation method based on the variational autoencoding framework. We also demonstrate that our embeddings achieve competitive results on standard benchmarks.

While off-policy temporal difference (TD) methods have widely been used in reinforcement learning due to their efficiency and simple implementation, their Bayesian counterparts have not been utilized as frequently. One reason is that the non-linear max operation in the Bellman optimality equation makes it difficult to define conjugate distributions over the value functions. In this paper, we introduce a novel Bayesian approach to off-policy TD methods using Assumed Density Filtering (ADFQ), which updates beliefs on state-action values (Q) through an online Bayesian inference method. Uncertainty measures in the beliefs provide a natural regularization for learning, and we show how ADFQ reduces in a limiting case to the traditional Q-learning algorithm. Our empirical results demonstrate that the proposed ADFQ algorithms outperform comparable algorithms on several task domains. Moreover, our algorithms are computationally more efficient than other existing approaches to Bayesian reinforcement learning.

Machine learning is a major component in the race towards artificial intelligence. Whether you're seeking true artificial intelligence or simply trying to gain insight from all the data you've been collecting, machine learning is a major step forward. But where to get started? If you're a beginner, machine learning can feel overwhelming – how to choose which algorithms to use, from the seemingly infinite options, and how to know just which one will provide the right predictions (data outputs). These top 5 machine learning algorithms for beginners offer a fine balance of ease, lower computational power, and immediate, accurate results.

The vast majority of network datasets contains errors and omissions, although this is rarely incorporated in traditional network analysis. Recently, an increasing effort has been made to fill this methodological gap by developing network reconstruction approaches based on Bayesian inference. These approaches, however, rely on assumptions of uniform error rates and on direct estimations of the existence of each edge via repeated measurements, something that is currently unavailable for the majority of network data. Here we develop a Bayesian reconstruction approach that lifts these limitations by not only allowing for heterogeneous errors, but also for individual edge measurements without direct error estimates. Our approach works by coupling the inference approach with structured generative network models, which enable the correlations between edges to be used as reliable error estimates. Although our approach is general, we focus on the stochastic block model as the basic generative process, from which efficient nonparametric inference can be performed, and yields a principled method to infer hierarchical community structure from noisy data. We demonstrate the efficacy of our approach with a variety of empirical and artificial networks.

With the world moving towards being increasingly dependent on computers and automation, one of the main challenges in the current decade has been to build secure applications, systems and networks. Alongside these challenges, the number of threats is rising exponentially due to the attack surface increasing through numerous interfaces offered for each service. To alleviate the impact of these threats, researchers have proposed numerous solutions; however, current tools often fail to adapt to ever-changing architectures, associated threats and 0-days. This manuscript aims to provide researchers with a taxonomy and survey of current dataset composition and current Intrusion Detection Systems (IDS) capabilities and assets. These taxonomies and surveys aim to improve both the efficiency of IDS and the creation of datasets to build the next generation IDS as well as to reflect networks threats more accurately in future datasets. To this end, this manuscript also provides a taxonomy and survey or network threats and associated tools. The manuscript highlights that current IDS only cover 25% of our threat taxonomy, while current datasets demonstrate clear lack of real-network threats and attack representation, but rather include a large number of deprecated threats, hence limiting the accuracy of current machine learning IDS. Moreover, the taxonomies are open-sourced to allow public contributions through a Github repository.

A simple framework Probabilistic Multi-view Graph Embedding (PMvGE) is proposed for multi-view feature learning with many-to-many associations so that it generalizes various existing multi-view methods. PMvGE is a probabilistic model for predicting new associations via graph embedding of the nodes of data vectors with links of their associations. Multi-view data vectors with many-to-many associations are transformed by neural networks to feature vectors in a shared space, and the probability of new association between two data vectors is modeled by the inner product of their feature vectors. While existing multi-view feature learning techniques can treat only either of many-to-many association or non-linear transformation, PMvGE can treat both simultaneously. By combining Mercer's theorem and the universal approximation theorem, we prove that PMvGE learns a wide class of similarity measures across views. Our likelihood-based estimator enables efficient computation of non-linear transformations of data vectors in large-scale datasets by minibatch SGD, and numerical experiments illustrate that PMvGE outperforms existing multi-view methods.