Abstract—We introduce Gaussian process dynamical models (GPDMs) for nonlinear time series analysis, with applications to learning models of human pose and motion from high-dimensional motion capture data. A GPDM is a latent variable model. It comprises a lowdimensional latent space with associated dynamics, as well as a map from the latent space to an observation space. We marginalize out the model parameters in closed form by using Gaussian process priors for both the dynamical and the observation mappings. This results in a nonparametric model for dynamical systems that accounts for uncertainty in the model. We demonstrate the approach and compare four learning algorithms on human motion capture data, in which each pose is 50-dimensional. Despite the use of small data sets, the GPDM learns an effective representation of the nonlinear dynamics in these spaces. Index Terms—Machine learning, motion, tracking, animation, stochastic processes, time series analysis. 1

Energy-Based Models (EBMs) capture dependencies between variables by associating a scalar energy to each configuration of the variables. Inference consists in clamping the value of observed variables and finding configurations of the remaining variables that minimize the energy. Learning consists in finding an energy function in which observed configurations of the variables are given lower energies than unobserved ones. The EBM approach provides a common theoretical framework for many learning models, including traditional discriminative and generative approaches, as well as graph-transformer networks, conditional random fields, maximum margin Markov networks, and several manifold learning methods. Probabilistic models must be properly normalized, which sometimes requires evaluating intractable integrals over the space of all possible variable configurations. Since EBMs have no requirement for proper normalization, this problem is naturally circumvented. EBMs can be viewed as a form of non-probabilistic factor graphs, and they provide considerably more flexibility in the design of architectures and training criteria than probabilistic approaches. 1

SybilInfer is an algorithm for labelling nodes in a social network as honest users or Sybils controlled by an adversary. At the heart of SybilInfer lies a probabilistic model of honest social networks, and an inference engine that returns potential regions of dishonest nodes. The Bayesian inference approach to Sybil detection comes with the advantage label has an assigned probability, indicating its degree of certainty. We prove through analytical results as well as experiments on simulated and real-world network topologies that, given standard constraints on the adversary, SybilInfer is secure, in that it successfully distinguishes between honest and dishonest nodes and is not susceptible to manipulation by the adversary. Furthermore, our results show that SybilInfer outperforms state of the art algorithms, both in being more widely applicable, as well as providing vastly more accurate results. 1

The Kalman Filter is a well-known recursive state estimator for linear systems. In practice the algorithm is often used for nonlinear systems by linearizing the system's process and measurement functions. Different Kalman Filter variants linearize the functions in different ways. This paper explains how the best known Kalman Filter variants -- i.e. the Extended Kalman Filter (EKF), Iterated Extended Kalman Filter (IEKF), the Central Difference Filter (CDF), the first order Divided Difference Filter (DD1) and the Unscented Kalman Filter (UKF) -- (i) linearize the process and measurement functions; (ii) take the linearization errors into account; and (iii) how the quality of the state estimates depends on the previous two choices. Besides some

In this paper we present a graphical model for polyphonic music transcription. Our model, formulated as a Dynamical Bayesian Network, embodies a transparent and computationally tractable approach to this acoustic analysis problem. An advantage of our approach is that it places emphasis on explicitly modelling the sound generation procedure. It provides a clear framework in which both high level (cognitive) prior information on music structure can be coupled with low level (acoustic physical) information in a principled manner to perform the analysis. The model is a special case of the, generally intractable, switching Kalman filter model. Where possible, we derive, exact polynomial time inference procedures, and otherwise efficient approximations. We argue that our generative model based approach is computationally feasible for many music applications and is readily extensible to more general auditory scene analysis scenarios.

Gaussian process priors can be used to define flexible, probabilistic classification models. Unfortunately exact Bayesian inference is analytically intractable and various approximation techniques have been proposed. In this work we review and compare Laplace’s method and Expectation Propagation for approximate Bayesian inference in the binary Gaussian process classification model. We present a comprehensive comparison of the approximations, their predictive performance and marginal likelihood estimates to results obtained by MCMC sampling. We explain theoretically and corroborate empirically the advantages of Expectation Propagation compared to Laplace’s method. Keywords: Gaussian process priors, probabilistic classification, Laplace’s approximation, expectation propagation, marginal likelihood, evidence, MCMC

There is growing interest in applying Bayesian techniques to NLP problems. There are a number of different estimators for Bayesian models, and it is useful to know what kinds of tasks each does well on. This paper compares a variety of different Bayesian estimators for Hidden Markov Model POS taggers with various numbers of hidden states on data sets of different sizes. Recent papers have given contradictory results when comparing Bayesian estimators to Expectation Maximization (EM) for unsupervised HMM POS tagging, and we show that the difference in reported results is largely due to differences in the size of the training data and the number of states in the HMM. We invesigate a variety of samplers for HMMs, including some that these earlier papers did not study. We find that all of Gibbs samplers do well with small data sets and few states, and that Variational Bayes does well on large data sets and is competitive with the Gibbs samplers. In terms of times of convergence, we find that Variational Bayes was the fastest of all the estimators, especially on large data sets, and that explicit Gibbs sampler (both pointwise and sentence-blocked) were generally faster than their collapsed counterparts on large data sets. 1

Abstract—Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, sub-Nyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can complement conventional CS methods based on linear programming or greedy algorithms. We perform asymptotically optimal Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast computation is obtained by reducing the size of the graphical model with sparse encoding matrices. To decode a length- signal containing large coefficients, our CS-BP decoding algorithm uses ( log ()) measurements and ( log 2 ()) computation. Finally, although we focus on a two-state mixture Gaussian model, CS-BP is easily adapted to other signal models. Index Terms—Bayesian inference, belief propagation, compressive sensing, fast algorithms, sparse matrices. I.

Compressed sensing is an emerging field that enables to reconstruct sparse or compressible signals from a small number of linear projections. We describe a specific measurement scheme using an LDPC-like measurement matrix, which is a real-valued analogue to LDPC techniques over a finite alphabet. We then describe the reconstruction details for mixture Gaussian signals. The technique can be extended to additional compressible signal models. 1

This paper considers the problem of performing decentralised coordination of low-power embedded devices (as is required within many environmental sensing and surveillance applications). Specifically, we address the generic problem of maximising social welfare within a group of interacting agents. We propose a novel representation of the problem, as a cyclic bipartite factor graph, composed of variable and function nodes (representing the agents’ states and utilities respectively). We show that such representation allows us to use an extension of the max-sum algorithm to generate approximate solutions to this global optimisation problem through local decentralised message passing. We empirically evaluate this approach on a canonical coordination problem (graph colouring), and benchmark it against state of the art approximate and complete algorithms (DSA and DPOP). We show that our approach is robust to lossy communication, that it generates solutions closer to those of DPOP than DSA is able to, and that it does so with a communication cost (in terms of total messages size) that scales very well with the number of agents in the system (compared to the exponential increase of DPOP). Finally, we describe a hardware implementation of our algorithm operating on low-power Chipcon CC2431 System-on-Chip sensor nodes.