Probability density estimation with tunable kernels using orthogonal forward regression

A generalized or tunable-kernel model is proposed for probability density function estimation based on an orthogonal forward regression procedure. Each stage of the density estimation process determines a tunable kernel, namely, its center vector and diagonal covariance matrix, by minimizing a leave-one-out test criterion. The kernel mixing weights of the constructed sparse density estimate are finally updated using the multiplicative nonnegative quadratic programming algorithm to ensure the nonnegative and unity constraints, and this weight-updating process additionally has the desired ability to further reduce the model size. The proposed tunable-kernel model has advantages, in terms of model generalization capability and model sparsity, over the standard fixed-kernel model that restricts kernel centers to the training data points and employs a single common kernel variance for every kernel. On the other hand, it does not optimize all the model parameters together and thus avoids the problems of high-dimensional ill-conditioned nonlinear optimization associated with the conventional finite mixture model. Several examples are included to demonstrate the ability of the proposed novel tunable-kernel model to effectively construct a very compact density estimate accurately

Population Synthesis via k-Nearest Neighbor Crossover Kernel

The recent development of multi-agent simulations brings about a need for population synthesis. It is a task of reconstructing the entire population from a sampling survey of limited size (1% or so), supplying the initial conditions from which simulations begin. This paper presents a new kernel density estimator for this task. Our method is an analogue of the classical Breiman-Meisel-Purcell estimator, but employs novel techniques that harness the huge degree of freedom which is required to model high-dimensional nonlinearly correlated datasets: the crossover kernel, the k-nearest neighbor restriction of the kernel construction set and the bagging of kernels. The performance as a statistical estimator is examined through real and synthetic datasets. We provide an "optimization-free" parameter selection rule for our method, a theory of how our method works and a computational cost analysis. To demonstrate the usefulness as a population synthesizer, our method is applied to a household synthesis task for an urban micro-simulator.Comment: 10 pages, 4 figures, IEEE International Conference on Data Mining (ICDM) 201

Sequential Monte Carlo Methods for System Identification

One of the key challenges in identifying nonlinear and possibly non-Gaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more than two decades ago), provide numerical solutions to the nonlinear state estimation problems arising in SSMs. When combined with additional identification techniques, these algorithms provide solid solutions to the nonlinear system identification problem. We describe two general strategies for creating such combinations and discuss why SMC is a natural tool for implementing these strategies.Comment: In proceedings of the 17th IFAC Symposium on System Identification (SYSID). Added cover pag

Particle filter-based Gaussian process optimisation for parameter inference

We propose a novel method for maximum likelihood-based parameter inference in nonlinear and/or non-Gaussian state space models. The method is an iterative procedure with three steps. At each iteration a particle filter is used to estimate the value of the log-likelihood function at the current parameter iterate. Using these log-likelihood estimates, a surrogate objective function is created by utilizing a Gaussian process model. Finally, we use a heuristic procedure to obtain a revised parameter iterate, providing an automatic trade-off between exploration and exploitation of the surrogate model. The method is profiled on two state space models with good performance both considering accuracy and computational cost.Comment: Accepted for publication in proceedings of the 19th World Congress of the International Federation of Automatic Control (IFAC), Cape Town, South Africa, August 2014. 6 pages, 4 figure

Semi-Supervised Sound Source Localization Based on Manifold Regularization

Conventional speaker localization algorithms, based merely on the received microphone signals, are often sensitive to adverse conditions, such as: high reverberation or low signal to noise ratio (SNR). In some scenarios, e.g. in meeting rooms or cars, it can be assumed that the source position is confined to a predefined area, and the acoustic parameters of the environment are approximately fixed. Such scenarios give rise to the assumption that the acoustic samples from the region of interest have a distinct geometrical structure. In this paper, we show that the high dimensional acoustic samples indeed lie on a low dimensional manifold and can be embedded into a low dimensional space. Motivated by this result, we propose a semi-supervised source localization algorithm which recovers the inverse mapping between the acoustic samples and their corresponding locations. The idea is to use an optimization framework based on manifold regularization, that involves smoothness constraints of possible solutions with respect to the manifold. The proposed algorithm, termed Manifold Regularization for Localization (MRL), is implemented in an adaptive manner. The initialization is conducted with only few labelled samples attached with their respective source locations, and then the system is gradually adapted as new unlabelled samples (with unknown source locations) are received. Experimental results show superior localization performance when compared with a recently presented algorithm based on a manifold learning approach and with the generalized cross-correlation (GCC) algorithm as a baseline