28,474 research outputs found
Visualizing and Understanding Sum-Product Networks
Sum-Product Networks (SPNs) are recently introduced deep tractable
probabilistic models by which several kinds of inference queries can be
answered exactly and in a tractable time. Up to now, they have been largely
used as black box density estimators, assessed only by comparing their
likelihood scores only. In this paper we explore and exploit the inner
representations learned by SPNs. We do this with a threefold aim: first we want
to get a better understanding of the inner workings of SPNs; secondly, we seek
additional ways to evaluate one SPN model and compare it against other
probabilistic models, providing diagnostic tools to practitioners; lastly, we
want to empirically evaluate how good and meaningful the extracted
representations are, as in a classic Representation Learning framework. In
order to do so we revise their interpretation as deep neural networks and we
propose to exploit several visualization techniques on their node activations
and network outputs under different types of inference queries. To investigate
these models as feature extractors, we plug some SPNs, learned in a greedy
unsupervised fashion on image datasets, in supervised classification learning
tasks. We extract several embedding types from node activations by filtering
nodes by their type, by their associated feature abstraction level and by their
scope. In a thorough empirical comparison we prove them to be competitive
against those generated from popular feature extractors as Restricted Boltzmann
Machines. Finally, we investigate embeddings generated from random
probabilistic marginal queries as means to compare other tractable
probabilistic models on a common ground, extending our experiments to Mixtures
of Trees.Comment: Machine Learning Journal paper (First Online), 24 page
The Incremental Multiresolution Matrix Factorization Algorithm
Multiresolution analysis and matrix factorization are foundational tools in
computer vision. In this work, we study the interface between these two
distinct topics and obtain techniques to uncover hierarchical block structure
in symmetric matrices -- an important aspect in the success of many vision
problems. Our new algorithm, the incremental multiresolution matrix
factorization, uncovers such structure one feature at a time, and hence scales
well to large matrices. We describe how this multiscale analysis goes much
farther than what a direct global factorization of the data can identify. We
evaluate the efficacy of the resulting factorizations for relative leveraging
within regression tasks using medical imaging data. We also use the
factorization on representations learned by popular deep networks, providing
evidence of their ability to infer semantic relationships even when they are
not explicitly trained to do so. We show that this algorithm can be used as an
exploratory tool to improve the network architecture, and within numerous other
settings in vision.Comment: Computer Vision and Pattern Recognition (CVPR) 2017, 10 page
- …