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79
Bayesian measures of model complexity and fit
 Journal of the Royal Statistical Society, Series B
, 2002
"... [Read before The Royal Statistical Society at a meeting organized by the Research ..."
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Cited by 132 (2 self)
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[Read before The Royal Statistical Society at a meeting organized by the Research
A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects
 Journal of Neurophysiology
, 2005
"... Multiple factors simultaneously affect the spiking activity of individual neurons. Determining the effects and relative importance of these factors is a challenging problem in neurophysiology. We propose a statistical framework based on the point process likelihood function to relate a neuron’s spik ..."
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Cited by 96 (7 self)
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Multiple factors simultaneously affect the spiking activity of individual neurons. Determining the effects and relative importance of these factors is a challenging problem in neurophysiology. We propose a statistical framework based on the point process likelihood function to relate a neuron’s spiking probability to three typical covariates: the neuron’s own spiking history, concurrent ensemble activity and extrinsic covariates such as stimuli or behavior. The framework uses parametric models of the conditional intensity function to define a neuron’s spiking probability in terms of the covariates. The discrete time likelihood function for point processes is used to carry out model fitting and model analysis. We show that, by modeling the logarithm of the conditional intensity function as a linear combination of functions of the covariates, the discrete time point process likelihood function is readily analyzed in the generalized linear model (GLM) framework. We illustrate our approach for both GLM and nonGLM likelihood functions using simulated data and multivariate single unit
Mutual information for the selection of relevant variables in spectrometric nonlinear modelling
, 2006
"... ..."
The variable selection problem
 Journal of the American Statistical Association
, 2000
"... The problem of variable selection is one of the most pervasive model selection problems in statistical applications. Often referred to as the problem of subset selection, it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables ..."
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Cited by 39 (2 self)
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The problem of variable selection is one of the most pervasive model selection problems in statistical applications. Often referred to as the problem of subset selection, it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables or predictors, but there is uncertainty about which subset to use. This vignette reviews some of the key developments which have led to the wide variety of approaches for this problem. 1
On Overfitting Avoidance As Bias
 SFI TR
, 1993
"... In supervised learning it is commonly believed that penalizing complex functions helps one avoid "overfitting" functions to data, and therefore improves generalization. It is also commonly believed that crossvalidation is an effective way to choose amongst algorithms for fitting functions to data. ..."
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Cited by 33 (6 self)
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In supervised learning it is commonly believed that penalizing complex functions helps one avoid "overfitting" functions to data, and therefore improves generalization. It is also commonly believed that crossvalidation is an effective way to choose amongst algorithms for fitting functions to data. In a recent paper, Schaffer (1993) presents experimental evidence disputing these claims. The current paper consists of a formal analysis of these contentions of Schaffer's. It proves that his contentions are valid, although some of his experiments must be interpreted with caution.
Neural Noise and MovementRelated Codes in the Macaque Supplementary Motor Area
 The Journal of Neuroscience
, 2003
"... We analyzed the variability of spike counts and the coding capacity of simultaneously recorded pairs of neurons in the macaque supplementary motor area (SMA). We analyzed the meanvariance functions for single neurons, as well as signal and noise correlations between pairs of neurons. All three stat ..."
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Cited by 26 (2 self)
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We analyzed the variability of spike counts and the coding capacity of simultaneously recorded pairs of neurons in the macaque supplementary motor area (SMA). We analyzed the meanvariance functions for single neurons, as well as signal and noise correlations between pairs of neurons. All three statistics showed a strong dependence on the bin width chosen for analysis. Changes in the correlation structure of single neuron spike trains over different bin sizes affected the meanvariance function, and signal and noise correlations between pairs of neurons were much smaller at small bin widths, increasing monotonically with the width of the bin. Analyses in the frequency domain showed that the noise between pairs of neurons, on average, was most strongly correlated at low frequencies, which explained the increase in noise correlation with increasing bin width. The coding performance was analyzed to determine whether the temporal precision of spike arrival times and the interactions within and between neurons could improve the prediction of the upcoming movement. We found that in �62 % of neuron pairs, the arrival times of spikes at a resolution between 66 and 40 msec carried more information than spike counts in a 200 msec bin. In addition, in 19 % of neuron pairs, inclusion of within (11%) or betweenneuron (8%) correlations in spike trains improved decoding accuracy. These results suggest that in some SMA neurons elements of the spatiotemporal pattern of activity may be relevant for neural coding. Key words: spike count variability; correlated noise; monkey; decoding; temporal code; rate code
Model Selection with CrossValidations and Bootstraps  Application to Time Series Prediction with RBFN Models
 Artificial Neural Networks and Neural Information Processing – ICANN/ICONIP 2003
, 2003
"... This paper compares several model selection methods, based on experimental estimates of their generalization errors. Experiments in the context of nonlinear time series prediction by RadialBasis Function Networks show the superiority of the bootstrap methodology over classical crossvalidations ..."
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Cited by 23 (15 self)
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This paper compares several model selection methods, based on experimental estimates of their generalization errors. Experiments in the context of nonlinear time series prediction by RadialBasis Function Networks show the superiority of the bootstrap methodology over classical crossvalidations and leaveoneout.
Bayesian Statistics
 in WWW', Computing Science and Statistics
, 1989
"... ∗ Signatures are on file in the Graduate School. This dissertation presents two topics from opposite disciplines: one is from a parametric realm and the other is based on nonparametric methods. The first topic is a jackknife maximum likelihood approach to statistical model selection and the second o ..."
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Cited by 20 (0 self)
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∗ Signatures are on file in the Graduate School. This dissertation presents two topics from opposite disciplines: one is from a parametric realm and the other is based on nonparametric methods. The first topic is a jackknife maximum likelihood approach to statistical model selection and the second one is a convex hull peeling depth approach to nonparametric massive multivariate data analysis. The second topic includes simulations and applications on massive astronomical data. First, we present a model selection criterion, minimizing the KullbackLeibler distance by using the jackknife method. Various model selection methods have been developed to choose a model of minimum KullbackLiebler distance to the true model, such as Akaike information criterion (AIC), Bayesian information criterion (BIC), Minimum description length (MDL), and Bootstrap information criterion. Likewise, the jackknife method chooses a model of minimum KullbackLeibler distance through bias reduction. This bias, which is inevitable in model
Statistical Ideas for Selecting Network Architectures
 Invited Presentation, Neural Information Processing Systems 8
, 1995
"... Choosing the architecture of a neural network is one of the most important problems in making neural networks practically useful, but accounts of applications usually sweep these details under the carpet. How many hidden units are needed? Should weight decay be used, and if so how much? What type of ..."
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Cited by 18 (3 self)
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Choosing the architecture of a neural network is one of the most important problems in making neural networks practically useful, but accounts of applications usually sweep these details under the carpet. How many hidden units are needed? Should weight decay be used, and if so how much? What type of output units should be chosen? And so on. We address these issues within the framework of statistical theory for model choice, which provides a number of workable approximate answers. This paper is principally concerned with architecture selection issues for feedforward neural networks (also known as multilayer perceptrons). Many of the same issues arise in selecting radial basis function networks, recurrent networks and more widely. These problems occur in a much wider context within statistics, and applied statisticians have been selecting and combining models for decades. Two recent discussions are [4, 5]. References [3, 20, 21, 22] discuss neural networks from a statistical perspecti...
Combining Generalizers Using Partitions Of The Learning Set
 1992 Lectures in Complex Systems
, 1992
"... : For any realworld generalization problem, there are always many generalizers which could be applied to the problem. This paper discusses some algorithmic techniques for dealing with this multiplicity of possible generalizers. All of these techniques rely on partitioning the provided learning set ..."
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Cited by 12 (1 self)
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: For any realworld generalization problem, there are always many generalizers which could be applied to the problem. This paper discusses some algorithmic techniques for dealing with this multiplicity of possible generalizers. All of these techniques rely on partitioning the provided learning set in two, many different times. The first technique discussed is crossvalidation, which is a winnertakesall strategy (based on the behavior of the generalizers on the partitions of the learning set, it picks one single generalizer from amongst the set of candidate generalizers, and tells you to use that generalizer). The second technique discussed, the one this paper concentrates on, is an extension of crossvalidation called stacked generalization. As opposed to crossvalidation's winnertakes all strategy, stacked generalization uses the partitions of the learning set to combine the generalizers, in a nonlinear manner, via another generalizer (hence the term "stacked generalization"). Af...