292 research outputs found
Efficient Decomposed Learning for Structured Prediction
Structured prediction is the cornerstone of several machine learning
applications. Unfortunately, in structured prediction settings with expressive
inter-variable interactions, exact inference-based learning algorithms, e.g.
Structural SVM, are often intractable. We present a new way, Decomposed
Learning (DecL), which performs efficient learning by restricting the inference
step to a limited part of the structured spaces. We provide characterizations
based on the structure, target parameters, and gold labels, under which DecL is
equivalent to exact learning. We then show that in real world settings, where
our theoretical assumptions may not completely hold, DecL-based algorithms are
significantly more efficient and as accurate as exact learning.Comment: ICML201
Constructing Buildings and Harmonic Maps
In a continuation of our previous work, we outline a theory which should lead
to the construction of a universal pre-building and versal building with a
-harmonic map from a Riemann surface, in the case of two-dimensional
buildings for the group . This will provide a generalization of the space
of leaves of the foliation defined by a quadratic differential in the classical
theory for . Our conjectural construction would determine the exponents
for WKB problems, and it can be put into practice on examples.Comment: 61 pages, 24 figures. Comments are welcom
Adaptive weights smoothing with applications to image segmentation
We propose a new method of nonparametric estimation which is based on locally constant smoothing with an adaptive choice of weights for every pair of data-points. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on some simulated univariate and bivariate examples and compare it with other nonparametric methods. Finally we discuss applications of this procedure to Magnetic Resonance Imaging
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