191 research outputs found
Ignorability for categorical data
We study the problem of ignorability in likelihood-based inference from
incomplete categorical data. Two versions of the coarsened at random assumption
(car) are distinguished, their compatibility with the parameter distinctness
assumption is investigated and several conditions for ignorability that do not
require an extra parameter distinctness assumption are established. It is shown
that car assumptions have quite different implications depending on whether the
underlying complete-data model is saturated or parametric. In the latter case,
car assumptions can become inconsistent with observed data.Comment: Published at http://dx.doi.org/10.1214/009053605000000363 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Numeric Input Relations for Relational Learning with Applications to Community Structure Analysis
Most work in the area of statistical relational learning (SRL) is focussed on
discrete data, even though a few approaches for hybrid SRL models have been
proposed that combine numerical and discrete variables. In this paper we
distinguish numerical random variables for which a probability distribution is
defined by the model from numerical input variables that are only used for
conditioning the distribution of discrete response variables. We show how
numerical input relations can very easily be used in the Relational Bayesian
Network framework, and that existing inference and learning methods need only
minor adjustments to be applied in this generalized setting. The resulting
framework provides natural relational extensions of classical probabilistic
models for categorical data. We demonstrate the usefulness of RBN models with
numeric input relations by several examples.
In particular, we use the augmented RBN framework to define probabilistic
models for multi-relational (social) networks in which the probability of a
link between two nodes depends on numeric latent feature vectors associated
with the nodes. A generic learning procedure can be used to obtain a
maximum-likelihood fit of model parameters and latent feature values for a
variety of models that can be expressed in the high-level RBN representation.
Specifically, we propose a model that allows us to interpret learned latent
feature values as community centrality degrees by which we can identify nodes
that are central for one community, that are hubs between communities, or that
are isolated nodes. In a multi-relational setting, the model also provides a
characterization of how different relations are associated with each community
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
Learning and Interpreting Multi-Multi-Instance Learning Networks
We introduce an extension of the multi-instance learning problem where
examples are organized as nested bags of instances (e.g., a document could be
represented as a bag of sentences, which in turn are bags of words). This
framework can be useful in various scenarios, such as text and image
classification, but also supervised learning over graphs. As a further
advantage, multi-multi instance learning enables a particular way of
interpreting predictions and the decision function. Our approach is based on a
special neural network layer, called bag-layer, whose units aggregate bags of
inputs of arbitrary size. We prove theoretically that the associated class of
functions contains all Boolean functions over sets of sets of instances and we
provide empirical evidence that functions of this kind can be actually learned
on semi-synthetic datasets. We finally present experiments on text
classification, on citation graphs, and social graph data, which show that our
model obtains competitive results with respect to accuracy when compared to
other approaches such as convolutional networks on graphs, while at the same
time it supports a general approach to interpret the learnt model, as well as
explain individual predictions.Comment: JML
A Complete Characterization of Projectivity for Statistical Relational Models
A generative probabilistic model for relational data consists of a family of
probability distributions for relational structures over domains of different
sizes. In most existing statistical relational learning (SRL) frameworks, these
models are not projective in the sense that the marginal of the distribution
for size- structures on induced sub-structures of size is equal to the
given distribution for size- structures. Projectivity is very beneficial in
that it directly enables lifted inference and statistically consistent learning
from sub-sampled relational structures. In earlier work some simple fragments
of SRL languages have been identified that represent projective models.
However, no complete characterization of, and representation framework for
projective models has been given. In this paper we fill this gap: exploiting
representation theorems for infinite exchangeable arrays we introduce a class
of directed graphical latent variable models that precisely correspond to the
class of projective relational models. As a by-product we also obtain a
characterization for when a given distribution over size- structures is the
statistical frequency distribution of size- sub-structures in much larger
size- structures. These results shed new light onto the old open problem of
how to apply Halpern et al.'s "random worlds approach" for probabilistic
inference to general relational signatures.Comment: Extended version (with proof appendix) of paper that is too appear in
Proceedings of IJCAI 202
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