Isolating Stock Prices Variation with Neural Networks

In this study we aim to define a mapping function that relates the general index value among a set of shares to the prices of individual shares. In more general terms this is problem of defining the relationship between multivariate data distributions and a specific source of variation within these distributions where the source of variation in question represents a quantity of interest related to a particular problem domain. In this respect we aim to learn a complex mapping function that can be used for mapping different values of the quantity of interest to typical novel samples of the distribution. In our investigation we compare the performance of standard neural network based methods like Multilayer Perceptrons (MLPs) and Radial Basis Functions (RBFs) as well as Mixture Density Networks (MDNs) and a latent variable method, the General Topographic Mapping (GTM). According to the results, MLPs and RBFs outperform MDNs and the GTM for this one-to-many mapping problem.

[1]  Geoffrey E. Hinton,et al.  Learning representations by back-propagation errors, nature , 1986 .

[2]  Miguel Á. Carreira-Perpiñán,et al.  Continuous latent variable models for dimensionality reduction and sequential data reconstruction , 2001 .

[3]  Martin Fodslette Møller,et al.  A scaled conjugate gradient algorithm for fast supervised learning , 1993, Neural Networks.

[4]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[5]  Miguel Á. Carreira-Perpiñán.  One-to-many mappings, continuity constraints and latent variable models , 1999 .

[6]  Christopher M. Bishop,et al.  GTM: The Generative Topographic Mapping , 1998, Neural Computation.

[7]  Korin Richmond,et al.  Mixture density networks, human articulatory data and acoustic-to-articulatory inversion of continuous speech. , 2001 .

[8]  Roelof K. Brouwer.  Feed-forward neural network for one-to-many mappings using fuzzy sets , 2004, Neurocomputing.

[9]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[10]  M. J. D. Powell,et al.  Radial basis functions for multivariable interpolation: a review , 1987 .

[11]  S. Srihari.  Mixture Density Networks , 1994 .

[12]  Stan Lipovetsky,et al.  Latent Variable Models and Factor Analysis , 2001, Technometrics.

[13]  David J.C. Mackay,et al.  Density networks , 2000 .

[14]  Daniel S. Yeung,et al.  A Quantified Sensitivity Measure for Multilayer Perceptron to Input Perturbation , 2003, Neural Computation.

[15]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..