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Computational experiences with equivalent degrees of freedoms
No full textNeural networks, radial basis functions and projection pursuit regression arenonlinear models which simultaneously project the m-dimensional input data into a p dimensionalspace and model nonlinear functions of the linear combinations of the inputsin this new space. Previous statistical theory for estimating the true error variance andconstructing approximated confidence intervals seems inappropriate, since the degrees offreedom of these models do not equal the number of adaptive parameters. We show inthis article that the problem maybe overcome by using the equivalent degrees of freedom(e.d.f.) based on the dimension of the projection space. We present the results of a MonteCarlo study on simulated data showing that e.d.f. : give numerical stable results and seemto work reasonably well in estimating the error variance and constructing confidence interval
On the degrees of freedom in richly parameterized models
Get PDFUsing richly parameterised models for small datasetscan be justified from a theoretical point of viewaccording to some results due to Bartlett which show that thegeneralization performance of a multi layer perceptron (MLP)depends more on the L1 norm of the weightsbetween the hidden and the output layer rather than on thenumber of parameters in the model.In this paper we investigate the problem of measuring the generalizationperformance and the complexity of richly parameterised procedures and,drawing on linear model theory, we propose a different notion of degrees of freedomto neural networks and other projection tools. This notion is compatible withsimilar ideas long associated with smoothers based models(like projection pursuit regression) and can be interpreted using the projectiontheory of linear models and showing some geometrical properties of neural networks.Results in this study lead to corrections insome goodness-of-fit statistics like AIC, BIC/SBC:the number of degrees of freedom in theseindexes are set equal to the dimension p of the projection spaceintrinsically found by the mapping function.An empirical study is presented in order toillustrate the behavior of the valuesof some selection model criteria
Modelli Neuronali per piccoli insiemi di dati
No full textNel lavoro si affronta il problema della costruzione di modelli statistici di tipo predittivo in situzioni in cui si dispone di un numero esiguo di dati e la relazionen di dipendenza che si vuole stimare è fortemente non lineare. Tipiche applicazioni riguardano le misurazioni indirette o i cosiddetti sensori virtuali. In tali casi il numero di predittori è spesso molto elevato e, a causa della struttura non lineare di dipendenza, non è possibile scegliere opportuni sottoinsiemi di variabili o di loro combinaizoni lineari. Nel presente lavoro tale problema viene affrontato mediante reti neurali a partire dai risultati di Bartlett concernenti le proprietà di generalizzazione di tali modelli. Alcuni criteri operativi vengono infine illustrati mediante due casi di studio concernenti il controllo statistico di qualita
Equivalent number of degrees of freedom for neural networks
No full textThe notion of equivalent number of degrees of freedom (e.d.f.) to be usedin neural network modeling from small datasets has been introduced in Ingrassiaand Morlini (2005). It is much smaller than the total number of parameters andit does not depend on the number of input variables. We generalize our previousresults and discuss the use of the e.d.f. in the general framework of multivariatenonparametric model selection. Through numerical simulations, we also investigatethe behavior of model selection criteria like AIC, GCV and BIC/SBC, when thee.d.f. is used instead of the total number of the adaptive parameters in the model
Computational studies with equivalent degrees of freedoms in neural networks
No full textThe notion of equivalent number of degrees of freedom (e.d.f.) has been recently proposed in the context of neural network modeling for small data sets. This quantity is much smaller than the number of the parameters in the network and it does not depend on the number of input variables. In this paper, we present numerical studies on both real and simulated data sets assuring the validity of e.d.f. in a general framework. Results confirm that e.d.f. performs more reliably than the total number W of adaptive parameters - which are usually assumed equal to the degrees of freedom of the model in common statistical softwares - for analyzing and comparing neural models. Numerical studies also point out that e.d.f. works well in estimating the error variance and constructing approximate confidence intervals. We then propose a comparison among some model selection criteria and results show that for neural networks GCV performs slightly better. We finally present a simple forward procedure which can be easily implemented for automatically selecting a neural model with good trade-off between learning error and generalization properties
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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