Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or "particle") representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

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A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

Can machine learning deliver AI? Theoretical results, inspiration from the brain and cognition, as well as machine learning experiments suggest that in order to learn the kind of complicated functions that can represent high-level abstractions (e.g. in vision, language, and other AI-level tasks), one would need deep architectures. Deep architectures are composed of multiple levels of non-linear operations, such as in neural nets with many hidden layers, graphical models with many levels of latent variables, or in complicated propositional formulae re-using many sub-formulae. Each level of the architecture represents features at a different level of abstraction, defined as a composition of lower-level features. Searching the parameter space of deep architectures is a difficult task, but new algorithms have been discovered and a new sub-area has emerged in the machine learning community since 2006, following these discoveries. Learning algorithms such as those for Deep Belief Networks and other related unsupervised learning algorithms have recently been proposed to train deep architectures, yielding exciting results and beating the state-of-the-art in certain areas. Learning Deep Architectures for AI discusses the motivations for and principles of learning algorithms for deep architectures. By analyzing and comparing recent results with different learning algorithms for deep architectures, explanations for their success are proposed and discussed, highlighting challenges and suggesting avenues for future explorations in this area.

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Learning Deep Architectures for AI

https://www.sfs.uni-tuebingen.de/~hbaayen/publications/baayenDavidsonBates.pdf

Mixed-effects modeling with crossed random effects for subjects and items

Markov chain Monte Carlo (MCMC) methods are powerful simulation-based techniques for sampling from high-dimensional and/or non-standard probability distributions. These methods have recently become very popular in the statistical and signal processing communities as they allow highly complex inference problems in defection and estimation to be addressed. However, MCMC is not currently well adapted to the problem of marginal maximum a posteriori (MMAP) estimation. In this paper, we present a simple and novel MCMC strategy called state-augmentation for marginal estimation (SAME), that allows MMAP estimates to be obtained for Bayesian models. The methodology is very general and we illustrate the simplicity and utility of the approach by examples in MAP parameter estimation for hidden Markov models (HMMs) and for missing data interpolation in autoregressive time series.

Marginal MAP estimation using Markov chain Monte Carlo

Recursive Maximum Likelihood (RML) is a popular methodology for estimating unknown static parameters in state-space models. We describe how a completely decentralized version of RML can be implemented in dynamic graphical models through the propagation of suitable messages that are exchanged between neighbouring nodes of the graph. The resulting algorithm can be interpreted as a generalization of the celebrated belief propagation algorithm to compute likelihood gradients. This algorithm is applied to solve the sensor registration and localisation problem for sensor networks. An exact implementation is given for dynamic linear Gaussian models without loop. If loops are present, a loopy version of the algorithm is described. For non-linear non Gaussian scenarios, a Sequential Monte Carlo (SMC) or particle filter implementation is sketched.

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A Distributed Recursive Maximum Likelihood Implementation for Sensor Registration

In multi-target tracking, one jointly estimates the number of targets and the individual target states from sensor measurements. This is a challenging problem due to the time varying number of targets and unknown measurement to target associations. We present a particle filtering method for multi-target tracking. The proposed method applies particle filtering techniques to a jump Markov system that models the multi-target dynamics. Simulation results using this particle method are also presented.

Particle filtering for multi-target tracking using jump Markov systems

We propose a new class of soft-input soft-output demodulation schemes for multiple-input multiple-output (MIMO) channels, based on the sequential Monte Carlo (SMC) framework under both stochastic and deterministic settings. The stochastic SMC sampler generates MIMO symbol samples based on importance sampling and resampling techniques, whereas the deterministic SMC approach recursively performs exploration and selection steps in a greedy manner. By exploiting the artificial sequential structure of the existing simple Bell-Labs layered space-time (BLAST) detection method based on nulling and cancellation, the proposed algorithms achieve an error proba- bility performance that is orders of magnitude better than the traditional BLAST detection schemes while maintaining a low computational complexity. In fact, the new methods offer perfor- mance comparable with that of the sphere decoding algorithm without attendant increase in complexity. More importantly, being soft-input soft-output in nature, both the stochastic and deterministic SMC detectors can be employed as the first-stage demodulator in a turbo receiver in coded MIMO systems. Such a turbo receiver successively improves the receiver performance by iteratively exchanging the so-called extrinsic information between the soft outer channel decoder and the inner soft MIMO demodulator under both known channel state and unknown channel state scenarios. Computer simulation results are provided to demonstrate the performance of the proposed algorithms.

A New Class of Soft MIMO

Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain synthetic datapoints. The denoising diffusion relies on approximations of the logarithmic derivatives of the noised data densities using score matching. Such models can also be used to perform approximate posterior simulation when one can only sample from the prior and likelihood. We propose a unifying framework generalising this approach to a wide class of spaces and leading to an original extension of score matching. We illustrate the resulting models on various applications.

Arnaud Doucet

Papers

Marginal MAP estimation using Markov chain Monte Carlo

A Distributed Recursive Maximum Likelihood Implementation for Sensor Registration

Particle filtering for multi-target tracking using jump Markov systems

A New Class of Soft MIMO

From Denoising Diffusions to Denoising Markov Models