The following recent PhD thesis may be of interest for readers of this
list:
CONTINUOUS LATENT VARIABLE MODELS FOR DIMENSIONALITY REDUCTION AND
SEQUENTIAL DATA RECONSTRUCTION
Miguel A. Carreira-Perpinan
Dept. of Computer Science, University of Sheffield, UK
February 2001
which can be retrieved in PostScript and PDF formats from:
http://www.dcs.shef.ac.uk/~miguel/papers/phd-thesis.html
http://cns.georgetown.edu/~miguel/papers/phd-thesis.html
>From the abstract:
The last part of this thesis proposes a new method for missing data
reconstruction of sequential data that includes as particular case the
inversion of many-to-one mappings. We define the problem, distinguish
it from inverse problems, and show when both coincide. The method is
based on multiple pointwise reconstruction and constraint
optimisation. Multiple pointwise reconstruction uses a Gaussian
mixture joint density model for the data, conveniently implemented
with a nonlinear continuous latent variable model (GTM). The modes of
the conditional distribution of missing values given present values at
each point in the sequence represent local candidate
reconstructions. A global sequence reconstruction is obtained by
efficiently optimising a constraint, such as continuity or smoothness,
with dynamic programming. We give a probabilistic interpretation of
the method. We derive two algorithms for exhaustive mode finding in
Gaussian mixtures, based on gradient-quadratic search and fixed-point
search, respectively; as well as estimates of error bars for each mode
and a measure of distribution sparseness. We discuss the advantages of
the method over previous work based on the conditional mean or on
universal mapping approximators (including ensembles and recurrent
networks), conditional distribution estimation, vector quantisation
and statistical analysis of missing data. We study the performance of
the method with synthetic data (a toy example and an inverse
kinematics problem) and real data (mapping between electropalatographic
and acoustic data). We describe the possible application of the method
to several well-known reconstruction or inversion problems: decoding
of neural population activity for hippocampal place cells; wind field
retrieval from scatterometer data; inverse kinematics and dynamics of
a redundant manipulator; acoustic-to-articulatory mapping; audiovisual
mappings for speech recognition; and recognition of occluded speech.
However, note that the emphasis is not on inference but on
reconstruction (of the missing values), and that it concentrates on
continuous variables and datasets satisfying constraints such as
continuity.
Best regards,
Miguel
--
Miguel A Carreira-Perpinan
Department of Neuroscience Tel. (202) 6878679
Georgetown University Medical Center Fax (202) 6870617
3900 Reservoir Road NW mailto:[email protected]
Washington, DC 20007, USA http://cns.georgetown.edu/~miguel
