--Belief Propagation (BP) is a message-passing algorithm for approximate inference over Probabilistic Graphical Models (PGMs), finding many applications such as computer vision, error-correcting codes, and protein-folding. While general, the convergence and speed of the algorithm has limited its practical use on difficult inference problems. As an algorithm that is highly amenable to parallelization, many-core Graphical Processing Units (GPUs) could significantly improve BP performance. Improving BP through many-core systems is nontrivial: the scheduling of messages in the algorithm strongly affects performance. We present a study of message scheduling for BP on GPUs. We demonstrate that BP exhibits a tradeoff between speed and convergence based on parallelism and show that existing message schedulings are not able to utilize this tradeoff. T o this end, we present a novel randomized message scheduling approach, Randomized BP (RnBP), which outperforms existing methods on the GPU. I NTRODUCTION Probabilistic Graphical Models (PGMs) are powerful, general machine learning models that encode distributions over random variables. PGM Inference, in which we seek to compute some probabilistic beliefs within the system modeled by the PGM, is in general an intractable problem, leading to dependence on approximate algorithms. Belief Propagation (BP) is a widely employed approximate inference algorithms for PGMs [1].

Concept drift is formally defined as the change in joint distribution of a set of input variables X and a target variable y. The two types of drift that are extensively studied are real drift and virtual drift where the former is the change in posterior probabilities p(y|X) while the latter is the change in distribution of X without affecting the posterior probabilities. Many approaches on concept drift detection either assume full availability of data labels, y or handle only the virtual drift. In a streaming environment, the assumption of full availability of data labels, y is questioned. On the other hand, approaches that deal with virtual drift failed to address real drift. Rather than improving the state-of-the-art methods, this paper presents a semi-supervised framework to deal with the challenges above. The objective of the proposed framework is to learn from streaming environment with limited data labels, y and detect real drift concurrently. This paper proposes a novel concept drift detection method utilizing the densities of posterior probabilities in partially labeled streaming environments. Experimental results on both synthetic and realworld datasets show that our proposed semi-supervised framework enables the detection of concept drift in such environment while achieving comparable prediction performance to the state-of-the-art methods.

Immersive simulations are increasingly used for teaching and training in many societally important arenas including healthcare, disaster response and science education. The interactions of participants in such settings lead to a complex array of emergent outcomes that present challenges for analysis. This paper studies a central element of such an analysis, namely the interpretability of models for inferring structure in time series data. This problem is explored in the context of modeling student interactions in an immersive ecological-system simulation. Unsupervised machine learning is applied to data on system dynamics with the aim of helping teachers determine the effects of students' actions on these dynamics. We address the question of choosing the optimal machine learning model, considering both statistical information criteria and interpretabilty quality. The results of a user study show that the models that are the best understood by people are not those that optimize information theoretic criteria. In addition, a model using a fully Bayesian approach performed well on both statistical measures and on human-subject tests of interpretabilty, making it a good candidate for automated model selection that does not require human-in-the-loop evaluation. The results from this paper are already being used in the classroom and can inform the design of interpretable models for a broad range of socially relevant domains. 1 Introduction There is increasing evidence of the value of multi-person embodied simulations for engaging learners in a variety of applications, such as healthcare, disaster response and education (Alinier et al. 2014; Amir and Gal 2013).

Active inference is a first (Bayesian) principles account of how autonomous agents might operate in dynamic, non-stationary environments. The optimization of congruent formulations of the free energy functional (variational and expected), in active inference, enables agents to make inferences about the environment and select optimal behaviors. The agent achieves this by evaluating (sensory) evidence in relation to its internal generative model that entails beliefs about future (hidden) states and sequence of actions that it can choose. In contrast to analogous frameworks $-$ by operating in a pure belief-based setting (free energy functional of beliefs about states) $-$ active inference agents can carry out epistemic exploration and naturally account for uncertainty about their environment. Through this review, we disambiguate these properties, by providing a condensed overview of the theory underpinning active inference. A T-maze simulation is used to demonstrate how these behaviors emerge naturally, as the agent makes inferences about the observed outcomes and optimizes its generative model (via belief updating). Additionally, the discrete state-space and time formulation presented provides an accessible guide on how to derive the (variational and expected) free energy equations and belief updating rules. We conclude by noting that this formalism can be applied in other engineering applications; e.g., robotic arm movement, playing Atari games, etc., if appropriate underlying probability distributions (i.e. generative model) can be formulated.

Given a data set and a subset of labels the problem of semi-supervised learning on point clouds is to extend the labels to the entire data set. In this paper we extend the labels by minimising the constrained discrete $p$-Dirichlet energy. Under suitable conditions the discrete problem can be connected, in the large data limit, with the minimiser of a weighted continuum $p$-Dirichlet energy with the same constraints. We take advantage of this connection by designing numerical schemes that first estimate the density of the data and then apply PDE methods, such as pseudo-spectral methods, to solve the corresponding Euler-Lagrange equation. We prove that our scheme is consistent in the large data limit for two methods of density estimation: kernel density estimation and spline kernel density estimation.

While it provides a good foundation to system modeling, analysis, and an understanding of the real world, its application to algorithm design suffers from computational intractability. In this work, we develop a new framework of uncertainty variables to model uncertainty. A simple uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set map, from a given realization of a variable to a set of possible realizations of another variable. We prove Bayes' law and the law of total probability equivalents for uncertainty variables. We define a notion of independence, conditional independence, and pairwise independence for a collection of uncertainty variables, and show that this new notion of independence preserves the properties of independence defined over random variables. We then develop a graphical model, namely Bayesian uncertainty network, a Bayesian network equivalent defined over a collection of uncertainty variables, and show that all the natural conditional independence properties, expected out of a Bayesian network, hold for the Bayesian uncertainty network. We also define the notion of point estimate, and show its relation with the maximum a posteriori estimate.

Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance unbiased estimators of derivatives at any order. Our objective is compatible with arbitrary advantage estimators, which allows the control of the bias and variance of any-order derivatives when using function approximation. Furthermore, we propose a method to trade off bias and variance of higher order derivatives by discounting the impact of more distant causal dependencies. We demonstrate the correctness and utility of our objective in analytically tractable MDPs and in meta-reinforcement-learning for continuous control.

For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer their modes from observations in real time. The modes can be real or complex. For a real mode, we infer its damping rate, mode shape and amplitude. For a complex mode, we infer its frequency, damping rate, (complex) mode shape and (complex) amplitude. The work is motivated and illustrated by the problem of detection of oscillations in power flow in AC electrical networks. Suggestions of other applications are given.

In the Bayesian analysis of signals immersed in noise [1], we seek a representation for the posterior probability of one or more parameters that govern the shape of the signals. Unless the parameter-to-signal map (the forward model) is very simple, the analysis (or inverse solution) comes at significant computational cost, as it requires the stochastic exploration of the likelihood surface at a large number of locations in parameter space. Such is the case, for instance, of parameter estimation for gravitational-wave sources such as the compact binaries detected by LIGO-Virgo [2, 3]; here each likelihood evaluation requires that we generate the gravitational waveform corresponding to a set of source parameters, and compute its noise-weighted correlation with detector data [4]. Waveform generation is usually the costlier operation, so gravitational-wave analysts often utilize faster, less accurate waveform models [5, 6], or accelerated surrogates of slower, more accurate models [7]. Extending the analysis from the data we have to the data we might measure (i.e., characterizing the parameter-estimation prospects of future experiments) compounds the expense, since we need to explore posteriors for many noise realizations, and across the domain of possible source parameters. For concreteness, we price the evaluation of a single Bayesian posterior at null 10 6 times the cost of generating a waveform, and the characterization of parameter-estimation prospects at null 10 6 times the cost of a posterior. With current computational resources, this means that (for instance) accurate component-mass estimates only become available hours or days after the detection of a binary black-hole coalescence [8, 9], while any extensive study of parameter-estimation prospects must rely on less reliable techniques such as the Fisher-matrix approximation [10]. In this Letter, we show how one-or two-dimensional marginalized Bayesian posteriors may be produced using deep neural networks [11] trained on large ensembles of signal noise data streams.

A framework to boost efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation, which we call the refined variational approximation. Its strength lies both in ease of implementation and in automatically tuning the sampler parameters to speed up mixing time. Several strategies to approximate the \emph{evidence lower bound} (ELBO) computation are introduced, including a rewriting of the ELBO objective. A specialization towards state-space models is proposed. Experimental evidence of its efficient performance is shown by solving an influence diagram in a high-dimensional space using a conditional variational autoencoder (cVAE) as a deep Bayes classifier; an unconditional VAE on density estimation tasks; and state-space models for time-series data.