23,227 research outputs found
Towards Building Deep Networks with Bayesian Factor Graphs
We propose a Multi-Layer Network based on the Bayesian framework of the
Factor Graphs in Reduced Normal Form (FGrn) applied to a two-dimensional
lattice. The Latent Variable Model (LVM) is the basic building block of a
quadtree hierarchy built on top of a bottom layer of random variables that
represent pixels of an image, a feature map, or more generally a collection of
spatially distributed discrete variables. The multi-layer architecture
implements a hierarchical data representation that, via belief propagation, can
be used for learning and inference. Typical uses are pattern completion,
correction and classification. The FGrn paradigm provides great flexibility and
modularity and appears as a promising candidate for building deep networks: the
system can be easily extended by introducing new and different (in cardinality
and in type) variables. Prior knowledge, or supervised information, can be
introduced at different scales. The FGrn paradigm provides a handy way for
building all kinds of architectures by interconnecting only three types of
units: Single Input Single Output (SISO) blocks, Sources and Replicators. The
network is designed like a circuit diagram and the belief messages flow
bidirectionally in the whole system. The learning algorithms operate only
locally within each block. The framework is demonstrated in this paper in a
three-layer structure applied to images extracted from a standard data set.Comment: Submitted for journal publicatio
Assessing multivariate predictors of financial market movements: A latent factor framework for ordinal data
Much of the trading activity in Equity markets is directed to brokerage
houses. In exchange they provide so-called "soft dollars," which basically are
amounts spent in "research" for identifying profitable trading opportunities.
Soft dollars represent about USD 1 out of every USD 10 paid in commissions.
Obviously they are costly, and it is interesting for an institutional investor
to determine whether soft dollar inputs are worth being used (and indirectly
paid for) or not, from a statistical point of view. To address this question,
we develop association measures between what broker--dealers predict and what
markets realize. Our data are ordinal predictions by two broker--dealers and
realized values on several markets, on the same ordinal scale. We develop a
structural equation model with latent variables in an ordinal setting which
allows us to test broker--dealer predictive ability of financial market
movements. We use a multivariate logit model in a latent factor framework,
develop a tractable estimator based on a Laplace approximation, and show its
consistency and asymptotic normality. Monte Carlo experiments reveal that both
the estimation method and the testing procedure perform well in small samples.
The method is then used to analyze our dataset.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS213 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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