26,375 research outputs found
Learning from Distributions via Support Measure Machines
This paper presents a kernel-based discriminative learning framework on
probability measures. Rather than relying on large collections of vectorial
training examples, our framework learns using a collection of probability
distributions that have been constructed to meaningfully represent training
data. By representing these probability distributions as mean embeddings in the
reproducing kernel Hilbert space (RKHS), we are able to apply many standard
kernel-based learning techniques in straightforward fashion. To accomplish
this, we construct a generalization of the support vector machine (SVM) called
a support measure machine (SMM). Our analyses of SMMs provides several insights
into their relationship to traditional SVMs. Based on such insights, we propose
a flexible SVM (Flex-SVM) that places different kernel functions on each
training example. Experimental results on both synthetic and real-world data
demonstrate the effectiveness of our proposed framework.Comment: Advances in Neural Information Processing Systems 2
A representer theorem for deep kernel learning
In this paper we provide a finite-sample and an infinite-sample representer
theorem for the concatenation of (linear combinations of) kernel functions of
reproducing kernel Hilbert spaces. These results serve as mathematical
foundation for the analysis of machine learning algorithms based on
compositions of functions. As a direct consequence in the finite-sample case,
the corresponding infinite-dimensional minimization problems can be recast into
(nonlinear) finite-dimensional minimization problems, which can be tackled with
nonlinear optimization algorithms. Moreover, we show how concatenated machine
learning problems can be reformulated as neural networks and how our
representer theorem applies to a broad class of state-of-the-art deep learning
methods
Locally linear approximation for Kernel methods : the Railway Kernel
In this paper we present a new kernel, the Railway Kernel, that works properly for
general (nonlinear) classification problems, with the interesting property that acts
locally as a linear kernel. In this way, we avoid potential problems due to the use of a
general purpose kernel, like the RBF kernel, as the high dimension of the induced
feature space. As a consequence, following our methodology the number of support
vectors is much lower and, therefore, the generalization capability of the proposed
kernel is higher than the obtained using RBF kernels. Experimental work is shown to
support the theoretical issues
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