3,193 research outputs found
Theoretical Properties of Projection Based Multilayer Perceptrons with Functional Inputs
Many real world data are sampled functions. As shown by Functional Data
Analysis (FDA) methods, spectra, time series, images, gesture recognition data,
etc. can be processed more efficiently if their functional nature is taken into
account during the data analysis process. This is done by extending standard
data analysis methods so that they can apply to functional inputs. A general
way to achieve this goal is to compute projections of the functional data onto
a finite dimensional sub-space of the functional space. The coordinates of the
data on a basis of this sub-space provide standard vector representations of
the functions. The obtained vectors can be processed by any standard method. In
our previous work, this general approach has been used to define projection
based Multilayer Perceptrons (MLPs) with functional inputs. We study in this
paper important theoretical properties of the proposed model. We show in
particular that MLPs with functional inputs are universal approximators: they
can approximate to arbitrary accuracy any continuous mapping from a compact
sub-space of a functional space to R. Moreover, we provide a consistency result
that shows that any mapping from a functional space to R can be learned thanks
to examples by a projection based MLP: the generalization mean square error of
the MLP decreases to the smallest possible mean square error on the data when
the number of examples goes to infinity
Reverse Engineering Gene Networks with ANN: Variability in Network Inference Algorithms
Motivation :Reconstructing the topology of a gene regulatory network is one
of the key tasks in systems biology. Despite of the wide variety of proposed
methods, very little work has been dedicated to the assessment of their
stability properties. Here we present a methodical comparison of the
performance of a novel method (RegnANN) for gene network inference based on
multilayer perceptrons with three reference algorithms (ARACNE, CLR, KELLER),
focussing our analysis on the prediction variability induced by both the
network intrinsic structure and the available data.
Results: The extensive evaluation on both synthetic data and a selection of
gene modules of "Escherichia coli" indicates that all the algorithms suffer of
instability and variability issues with regards to the reconstruction of the
topology of the network. This instability makes objectively very hard the task
of establishing which method performs best. Nevertheless, RegnANN shows MCC
scores that compare very favorably with all the other inference methods tested.
Availability: The software for the RegnANN inference algorithm is distributed
under GPL3 and it is available at the corresponding author home page
(http://mpba.fbk.eu/grimaldi/regnann-supmat
Modeling Financial Time Series with Artificial Neural Networks
Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.CELEST, a National Science Foundation Science of Learning Center (SBE-0354378); SyNAPSE program of the Defense Advanced Research Project Agency (HR001109-03-0001
Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis
In this paper, we study a natural extension of Multi-Layer Perceptrons (MLP)
to functional inputs. We show that fundamental results for classical MLP can be
extended to functional MLP. We obtain universal approximation results that show
the expressive power of functional MLP is comparable to that of numerical MLP.
We obtain consistency results which imply that the estimation of optimal
parameters for functional MLP is statistically well defined. We finally show on
simulated and real world data that the proposed model performs in a very
satisfactory way.Comment: http://www.sciencedirect.com/science/journal/0893608
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