5,455 research outputs found
Structured Learning via Logistic Regression
A successful approach to structured learning is to write the learning
objective as a joint function of linear parameters and inference messages, and
iterate between updates to each. This paper observes that if the inference
problem is "smoothed" through the addition of entropy terms, for fixed
messages, the learning objective reduces to a traditional (non-structured)
logistic regression problem with respect to parameters. In these logistic
regression problems, each training example has a bias term determined by the
current set of messages. Based on this insight, the structured energy function
can be extended from linear factors to any function class where an "oracle"
exists to minimize a logistic loss.Comment: Advances in Neural Information Processing Systems 201
Morphological Network: How Far Can We Go with Morphological Neurons?
In recent years, the idea of using morphological operations as networks has
received much attention. Mathematical morphology provides very efficient and
useful image processing and image analysis tools based on basic operators like
dilation and erosion, defined in terms of kernels. Many other morphological
operations are built up using the dilation and erosion operations. Although the
learning of structuring elements such as dilation or erosion using the
backpropagation algorithm is not new, the order and the way these morphological
operations are used is not standard. In this paper, we have theoretically
analyzed the use of morphological operations for processing 1D feature vectors
and shown that this gets extended to the 2D case in a simple manner. Our
theoretical results show that a morphological block represents a sum of hinge
functions. Hinge functions are used in many places for classification and
regression tasks (Breiman (1993)). We have also proved a universal
approximation theorem -- a stack of two morphological blocks can approximate
any continuous function over arbitrary compact sets. To experimentally validate
the efficacy of this network in real-life applications, we have evaluated its
performance on satellite image classification datasets since morphological
operations are very sensitive to geometrical shapes and structures. We have
also shown results on a few tasks like segmentation of blood vessels from
fundus images, segmentation of lungs from chest x-ray and image dehazing. The
results are encouraging and further establishes the potential of morphological
networks.Comment: 35 pages, 19 figures, 7 table
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