140,048 research outputs found
Domain Generalization by Marginal Transfer Learning
In the problem of domain generalization (DG), there are labeled training data
sets from several related prediction problems, and the goal is to make accurate
predictions on future unlabeled data sets that are not known to the learner.
This problem arises in several applications where data distributions fluctuate
because of environmental, technical, or other sources of variation. We
introduce a formal framework for DG, and argue that it can be viewed as a kind
of supervised learning problem by augmenting the original feature space with
the marginal distribution of feature vectors. While our framework has several
connections to conventional analysis of supervised learning algorithms, several
unique aspects of DG require new methods of analysis.
This work lays the learning theoretic foundations of domain generalization,
building on our earlier conference paper where the problem of DG was introduced
Blanchard et al., 2011. We present two formal models of data generation,
corresponding notions of risk, and distribution-free generalization error
analysis. By focusing our attention on kernel methods, we also provide more
quantitative results and a universally consistent algorithm. An efficient
implementation is provided for this algorithm, which is experimentally compared
to a pooling strategy on one synthetic and three real-world data sets
-generalization of Gauss' law of error
Based on the -deformed functions (-exponential and
-logarithm) and associated multiplication operation (-product)
introduced by Kaniadakis (Phys. Rev. E \textbf{66} (2002) 056125), we present
another one-parameter generalization of Gauss' law of error. The likelihood
function in Gauss' law of error is generalized by means of the
-product. This -generalized maximum likelihood principle leads
to the {\it so-called} -Gaussian distributions.Comment: 9 pages, 1 figure, latex file using elsart.cls style fil
Bounded-Distortion Metric Learning
Metric learning aims to embed one metric space into another to benefit tasks
like classification and clustering. Although a greatly distorted metric space
has a high degree of freedom to fit training data, it is prone to overfitting
and numerical inaccuracy. This paper presents {\it bounded-distortion metric
learning} (BDML), a new metric learning framework which amounts to finding an
optimal Mahalanobis metric space with a bounded-distortion constraint. An
efficient solver based on the multiplicative weights update method is proposed.
Moreover, we generalize BDML to pseudo-metric learning and devise the
semidefinite relaxation and a randomized algorithm to approximately solve it.
We further provide theoretical analysis to show that distortion is a key
ingredient for stability and generalization ability of our BDML algorithm.
Extensive experiments on several benchmark datasets yield promising results
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