The normalizing constants of these distributions depend on gamma functions whose arguments include shape (gamma, inverse gamma) and concentration (beta, Dirichlet) parameters. Bayesian learning of parameters nested inside the gamma function presents significant technical difficulties, since there is no known conjugate prior distribution. In fact, inferring the shape parameter in the gamma distribution is a long-studied problem in Bayesian inference (Damsleth, 1975; Rossell et al., 2009; Miller, 2018). In this paper, we develop the theoretical and algorithmic foundation of a P olya-inverse Gamma (PIG) data augmentation scheme for fully Bayesian inference of shape and concentration parameters in gamma, inverse gamma, and Dirichlet models, respectively . PIG data augmentation may be utilized to design efficient Markov chain Monte Carlo (MCMC) algorithms in latent Dirichlet allocation (Blei et al., 2003), Beta-negative binomial models (Zhou et al., 2012), and Gamma-Gamma (GaGa) hierarchical models (Rossell et al., 2009).

We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of nonlinear mixed-effects (NLME) dynamical systems, the statistical workhorse for many experimental sciences. We cast parameter inference as stochastic optimisation of an end-to-end differentiable, block-conditional variational autoencoder. We specify the dynamics of the data-generating process as an ordinary differential equation (ODE) such that both the ODE and its solver are fully differentiable. This model class is highly flexible: the ODE right-hand sides can be a mixture of user-prescribed or "white-box" sub-components and neural network or "black-box" sub-components. Using stochastic optimisation, our amortised inference algorithm could seamlessly scale up to massive data collection pipelines (common in labs with robotic automation). Finally, our framework supports interpretability with respect to the underlying dynamics, as well as predictive generalization to unseen combinations of group components (also called "zero-shot" learning). We empirically validate our method by predicting the dynamic behaviour of bacteria that were genetically engineered to function as biosensors.

We construct a new distribution for the simplex using the Kumaraswamy distribution and an ordered stick-breaking process. We explore and develop the theoretical properties of this new distribution and prove that it exhibits symmetry under the same conditions as the well-known Dirichlet. Like the Dirichlet, the new distribution is adept at capturing sparsity but, unlike the Dirichlet, has an exact and closed form reparameterization--making it well suited for deep variational Bayesian modeling. We demonstrate the distribution's utility in a variety of semi-supervised auto-encoding tasks. In all cases, the resulting models achieve competitive performance commensurate with their simplicity, use of explicit probability models, and abstinence from adversarial training.

We introduce a unified probabilistic approach for deep continual learning based on variational Bayesian inference with open set recognition. Our model combines a probabilistic encoder with a generative model and a generative linear classifier that get shared across tasks. The open set recognition bounds the approximate posterior by fitting regions of high density on the basis of correctly classified data points and balances open-space risk with recognition errors. Catastrophic inference for both generative models is significantly alleviated through generative replay, where the open set recognition is used to sample from high density areas of the class specific posterior and reject statistical outliers. Our approach naturally allows for forward and backward transfer while maintaining past knowledge without the necessity of storing old data, regularization or inferring task labels. We demonstrate compelling results in the challenging scenario of incrementally expanding the single-head classifier for both class incremental visual and audio classification tasks, as well as incremental learning of datasets across modalities.

We consider Bayesian classification with Gaussian processes (GPs) and define robustness of a classifier in terms of the worst-case difference in the classification probabilities with respect to input perturbations. For a subset of the input space $T\subseteq \mathbb{R}^m$ such properties reduce to computing the infimum and supremum of the classification probabilities for all points in $T$. Unfortunately, computing the above values is very challenging, as the classification probabilities cannot be expressed analytically. Nevertheless, using the theory of Gaussian processes, we develop a framework that, for a given dataset $\mathcal{D}$, a compact set of input points $T\subseteq \mathbb{R}^m$ and an error threshold $\epsilon>0$, computes lower and upper bounds of the classification probabilities by over-approximating the exact range with an error bounded by $\epsilon$. We provide experimental comparison of several approximate inference methods for classification on tasks associated to MNIST and SPAM datasets showing that our results enable quantification of uncertainty in adversarial classification settings.

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.