Symmetric RBF classifier for nonlinear detection in multiple-antenna aided systems

In this paper, we propose a powerful symmetric radial basis function (RBF) classifier for nonlinear detection in the so-called “overloaded” multiple-antenna-aided communication systems. By exploiting the inherent symmetry property of the optimal Bayesian detector, the proposed symmetric RBF classifier is capable of approaching the optimal classification performance using noisy training data. The classifier construction process is robust to the choice of the RBF width and is computationally efficient. The proposed solution is capable of providing a signal-to-noise ratio (SNR) gain in excess of 8 dB against the powerful linear minimum bit error rate (BER) benchmark, when supporting four users with the aid of two receive antennas or seven users with four receive antenna elements. Index Terms—Classification, multiple-antenna system, orthogonal forward selection, radial basis function (RBF), symmetry

Approximation errors of online sparsification criteria

Many machine learning frameworks, such as resource-allocating networks, kernel-based methods, Gaussian processes, and radial-basis-function networks, require a sparsification scheme in order to address the online learning paradigm. For this purpose, several online sparsification criteria have been proposed to restrict the model definition on a subset of samples. The most known criterion is the (linear) approximation criterion, which discards any sample that can be well represented by the already contributing samples, an operation with excessive computational complexity. Several computationally efficient sparsification criteria have been introduced in the literature, such as the distance, the coherence and the Babel criteria. In this paper, we provide a framework that connects these sparsification criteria to the issue of approximating samples, by deriving theoretical bounds on the approximation errors. Moreover, we investigate the error of approximating any feature, by proposing upper-bounds on the approximation error for each of the aforementioned sparsification criteria. Two classes of features are described in detail, the empirical mean and the principal axes in the kernel principal component analysis.Comment: 10 page

MATSuMoTo: The MATLAB Surrogate Model Toolbox For Computationally Expensive Black-Box Global Optimization Problems

MATSuMoTo is the MATLAB Surrogate Model Toolbox for computationally expensive, black-box, global optimization problems that may have continuous, mixed-integer, or pure integer variables. Due to the black-box nature of the objective function, derivatives are not available. Hence, surrogate models are used as computationally cheap approximations of the expensive objective function in order to guide the search for improved solutions. Due to the computational expense of doing a single function evaluation, the goal is to find optimal solutions within very few expensive evaluations. The multimodality of the expensive black-box function requires an algorithm that is able to search locally as well as globally. MATSuMoTo is able to address these challenges. MATSuMoTo offers various choices for surrogate models and surrogate model mixtures, initial experimental design strategies, and sampling strategies. MATSuMoTo is able to do several function evaluations in parallel by exploiting MATLAB's Parallel Computing Toolbox.Comment: 13 pages, 7 figure

An Optimal Dimensionality Multi-shell Sampling Scheme with Accurate and Efficient Transforms for Diffusion MRI

This paper proposes a multi-shell sampling scheme and corresponding transforms for the accurate reconstruction of the diffusion signal in diffusion MRI by expansion in the spherical polar Fourier (SPF) basis. The sampling scheme uses an optimal number of samples, equal to the degrees of freedom of the band-limited diffusion signal in the SPF domain, and allows for computationally efficient reconstruction. We use synthetic data sets to demonstrate that the proposed scheme allows for greater reconstruction accuracy of the diffusion signal than the multi-shell sampling schemes obtained using the generalised electrostatic energy minimisation (gEEM) method used in the Human Connectome Project. We also demonstrate that the proposed sampling scheme allows for increased angular discrimination and improved rotational invariance of reconstruction accuracy than the gEEM schemes.Comment: 4 pages, 4 figures presented at ISBI 201

A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks

We propose a nonparametric method for estimating the pricing formula of a derivative asset using learning networks. Although not a substitute for the more traditional arbitrage-based pricing formulas, network pricing formulas may be more accurate and computationally more efficient alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with no-arbitrage condition cannot be solved analytically. To assess the potential value of network pricing formulas, we simulate Black-Scholes option prices and show that learning networks can recover the Black-Scholes formula from a two-year training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta-hedge options out-of-sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis function networks, multilayer perceptron networks, and projection pursuit. To illustrate the practical relevance of our network pricing approach, we apply it to the pricing and delta-hedging of S&P 500 futures options from 1987 to 1991.

An Efficient Algorithm for Automatic Structure Optimization in X-ray Standing-Wave Experiments

X-ray standing-wave photoemission experiments involving multilayered samples are emerging as unique probes of the buried interfaces that are ubiquitous in current device and materials research. Such data require for their analysis a structure optimization process comparing experiment to theory that is not straightforward. In this work, we present a new computer program for optimizing the analysis of standing-wave data, called SWOPT, that automates this trial-and-error optimization process. The program includes an algorithm that has been developed for computationally expensive problems: so-called black-box simulation optimizations. It also includes a more efficient version of the Yang X-ray Optics Program (YXRO) [Yang, S.-H., Gray, A.X., Kaiser, A.M., Mun, B.S., Sell, B.C., Kortright, J.B., Fadley, C.S., J. Appl. Phys. 113, 1 (2013)] which is about an order of magnitude faster than the original version. Human interaction is not required during optimization. We tested our optimization algorithm on real and hypothetical problems and show that it finds better solutions significantly faster than a random search approach. The total optimization time ranges, depending on the sample structure, from minutes to a few hours on a modern laptop computer, and can be up to 100x faster than a corresponding manual optimization. These speeds make the SWOPT program a valuable tool for realtime analyses of data during synchrotron experiments