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.

The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbers and report a remarkable improvement over previous efforts, (2) query for favourability, and (3) predict discrete symmetries, a highly imbalanced problem to which the Synthetic Minority Oversampling Technique (SMOTE) is applied to boost performance. In each case study, we employ a genetic algorithm to optimise the hyperparameters of the neural network. We demonstrate that our approach provides quick diagnostic tools capable of shortlisting quasi-realistic string models based on compactification over smooth CICYs and further supports the paradigm that classes of problems in algebraic geometry can be machine learned.

Analyzing large-scale, multi-experiment studies requires scientists to test each experimental outcome for statistical significance and then assess the results as a whole. We present Black Box FDR (BB-FDR), an empirical-Bayes method for analyzing multi-experiment studies when many covariates are gathered per experiment. BB-FDR learns a series of black box predictive models to boost power and control the false discovery rate (FDR) at two stages of study analysis. In Stage 1, it uses a deep neural network prior to report which experiments yielded significant outcomes. In Stage 2, a separate black box model of each covariate is used to select features that have significant predictive power across all experiments. In benchmarks, BB-FDR outperforms competing state-of-the-art methods in both stages of analysis. We apply BB-FDR to two real studies on cancer drug efficacy. For both studies, BB-FDR increases the proportion of significant outcomes discovered and selects variables that reveal key genomic drivers of drug sensitivity and resistance in cancer.

Despite the recent successes of probabilistic programming languages (PPLs) in AI applications, PPLs offer only limited support for random variables whose distributions combine discrete and continuous elements. We develop the notion of measure-theoretic Bayesian networks (MTBNs) and use it to provide more general semantics for PPLs with arbitrarily many random variables defined over arbitrary measure spaces. We develop two new general sampling algorithms that are provably correct under the MTBN framework: the lexicographic likelihood weighting (LLW) for general MTBNs and the lexicographic particle filter (LPF), a specialized algorithm for state-space models. We further integrate MTBNs into a widely used PPL system, BLOG, and verify the effectiveness of the new inference algorithms through representative examples.