Eric Moulines

An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo

It is now over a decade since the pioneering contribution of Gordon (1993), which is commonly regarded as the first instance of modern sequential Monte Carlo (SMC) approaches. Initially focussed on applications to tracking and vision, these techniques are now very widespread and have had a significant impact in virtually all areas of signal and image processing concerned with Bayesian dynamical models. This paper is intended to serve both as an introduction to SMC algorithms for nonspecialists and as a reference to recent contributions in domains where the techniques are still under significant development, including smoothing, estimation of fixed parameters and use of SMC methods beyond the standard filtering contexts.

Continuous probabilistic transform for voice conversion

Voice conversion, as considered in this paper, is defined as modifying the speech signal of one speaker (source speaker) so that it sounds as if it had been pronounced by a different speaker (target speaker). Our contribution includes the design of a new methodology for representing the relationship between two sets of spectral envelopes. The proposed method is based on the use of a Gaussian mixture model of the source speaker spectral envelopes. The conversion itself is represented by a continuous parametric function which takes into account the probabilistic classification provided by the mixture model. The parameters of the conversion function are estimated by least squares optimization on the training data. This conversion method is implemented in the context of the HNM (harmonic+noise model) system, which allows high-quality modifications of speech signals. Compared to earlier methods based on vector quantization, the proposed conversion scheme results in a much better match between the converted envelopes and the target envelopes. Evaluation by objective tests and formal listening tests shows that the proposed transform greatly improves the quality and naturalness of the converted speech signals compared with previous proposed conversion methods.

Non-parametric techniques for pitch-scale and time-scale modification of speech

Abstract Time-scale and, to a lesser extent, pitch-scale modifications of speech and audio signals are the subject of major theoretical and practical interest. Applications are numerous, including, to name but a few, text-to-speech synthesis (based on acoustical unit concatenation), transformation of voice characteristics, foreign language learning but also audio monitoring or film/soundtrack post-synchronization. To fulfill the need for high-quality time and pitch-scaling, a number of algorithms have been proposed recently, along with their real-time implementation, sometimes for very inexpensive hardware. It appears that most of these algorithms can be viewed as slight variations of a small number of basic schemes. This contribution reviews frequency-domain algorithms (phase-vocoder) and time-domain algorithms (Time-Domain Pitch-Synchronous Overlap/Add and the like) in the same framework. More recent variations of these schemes are also presented.

A subspace algorithm for certain blind identification problems

The problem of blind identification of p-inputs/q-outputs FIR transfer functions is addressed. Existing subspace identification methods derived for p=1 are first reformulated. In particular, the links between the noise subspace of a certain covariance matrix of the output signals (on which subspace methods build on) and certain rational subspaces associated with the transfer function to be identified are elucidated. Based on these relations, we study the behavior of the subspace method in the case where the order of the transfer function is overestimated. Next, an asymptotic performance analysis of this estimation method is carried out. Consistency and asymptotical normality of the estimates is established. A closed-form expression for the asymptotic covariance of the estimates is given. Numerical simulations and investigations are presented to demonstrate the potential of the subspace method. Finally, we take advantage of our new reformulation to discuss the extension of the subspace method to the case p>1. We show where the difficulties lie, and we briefly indicate how to solve the corresponding problems. The possible connections with classical approaches for MA model estimations are also outlined.

Voice transformation using PSOLA technique

Abstract In this contribution, a new system for voice conversion is described. The proposed architecture combines a PSOLA (Pitch Synchronous Overlap and Add)-derived synthesizer and a module for spectral transformation. The synthesizer based on the classical source-filter decomposition allows prosodic and spectral transformations to be performed independently. Prosodic modifications are applied on the excitation signal using the TD-PSOLA scheme; converted speech is then synthesized using the transformed spectral parameters. Two different approaches to derive spectral transformations, borrowed from the speech-recognition domain, are compared: Linear Multivariate Regression (LMR) and Dynamic Frequency Warping (DFW). Vector-quantization is carried out as a preliminary stage to render the spectral transformations dependent of the acoustical realization of sounds. A formal listening test shows that the synthesizer produces a satisfyingly natural “transformed” voice. LMR proves yet to allow a slightly better conversion than DFW. Still there is room for improvement in the spectral transformation stage.

On-line expectation–maximization algorithm for latent data models

In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the algorithm of Titterington (1984), this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete data distribution. The resulting algorithm is usually simpler and is shown to achieve convergence to the stationary points of the Kullback-Leibler divergence between the marginal distribution of the observation and the model distribution at the optimal rate, i.e., that of the maximum likelihood estimator. In addition, the proposed approach is also suitable for conditional (or regression) models, as illustrated in the case of the mixture of linear regressions model.

On the Ergodicity Properties of some Adaptive MCMC Algorithms

In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a so-called adaptive MCMC sampler converge to the required value and can even, under more stringent assumptions, satisfy a central limit theorem. We prove that the conditions required are satisfied for the independent Metropolis–Hastings algorithm and the random walk Metropolis algorithm with symmetric increments. Finally, we propose an application of these results to the case where the proposal distribution of the Metropolis–Hastings update is a mixture of distributions from a curved exponential family.

Least‐squares Estimation of an Unknown Number of Shifts in a Time Series

In this contribution, general results on the off-line least-squares estimate of changes in the mean of a random process are presented. First, a generalisation of the Hajek-Renyi inequality, dealing with the fluctuations of the normalized partial sums, is given. This preliminary result is then used to derive the consistency and the rate of convergence of the change-points estimate, in the situation where the number of changes is known. Strong consistency is obtained under some mixing conditions. The limiting distribution is also computed under an invariance principle. The case where the number of changes is unknown is then addressed. All these results apply to a large class of dependent processes, including strongly mixing and also long-range dependent processes.

Maximum likelihood for blind separation and deconvolution of noisy signals using mixture models

An approximate maximum likelihood method for blind source separation and deconvolution of noisy signal is proposed. This technique relies upon a data augmentation scheme, where the (unobserved) input are viewed as the missing data. In the technique described, the input signal distribution is modeled by a mixture of Gaussian distributions, enabling the use of explicit formula for computing the posterior density and conditional expectation and thus avoiding Monte-Carlo integrations. Because this technique is able to capture some salient features of the input signal distribution, it performs generally much better than third-order or fourth-order cumulant based techniques.

Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.