arXiv subjects

Pierre Courrieu

Publications and source records attributed to Pierre Courrieu.

6 recordsLinked to original sources

arXiv2011

Validated Intraclass Correlation Statistics to Test Item Performance Models

A new method, with an application program in Matlab code, is proposed for testing item performance models on empirical databases. This method uses data intraclass correlation statistics as expected correlations to which one compares simple functions of correlations between model predictions and observed item performance. The method rests on a data population model whose validity for the considered data is suitably tested, and has been verified for three behavioural measure databases. Contrarily to usual model selection criteria, this method provides an effective way of testing under-fitting and over-fitting, answering the usually neglected question "does this model suitably account for these data?"

stat.ME↗

arXiv2011

Missing Data Imputation and Corrected Statistics for Large-Scale Behavioral Databases

This paper presents a new methodology to solve problems resulting from missing data in large-scale item performance behavioral databases. Useful statistics corrected for missing data are described, and a new method of imputation for missing data is proposed. This methodology is applied to the DLP database recently published by Keuleers et al. (2010), which allows us to conclude that this database fulfills the conditions of use of the method recently proposed by Courrieu et al. (2011) to test item performance models. Two application programs in Matlab code are provided for the imputation of missing data in databases, and for the computation of corrected statistics to test models.

stat.ME↗

arXiv2009

Fast solving of Weighted Pairing Least-Squares systems

This paper presents a generalization of the "weighted least-squares" (WLS), named "weighted pairing least-squares" (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods, suitable for solving full rank systems as well as rank deficient systems, are studied. Computational experiments clearly show that the best method, in terms of speed, accuracy, and numerical stability, is based on a special {1, 2, 3}-inverse, whose computation reduces to a very simple generalization of the usual "Cholesky factorization-backward substitution" method for solving linear systems.

cs.MS↗

arXiv2008

Fast Density Codes for Image Data

Recently, a new method for encoding data sets in the form of "Density Codes" was proposed in the literature (Courrieu, 2006). This method allows to compare sets of points belonging to every multidimensional space, and to build shape spaces invariant to a wide variety of affine and non-affine transformations. However, this general method does not take advantage of the special properties of image data, resulting in a quite slow encoding process that makes this tool practically unusable for processing large image databases with conventional computers. This paper proposes a very simple variant of the density code method that directly works on the image function, which is thousands times faster than the original Parzen window based method, without loss of its useful properties.

cs.NE↗

arXiv2008

Solving Time of Least Square Systems in Sigma-Pi Unit Networks

The solving of least square systems is a useful operation in neurocomputational modeling of learning, pattern matching, and pattern recognition. In these last two cases, the solution must be obtained on-line, thus the time required to solve a system in a plausible neural architecture is critical. This paper presents a recurrent network of Sigma-Pi neurons, whose solving time increases at most like the logarithm of the system size, and of its condition number, which provides plausible computation times for biological systems.

cs.NE↗

arXiv2008

Fast Computation of Moore-Penrose Inverse Matrices

Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors of synaptic weights, which contribute to the regularization of the input-output mapping. It is thus of interest to develop fast and accurate algorithms for computing Moore-Penrose inverse matrices. In this paper, an algorithm based on a full rank Cholesky factorization is proposed. The resulting pseudoinverse matrices are similar to those provided by other algorithms. However the computation time is substantially shorter, particularly for large systems.

cs.NE↗