We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth term and multiple stochastic nonsmooth terms. In each iteration, our splitting technique only requires access to a stochastic gradient of the smooth term and a stochastic proximal operator for each of the nonsmooth terms. We establish nonasymptotic sublinear and linear convergence rates under convexity and strong convexity of the smooth term, respectively, expressed in terms of the KL divergence and Wasserstein distance. We illustrate the efficiency of our sampling technique through numerical simulations on a Bayesian learning task.

General intelligence, the ability to solve arbitrary solvable problems, is supposed by many to be artificially constructible. Narrow intelligence, the ability to solve a given particularly difficult problem, has seen impressive recent development. Notable examples include self-driving cars, Go engines, image classifiers, and translators. Artificial General Intelligence (AGI) presents dangers that narrow intelligence does not: if something smarter than us across every domain were indifferent to our concerns, it would be an existential threat to humanity, just as we threaten many species despite no ill will. Even the theory of how to maintain the alignment of an AGI's goals with our own has proven highly elusive. We present the first algorithm we are aware of for asymptotically unambitious AGI, where "unambitiousness" includes not seeking arbitrary power. Thus, we identify an exception to the Instrumental Convergence Thesis, which is roughly that by default, an AGI would seek power, including over us.

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from experiments, field measurements, and large-scale simulations at multiple spatiotemporal scales. Machine learning presents us with a wealth of techniques to extract information from data that can be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. We outline fundamental machine learning methodologies and discuss their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that links data with modeling, experiments, and simulations. Machine learning provides a powerful information processing framework that can augment, and possibly even transform, current lines of fluid mechanics research and industrial applications.

We introduce a conditional density estimation model termed the conditional density operator. It naturally captures multivariate, multimodal output densities and is competitive with recent neural conditional density models and Gaussian processes. To derive the model, we propose a novel approach to the reconstruction of probability densities from their kernel mean embeddings by drawing connections to estimation of Radon-Nikodym derivatives in the reproducing kernel Hilbert space (RKHS). We prove finite sample error bounds which are independent of problem dimensionality. Furthermore, the resulting conditional density model is applied to real-world data and we demonstrate its versatility and competitive performance.

Capsule Networks are a recently proposed alternative for constructing Neural Networks, and early indications suggest that they can provide greater generalisation capacity using fewer parameters. In capsule networks scalar neurons are replaced with capsule vectors or matrices, whose entries represent different properties of objects. The relationships between objects and its parts are learned via trainable viewpoint-invariant transformation matrices, and the presence of a given object is decided by the level of agreement among votes from its parts. This interaction occurs between capsule layers and is a process called routing-by-agreement. Although promising, capsule networks remain underexplored by the community, and in this paper we present a new capsule routing algorithm based of Variational Bayes for a mixture of transforming gaussians. Our Bayesian approach addresses some of the inherent weaknesses of EM routing such as the 'variance collapse' by modelling uncertainty over the capsule parameters in addition to the routing assignment posterior probabilities. We test our method on public domain datasets and outperform the state-of-the-art performance on smallNORB using 50% less capsules.

Inference in Gaussian process (GP) models is computationally challenging for large data, and often difficult to approximate with a small number of inducing points. We explore an alternative approximation that employs stochastic inference networks for a flexible inference. Unfortunately, for such networks, minibatch training is difficult to be able to learn meaningful correlations over function outputs for a large dataset. We propose an algorithm that enables such training by tracking a stochastic, functional mirror-descent algorithm. At each iteration, this only requires considering a finite number of input locations, resulting in a scalable and easy-to-implement algorithm. Empirical results show comparable and, sometimes, superior performance to existing sparse variational GP methods.

Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static graphs. However, many applications involve evolving graphs. This introduces important challenges for learning and inference since nodes, attributes, and edges change over time. In this survey, we review the recent advances in representation learning for dynamic graphs, including dynamic knowledge graphs. We describe existing models from an encoder-decoder perspective, categorize these encoders and decoders based on the techniques they employ, and analyze the approaches in each category. We also review several prominent applications and widely used datasets, and highlight directions for future research.

Complex structures are typical in machine learning. Tailoring learning algorithms for every structure requires an effort that may be saved by defining a generic learning procedure adaptive to any complex structure. In this paper, we propose to map any complex structure onto a generic form, called serialization, over which we can apply any sequence-based density estimator. We then show how to transfer the learned density back onto the space of original structures. To expose the learning procedure to the structural particularities of the original structures, we take care that the serializations reflect accurately the structures' properties. Enumerating all serializations is infeasible. We propose an effective way to sample representative serializations from the complete set of serializations which preserves the statistics of the complete set. Our method is competitive or better than state of the art learning algorithms that have been specifically designed for given structures. In addition, since the serialization involves sampling from a combinatorial process it provides considerable protection from overfitting, which we clearly demonstrate on a number of experiments.

The probability density function for the visible sector of a Riemann-Theta Boltzmann machine can be taken conditional on a subset of the visible units. We derive that the corresponding conditional density function is given by a reparameterization of the Riemann-Theta Boltzmann machine modelling the original probability density function. Therefore the conditional densities can be directly inferred from the Riemann-Theta Boltzmann machine.

Complex phenomena are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to use an approximate likelihood or faster emulator model for efficient statistical inference. We describe a new two-sample testing framework for quantifying the quality of the fit to simulations at fixed parameter values. This framework can leverage any regression method to handle complex high-dimensional data and attain higher power in settings where well-known distance-based tests would not. We also introduce a statistically rigorous test for assessing global goodness-of-fit across simulation parameters. In cases where the fit is inadequate, our method provides valuable diagnostics by allowing one to identify regions in both feature and parameter space which the model fails to reproduce well. We provide both theoretical results and examples which illustrate the effectiveness of our approach.