29 research outputs found
Distribution matching for transduction
Many transductive inference algorithms assume that distributions over training and test estimates should be related, e.g. by providing a large margin of separation on both sets. We use this idea to design a transduction algorithm which can be used without modification for classification, regression, and structured estimation. At its heart we exploit the fact that for a good learner the distributions over the outputs on training and test sets should match. This is a classical two-sample problem which can be solved efficiently in its most general form by using distance measures in Hilbert Space. It turns out that a number of existing heuristics can be viewed as special cases of our approach.
Multitask learning without label correspondences
We propose an algorithm to perform multitask learning where each task has potentially distinct label sets and label correspondences are not readily available. This is in contrast with existing methods which either assume that the label sets shared by different tasks are the same or that there exists a label mapping oracle. Our method directly maximizes the mutual information among the labels, and we show that the resulting objective function can be efficiently optimized using existing algorithms. Our proposed approach has a direct application for data integration with different label spaces for the purpose of classification, such as integrating Yahoo! and DMOZ web directories
Low-rank matrix recovery with Ky Fan 2-k-norm
We propose Ky Fan 2-k-norm-based models for the non-convex low-rank matrix recovery problem. A general difference of convex algorithm (DCA) is developed to solve these models. Numerical results show that the proposed models achieve high recoverability rates
A D.C. Algorithm via Convex Analysis Approach for Solving a Location Problem Involving Sets
We study a location problem that involves a weighted sum of distances to
closed convex sets. As several of the weights might be negative, traditional
solution methods of convex optimization are not applicable. After obtaining
some existence theorems, we introduce a simple, but effective, algorithm for
solving the problem. Our method is based on the Pham Dinh - Le Thi algorithm
for d.c. programming and a generalized version of the Weiszfeld algorithm,
which works well for convex location problems
A DC Programming Approach for Solving Multicast Network Design Problems via the Nesterov Smoothing Technique
This paper continues our effort initiated in [9] to study Multicast
Communication Networks, modeled as bilevel hierarchical clustering problems, by
using mathematical optimization techniques. Given a finite number of nodes, we
consider two different models of multicast networks by identifying a certain
number of nodes as cluster centers, and at the same time, locating a particular
node that serves as a total center so as to minimize the total transportation
cost through the network. The fact that the cluster centers and the total
center have to be among the given nodes makes this problem a discrete
optimization problem. Our approach is to reformulate the discrete problem as a
continuous one and to apply Nesterov smoothing approximation technique on the
Minkowski gauges that are used as distance measures. This approach enables us
to propose two implementable DCA-based algorithms for solving the problems.
Numerical results and practical applications are provided to illustrate our
approach