Bayesian estimation of simultaneous musical notes based on frequency domain modelling

This paper proposes a Bayesian method for polyphonic music description. The method first divides an input audio signal into a series of sections called snapshots, and then estimates parameters such as fundamental frequencies and amplitudes of the notes contained in each snapshot. The parameter estimation process is based on a frequency domain modelling and Gibbs sampling. Experimental results obtained from audio signals of test note patterns are encouraging; the accuracy is better than 80% for the estimation of fundamental frequencies in terms of semitones and instrument names when the number of simultaneous notes is two.

Blind frequency synchronisation for OFDM systems with pulse shaping

In multi-carrier systems, small carrier frequency offsets result in significant degradation of performance and this offset should be compensated before demodulation can be performed. In this paper, we consider a generic multi-carrier system with pulse shaping and estimate the frequency offset by exploiting the cyclostationarity of the received signal. By transforming the time domain signal to the cyclic correlation domain we are able to estimate the frequency offset without the aid of pilot symbols or the cyclic prefix. The Bayesian framework is used to obtain the estimate and we show how we can simplify the estimation process. © 1999 IEEE.

Temporally adaptive estimation of logistic classifiers on data streams

Modern technology has allowed real-time data collection in a variety of domains, ranging from environmental monitoring to healthcare. Consequently, there is a growing need for algorithms capable of performing inferential tasks in an online manner, continuously revising their estimates to reflect the current status of the underlying process. In particular, we are interested in constructing online and temporally adaptive classifiers capable of handling the possibly drifting decision boundaries arising in streaming environments. We first make a quadratic approximation to the log-likelihood that yields a recursive algorithm for fitting logistic regression online. We then suggest a novel way of equipping this framework with self-tuning forgetting factors. The resulting scheme is capable of tracking changes in the underlying probability distribution, adapting the decision boundary appropriately and hence maintaining high classification accuracy in dynamic or unstable environments. We demonstrate the scheme's effectiveness in both real and simulated streaming environments. © Springer-Verlag 2009.

Fixed-lag blind equalization and sequence estimation in digital communications systems using sequential importance sampling

We present methods for fixed-lag smoothing using Sequential Importance sampling (SIS) on a discrete non-linear, non-Gaussian state space system with unknown parameters. Our particular application is in the field of digital communication systems. Each input data point is taken from a finite set of symbols. We represent transmission media as a fixed filter with a finite impulse response (FIR), hence a discrete state-space system is formed. Conventional Markov chain Monte Carlo (MCMC) techniques such as the Gibbs sampler are unsuitable for this task because they can only perform processing on a batch of data. Data arrives sequentially, so it would seem sensible to process it in this way. In addition, many communication systems are interactive, so there is a maximum level of latency that can be tolerated before a symbol is decoded. We will demonstrate this method by simulation and compare its performance to existing techniques.

Multiple pitch estimation using non-homogeneous poisson processes

Novel statistical models are proposed and developed in this paper for automated multiple-pitch estimation problems. Point estimates of the parameters of partial frequencies of a musical note are modeled as realizations from a non-homogeneous Poisson process defined on the frequency axis. When several notes are combined, the processes for the individual notes combine to give a new Poisson process whose likelihood is easy to compute. This model avoids the data-association step of linking the harmonics of each note with the corresponding partials and is ideal for efficient Bayesian inference of unknown multiple fundamental frequencies in a signal. © 2011 IEEE.

Reinforcement learning for parameter estimation in statistical spoken dialogue systems

Reinforcement techniques have been successfully used to maximise the expected cumulative reward of statistical dialogue systems. Typically, reinforcement learning is used to estimate the parameters of a dialogue policy which selects the system's responses based on the inferred dialogue state. However, the inference of the dialogue state itself depends on a dialogue model which describes the expected behaviour of a user when interacting with the system. Ideally the parameters of this dialogue model should be also optimised to maximise the expected cumulative reward. This article presents two novel reinforcement algorithms for learning the parameters of a dialogue model. First, the Natural Belief Critic algorithm is designed to optimise the model parameters while the policy is kept fixed. This algorithm is suitable, for example, in systems using a handcrafted policy, perhaps prescribed by other design considerations. Second, the Natural Actor and Belief Critic algorithm jointly optimises both the model and the policy parameters. The algorithms are evaluated on a statistical dialogue system modelled as a Partially Observable Markov Decision Process in a tourist information domain. The evaluation is performed with a user simulator and with real users. The experiments indicate that model parameters estimated to maximise the expected reward function provide improved performance compared to the baseline handcrafted parameters. © 2011 Elsevier Ltd. All rights reserved.

Parameter estimation for agenda-based user simulation

This paper presents an agenda-based user simulator which has been extended to be trainable on real data with the aim of more closely modelling the complex rational behaviour exhibited by real users. The train-able part is formed by a set of random decision points that may be encountered during the process of receiving a system act and responding with a user act. A sample-based method is presented for using real user data to estimate the parameters that control these decisions. Evaluation results are given both in terms of statistics of generated user behaviour and the quality of policies trained with different simulators. Compared to a handcrafted simulator, the trained system provides a much better fit to corpus data and evaluations suggest that this better fit should result in improved dialogue performance. © 2010 Association for Computational Linguistics.

The Gaussian process density sampler

We present the Gaussian Process Density Sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a fixed density function that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We can also infer the hyperparameters of the Gaussian process. We compare this density modeling technique to several existing techniques on a toy problem and a skullreconstruction task.

State estimation schemes for independent component coupled hidden Markov models

Conventional Hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive noise. This general class of model has enjoyed a huge and diverse range of applications, for example, speech processing, biomedical signal processing and more recently quantitative finance. However, a lesser known extension of this general class of model is the so-called Factorial Hidden Markov Model (FHMM). FHMMs also have diverse applications, notably in machine learning, artificial intelligence and speech recognition [13, 17]. FHMMs extend the usual class of HMMs, by supposing the partially observed state process is a finite collection of distinct Markov chains, either statistically independent or dependent. There is also considerable current activity in applying collections of partially observed Markov chains to complex action recognition problems, see, for example, [6]. In this article we consider the Maximum Likelihood (ML) parameter estimation problem for FHMMs. Much of the extant literature concerning this problem presents parameter estimation schemes based on full data log-likelihood EM algorithms. This approach can be slow to converge and often imposes heavy demands on computer memory. The latter point is particularly relevant for the class of FHMMs where state space dimensions are relatively large. The contribution in this article is to develop new recursive formulae for a filter-based EM algorithm that can be implemented online. Our new formulae are equivalent ML estimators, however, these formulae are purely recursive and so, significantly reduce numerical complexity and memory requirements. A computer simulation is included to demonstrate the performance of our results. © Taylor & Francis Group, LLC.

Kernel conditional quantile estimation via reduction revisited

Quantile regression refers to the process of estimating the quantiles of a conditional distribution and has many important applications within econometrics and data mining, among other domains. In this paper, we show how to estimate these conditional quantile functions within a Bayes risk minimization framework using a Gaussian process prior. The resulting non-parametric probabilistic model is easy to implement and allows non-crossing quantile functions to be enforced. Moreover, it can directly be used in combination with tools and extensions of standard Gaussian Processes such as principled hyperparameter estimation, sparsification, and quantile regression with input-dependent noise rates. No existing approach enjoys all of these desirable properties. Experiments on benchmark datasets show that our method is competitive with state-of-the-art approaches. © 2009 IEEE.

An experimental study on engine dynamics model based in-cylinder pressure estimation

The information provided by the in-cylinder pressure signal is of great importance for modern engine management systems. The obtained information is implemented to improve the control and diagnostics of the combustion process in order to meet the stringent emission regulations and to improve vehicle reliability and drivability. The work presented in this paper covers the experimental study and proposes a comprehensive and practical solution for the estimation of the in-cylinder pressure from the crankshaft speed fluctuation. Also, the paper emphasizes the feasibility and practicality aspects of the estimation techniques, for the real-time online application. In this study an engine dynamics model based estimation method is proposed. A discrete-time transformed form of a rigid-body crankshaft dynamics model is constructed based on the kinetic energy theorem, as the basis expression for total torque estimation. The major difficulties, including load torque estimation and separation of pressure profile from adjacent-firing cylinders, are addressed in this work and solutions to each problem are given respectively. The experimental results conducted on a multi-cylinder diesel engine have shown that the proposed method successfully estimate a more accurate cylinder pressure over a wider range of crankshaft angles. Copyright © 2012 SAE International.