Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov Chain Monte Carlo (MCMC) methods, namely, Hamiltonian Monte Carlo (HMC). The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the art methods

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

Finding kernel function for stock market prediction with support vector regression

Stock market prediction is one of the fascinating issues of stock market research. Accurate stock prediction becomes the biggest challenge in investment industry because the distribution of stock data is changing over the time. Time series forcasting, Neural Network (NN) and Support Vector Machine (SVM) are once commonly used for prediction on stock price. In this study, the data mining operation called time series forecasting is implemented. The large amount of stock data collected from Kuala Lumpur Stock Exchange is used for the experiment to test the validity of SVMs regression. SVM is a new machine learning technique with principle of structural minimization risk, which have greater generalization ability and proved success in time series prediction. Two kernel functions namely Radial Basis Function and polynomial are compared for finding the accurate prediction values. Besides that, backpropagation neural network are also used to compare the predictions performance. Several experiments are conducted and some analyses on the experimental results are done. The results show that SVM with polynomial kernels provide a promising alternative tool in KLSE stock market prediction