Gaussian Process training with input noise

In standard Gaussian Process regression input locations are assumed to be noise free. We present a simple yet effective GP model for training on input points corrupted by i.i.d. Gaussian noise. To make computations tractable we use a local linear expansion about each input point. This allows the input noise to be recast as output noise proportional to the squared gradient of the GP posterior mean. The input noise variances are inferred from the data as extra hyperparameters. They are trained alongside other hyperparameters by the usual method of maximisation of the marginal likelihood. Training uses an iterative scheme, which alternates between optimising the hyperparameters and calculating the posterior gradient. Analytic predictive moments can then be found for Gaussian distributed test points. We compare our model to others over a range of different regression problems and show that it improves over current methods.

Bayesian approach to signal modelling

In this paper, an introduction to Bayesian methods in signal processing will be given. The paper starts by considering the important issues of model selection and parameter estimation and derives analytic expressions for the model probabilities of two simple models. The idea of marginal estimation of certain model parameter is then introduced and expressions are derived for the marginal probability densities for frequencies in white Gaussian noise and a Bayesian approach to general changepoint analysis is given. Numerical integration methods are introduced based on Markov chain Monte Carlo techniques and the Gibbs sampler in particular.

The Bayesian Approach to Signal Modelling

In this paper, an introduction to Bayesian methods in signal processing will be given. The paper starts by considering the important issues of model selection and parameter estimation and derives analytic expressions for the model probabilities of two simple models. The idea of marginal estimation of certain model parameter is then introduced and expressions are derived for the marginal probabilitiy densities for frequencies in white Gaussian noise and a Bayesian approach to general changepoint analysis is given. Numerical integration methods are introduced based on Markov chain Monte Carlo techniques and the Gibbs sampler in particular.

Impact of heterogeneous link qualities and network connectivity on binary consensus

In this paper we consider a network that is trying to reach consensus over the occurrence of an event while communicating over Additive White Gaussian Noise (AWGN) channels. We characterize the impact of different link qualities and network connectivity on consensus performance by analyzing both the asymptotic and transient behaviors. More specifically, we derive a tight approximation for the second largest eigenvalue of the probability transition matrix. We furthermore characterize the dynamics of each individual node. © 2009 AACC.

Mixed source model and its adapted vocal tract filter estimate for voice transformation and synthesis

In current methods for voice transformation and speech synthesis, the vocal tract filter is usually assumed to be excited by a flat amplitude spectrum. In this article, we present a method using a mixed source model defined as a mixture of the Liljencrants-Fant (LF) model and Gaussian noise. Using the LF model, the base approach used in this presented work is therefore close to a vocoder using exogenous input like ARX-based methods or the Glottal Spectral Separation (GSS) method. Such approaches are therefore dedicated to voice processing promising an improved naturalness compared to generic signal models. To estimate the Vocal Tract Filter (VTF), using spectral division like in GSS, we show that a glottal source model can be used with any envelope estimation method conversely to ARX approach where a least square AR solution is used. We therefore derive a VTF estimate which takes into account the amplitude spectra of both deterministic and random components of the glottal source. The proposed mixed source model is controlled by a small set of intuitive and independent parameters. The relevance of this voice production model is evaluated, through listening tests, in the context of resynthesis, HMM-based speech synthesis, breathiness modification and pitch transposition. © 2012 Elsevier B.V. All rights reserved.

Delayed-decision making in noisy bistable switches

Bistable switches are frequently encountered in biological systems. Typically, a bistable switch models a binary decision where each decision corresponds to one of the two stable equilibria. Recently, we showed that the global decision-making process in bistable switches strongly depends on a particular equilibrium point of these systems, their saddle point. In particular, we showed that a saddle point with a time-scale separation between its attractive and repulsive directions can delay the decision-making process. In this paper, we study the effects of white Gaussian noise on this mechanism of delayed decision-making induced by the saddle point. Results show that the mean decision-time strongly depends on the balance between the initial distance to the separatrix and the noise strength. © IFAC.

Robust noise reduction for speech and audio signals

Statistical model-based methods are presented for the reconstruction of autocorrelated signals in impulsive plus continuous noise environments. Signals are modelled as autoregressive and noise sources as discrete and continuous mixtures of Gaussians, allowing for robustness in highly impulsive and non-Gaussian environments. Markov Chain Monte Carlo methods are used for reconstruction of the corrupted waveforms within a Bayesian probabilistic framework and results are presented for contaminated voice and audio signals.

Gaussian Process Regression Networks

We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates input dependent signal and noise correlations between multiple response variables, input dependent length-scales and amplitudes, and heavy-tailed predictive distributions. We derive both efficient Markov chain Monte Carlo and variational Bayes inference procedures for this model. We apply GPRN as a multiple output regression and multivariate volatility model, demonstrating substantially improved performance over eight popular multiple output (multi-task) Gaussian process models and three multivariate volatility models on benchmark datasets, including a 1000 dimensional gene expression dataset.

Nearest neighbour decoding and pilot-aided channel estimation in stationary Gaussian flat-fading channels

We study the information rates of non-coherent, stationary, Gaussian, multiple-input multiple-output (MIMO) flat-fading channels that are achievable with nearest neighbour decoding and pilot-aided channel estimation. In particular, we analyse the behaviour of these achievable rates in the limit as the signal-to-noise ratio (SNR) tends to infinity. We demonstrate that nearest neighbour decoding and pilot-aided channel estimation achieves the capacity pre-logwhich is defined as the limiting ratio of the capacity to the logarithm of SNR as the SNR tends to infinityof non-coherent multiple-input single-output (MISO) flat-fading channels, and it achieves the best so far known lower bound on the capacity pre-log of non-coherent MIMO flat-fading channels. © 2011 IEEE.

Gaussian fading is the worst fading

The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented. © 2006 IEEE.