NARX-based nonlinear system identification using orthogonal least squares basis hunting

An orthogonal least squares technique for basis hunting (OLS-BH) is proposed to construct sparse radial basis function (RBF) models for NARX-type nonlinear systems. Unlike most of the existing RBF or kernel modelling methods, whichplaces the RBF or kernel centers at the training input data points and use a fixed common variance for all the regressors, the proposed OLS-BH technique tunes the RBF center and diagonal covariance matrix of individual regressor by minimizing the training mean square error. An efficient optimization method isadopted for this basis hunting to select regressors in an orthogonal forward selection procedure. Experimental results obtained using this OLS-BH technique demonstrate that it offers a state-of-the-art method for constructing parsimonious RBF models with excellent generalization performance

Elastic net prefiltering for two class classification

A two-stage linear-in-the-parameter model construction algorithm is proposed aimed at noisy two-class classification problems. The purpose of the first stage is to produce a prefiltered signal that is used as the desired output for the second stage which constructs a sparse linear-in-the-parameter classifier. The prefiltering stage is a two-level process aimed at maximizing a model’s generalization capability, in which a new elastic-net model identification algorithm using singular value decomposition is employed at the lower level, and then, two regularization parameters are optimized using a particle-swarm-optimization algorithm at the upper level by minimizing the leave-one-out (LOO) misclassification rate. It is shown that the LOO misclassification rate based on the resultant prefiltered signal can be analytically computed without splitting the data set, and the associated computational cost is minimal due to orthogonality. The second stage of sparse classifier construction is based on orthogonal forward regression with the D-optimality algorithm. Extensive simulations of this approach for noisy data sets illustrate the competitiveness of this approach to classification of noisy data problems

Nonlinear identification using orthogonal forward regression with nested optimal regularization

An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm

European exchange trading funds trading with locally weighted support vector regression

In this paper, two different Locally Weighted Support Vector Regression (wSVR) algorithms are generated and applied to the task of forecasting and trading five European Exchange Traded Funds. The trading application covers the recent European Monetary Union debt crisis. The performance of the proposed models is benchmarked against traditional Support Vector Regression (SVR) models. The Radial Basis Function, the Wavelet and the Mahalanobis kernel are explored and tested as SVR kernels. Finally, a novel statistical SVR input selection procedure is introduced based on a principal component analysis and the Hansen, Lunde, and Nason (2011) model confidence test. The results demonstrate the superiority of the wSVR models over the traditional SVRs and of the v-SVR over the ε-SVR algorithms. We note that the performance of all models varies and considerably deteriorates in the peak of the debt crisis. In terms of the kernels, our results do not confirm the belief that the Radial Basis Function is the optimum choice for financial series

Coupled Depth Learning

In this paper we propose a method for estimating depth from a single image using a coarse to fine approach. We argue that modeling the fine depth details is easier after a coarse depth map has been computed. We express a global (coarse) depth map of an image as a linear combination of a depth basis learned from training examples. The depth basis captures spatial and statistical regularities and reduces the problem of global depth estimation to the task of predicting the input-specific coefficients in the linear combination. This is formulated as a regression problem from a holistic representation of the image. Crucially, the depth basis and the regression function are {\bf coupled} and jointly optimized by our learning scheme. We demonstrate that this results in a significant improvement in accuracy compared to direct regression of depth pixel values or approaches learning the depth basis disjointly from the regression function. The global depth estimate is then used as a guidance by a local refinement method that introduces depth details that were not captured at the global level. Experiments on the NYUv2 and KITTI datasets show that our method outperforms the existing state-of-the-art at a considerably lower computational cost for both training and testing.Comment: 10 pages, 3 Figures, 4 Tables with quantitative evaluation

Multi-View Face Recognition From Single RGBD Models of the Faces

This work takes important steps towards solving the following problem of current interest: Assuming that each individual in a population can be modeled by a single frontal RGBD face image, is it possible to carry out face recognition for such a population using multiple 2D images captured from arbitrary viewpoints? Although the general problem as stated above is extremely challenging, it encompasses subproblems that can be addressed today. The subproblems addressed in this work relate to: (1) Generating a large set of viewpoint dependent face images from a single RGBD frontal image for each individual; (2) using hierarchical approaches based on view-partitioned subspaces to represent the training data; and (3) based on these hierarchical approaches, using a weighted voting algorithm to integrate the evidence collected from multiple images of the same face as recorded from different viewpoints. We evaluate our methods on three datasets: a dataset of 10 people that we created and two publicly available datasets which include a total of 48 people. In addition to providing important insights into the nature of this problem, our results show that we are able to successfully recognize faces with accuracies of 95% or higher, outperforming existing state-of-the-art face recognition approaches based on deep convolutional neural networks

Sparse multivariate Gaussian mixture regression

Fitting a multivariate Gaussian mixture to data represents an attractive, as well as challenging problem, in especial when sparsity in the solution is demanded. Achieving this objective requires the concurrent update of all parameters (weight, centers, and precisions) of all multivariate Gaussian functions during the learning process. Such is the focus of this paper, which presents a novel method founded on the minimization of the error of the generalized logarithmic utility function (GLUF). This choice, which allows us to move smoothly from the mean square error (MSE) criterion to the one based on the logarithmic error, yields an optimization problem that resembles a locally convex problem and can be solved with a quasi-Newton method. The GLUF framework also facilitates the comparative study between both extremes, concluding that the classical MSE optimization is not the most adequate for the task. The performance of the proposed novel technique is demonstrated on simulated as well as realistic scenarios