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Tensorial Mixture Models | | Or Sharir
; Ronen Tamari
; Nadav Cohen
; Amnon Shashua
; | | Date: |
13 Oct 2016 | | Abstract: | We introduce a generative model, we call Tensorial Mixture Models (TMMs)
based on mixtures of basic component distributions over local structures (e.g.
patches in an image) where the dependencies between the local-structures are
represented by a "priors tensor" holding the prior probabilities of assigning a
component distribution to each local-structure.
In their general form, TMMs are intractable as the prior tensor is typically
of exponential size. However, when the priors tensor is decomposed it gives
rise to an arithmetic circuit which in turn transforms the TMM into a
Convolutional Arithmetic Circuit (ConvAC). A ConvAC corresponds to a shallow
(single hidden layer) network when the priors tensor is decomposed by a CP (sum
of rank-1) approach and corresponds to a deep network when the decomposition
follows the Hierarchical Tucker (HT) model.
The ConvAC representation of a TMM possesses several attractive properties.
First, the inference is tractable and is implemented by a forward pass through
a deep network. Second, the architectural design of the model follows the deep
networks community design, i.e., the structure of TMMs is determined by just
two easily understood factors: size of pooling windows and number of channels.
Finally, we demonstrate the effectiveness of our model when tackling the
problem of classification with missing data, leveraging TMMs unique ability of
tractable marginalization which leads to optimal classifiers regardless of the
missingness distribution. | | Source: | arXiv, 1610.4167 | | Services: | Forum | Review | PDF | Favorites | |
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