43,504 research outputs found
Multilinear tensor regression for longitudinal relational data
A fundamental aspect of relational data, such as from a social network, is
the possibility of dependence among the relations. In particular, the relations
between members of one pair of nodes may have an effect on the relations
between members of another pair. This article develops a type of regression
model to estimate such effects in the context of longitudinal and multivariate
relational data, or other data that can be represented in the form of a tensor.
The model is based on a general multilinear tensor regression model, a special
case of which is a tensor autoregression model in which the tensor of relations
at one time point are parsimoniously regressed on relations from previous time
points. This is done via a separable, or Kronecker-structured, regression
parameter along with a separable covariance model. In the context of an
analysis of longitudinal multivariate relational data, it is shown how the
multilinear tensor regression model can represent patterns that often appear in
relational and network data, such as reciprocity and transitivity.Comment: Published at http://dx.doi.org/10.1214/15-AOAS839 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A practical Bayesian framework for backpropagation networks
A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible (1) objective comparisons between solutions using alternative network architectures, (2) objective stopping rules for network pruning or growing procedures, (3) objective choice of magnitude and type of weight decay terms or additive regularizers (for penalizing large weights, etc.), (4) a measure of the effective number of well-determined parameters in a model, (5) quantified estimates of the error bars on network parameters and on network output, and (6) objective comparisons with alternative learning and interpolation models such as splines and radial basis functions. The Bayesian "evidence" automatically embodies "Occam's razor," penalizing overflexible and overcomplex models. The Bayesian approach helps detect poor underlying assumptions in learning models. For learning models well matched to a problem, a good correlation between generalization ability and the Bayesian evidence is obtained
PTOMSM: A modified version of Topological Overlap Measure used for predicting Protein-Protein Interaction Network
A variety of methods are developed to integrating diverse biological data to predict novel interaction relationship between proteins. However, traditional integration can only generate protein interaction pairs within existing relationships. Therefore, we propose a modified version of Topological Overlap Measure to identify not only extant direct PPIs links, but also novel protein interactions that can be indirectly inferred from various relationships between proteins. Our method is more powerful than a naïve Bayesian-network-based integration in PPI prediction, and could generate more reliable candidate PPIs. Furthermore, we examined the influence of the sizes of training and test datasets on prediction, and further demonstrated the effectiveness of PTOMSM in predicting PPI. More importantly, this method can be extended naturally to predict other types of biological networks, and may be combined with Bayesian method to further improve the prediction
Bayesian nonparametric sparse VAR models
High dimensional vector autoregressive (VAR) models require a large number of
parameters to be estimated and may suffer of inferential problems. We propose a
new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional
VAR models that can improve estimation efficiency and prediction accuracy. Our
hierarchical prior overcomes overparametrization and overfitting issues by
clustering the VAR coefficients into groups and by shrinking the coefficients
of each group toward a common location. Clustering and shrinking effects
induced by the BNP-Lasso prior are well suited for the extraction of causal
networks from time series, since they account for some stylized facts in
real-world networks, which are sparsity, communities structures and
heterogeneity in the edges intensity. In order to fully capture the richness of
the data and to achieve a better understanding of financial and macroeconomic
risk, it is therefore crucial that the model used to extract network accounts
for these stylized facts.Comment: Forthcoming in "Journal of Econometrics" ---- Revised Version of the
paper "Bayesian nonparametric Seemingly Unrelated Regression Models" ----
Supplementary Material available on reques
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