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Correlated random features for fast semi-supervised learning

Neural Information Processing Systems

This paper presents Correlated Nystrom Views (XNV), a fast semi-supervised algorithm for regression and classification. The algorithm draws on two main ideas. First, it generates two views consisting of computationally inexpensive random features. It has been shown that CCA regression can substantially reduce variance with a minimal increase in bias if the views contains accurate estimators. Recent theoretical and empirical work shows that regression with random features closely approximates kernel regression, implying that the accuracy requirement holds for random views.


Semi-supervised learning

arXiv.org Machine Learning

Semi-supervised learning deals with the problem of how, if possible, to take advantage of a huge amount of not classified data, to perform classification, in situations when, typically, the labelled data are few. Even though this is not always possible (it depends on how useful is to know the distribution of the unlabelled data in the inference of the labels), several algorithm have been proposed recently. A new algorithm is proposed, that under almost neccesary conditions, attains asymptotically the performance of the best theoretical rule, when the size of unlabeled data tends to infinity. The set of necessary assumptions, although reasonables, show that semi-parametric classification only works for very well conditioned problems.


The Pessimistic Limits of Margin-based Losses in Semi-supervised Learning

arXiv.org Machine Learning

We show that for linear classifiers defined by convex margin-based surrogate losses that are monotonically decreasing, it is impossible to construct any semi-supervised approach that is able to guarantee an improvement over the supervised classifier measured by this surrogate loss. For non-monotonically decreasing loss functions, we demonstrate safe improvements are possible.


Implicitly Constrained Semi-Supervised Least Squares Classification

arXiv.org Machine Learning

We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-supervised methods, our approach does not introduce explicit additional assumptions into the objective function, but leverages implicit assumptions already present in the choice of the supervised least squares classifier. We show this approach can be formulated as a quadratic programming problem and its solution can be found using a simple gradient descent procedure. We prove that, in a certain way, our method never leads to performance worse than the supervised classifier. Experimental results corroborate this theoretical result in the multidimensional case on benchmark datasets, also in terms of the error rate.


Semi-Supervised Learning with Manifold Fitted Graphs

AAAI Conferences

In this paper, we propose a locality-constrained and sparsity-encouraged manifold fitting approach, aiming at capturing the locally sparse manifold structure into neighborhood graph construction by exploiting a principled optimization model. The proposed model formulates neighborhood graph construction as a sparse coding problem with the locality constraint, therefore achieving simultaneous neighbor selection and edge weight optimization. The core idea underlying our model is to perform a sparse manifold fitting task for each data point so that close-by points lying on the same local manifold are automatically chosen to connect and meanwhile the connection weights are acquired by simple geometric reconstruction. We term the novel neighborhood graph generated by our proposed optimization model M-Fitted Graph since such a graph stems from sparse manifold fitting. To evaluate the robustness and effectiveness ofM -fitted graphs, we leverage graph-based semisupervised learning as the testbed. Extensive experiments carried out on six benchmark datasets validate that the proposed M -fitted graph is superior to state-of-the-art neighborhood graphs in terms of classification accuracy using popular graph-based semi-supervised learning methods.