3,415 research outputs found
Inference, Learning, and Population Size: Projectivity for SRL Models
A subtle difference between propositional and relational data is that in many
relational models, marginal probabilities depend on the population or domain
size. This paper connects the dependence on population size to the classic
notion of projectivity from statistical theory: Projectivity implies that
relational predictions are robust with respect to changes in domain size. We
discuss projectivity for a number of common SRL systems, and identify syntactic
fragments that are guaranteed to yield projective models. The syntactic
conditions are restrictive, which suggests that projectivity is difficult to
achieve in SRL, and care must be taken when working with different domain
sizes
Computing Multi-Relational Sufficient Statistics for Large Databases
Databases contain information about which relationships do and do not hold
among entities. To make this information accessible for statistical analysis
requires computing sufficient statistics that combine information from
different database tables. Such statistics may involve any number of {\em
positive and negative} relationships. With a naive enumeration approach,
computing sufficient statistics for negative relationships is feasible only for
small databases. We solve this problem with a new dynamic programming algorithm
that performs a virtual join, where the requisite counts are computed without
materializing join tables. Contingency table algebra is a new extension of
relational algebra, that facilitates the efficient implementation of this
M\"obius virtual join operation. The M\"obius Join scales to large datasets
(over 1M tuples) with complex schemas. Empirical evaluation with seven
benchmark datasets showed that information about the presence and absence of
links can be exploited in feature selection, association rule mining, and
Bayesian network learning.Comment: 11pages, 8 figures, 8 tables, CIKM'14,November 3--7, 2014, Shanghai,
Chin
Computing Expected Motif Counts for Exchangeable Graph Generative Models
Estimating the expected value of a graph statistic is an important inference
task for using and learning graph models. This note presents a scalable
estimation procedure for expected motif counts, a widely used type of graph
statistic. The procedure applies for generative mixture models of the type used
in neural and Bayesian approaches to graph data.Comment: 8 page
From Graph Generation to Graph Classification
This note describes a new approach to classifying graphs that leverages graph
generative models (GGM). Assuming a GGM that defines a joint probability
distribution over graphs and their class labels, I derive classification
formulas for the probability of a class label given a graph. A new conditional
ELBO can be used to train a generative graph auto-encoder model for
discrimination. While leveraging generative models for classification has been
well explored for non-relational i.i.d. data, to our knowledge it is a novel
approach to graph classification.Comment: I welcome suggestions, comments, and proposals for collaboration to
develop further the ideas in this paper. Please email [email protected]. I
am grateful to Renjie Liao for helpful comment
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