1,339 research outputs found
High-Dimensional Feature Selection by Feature-Wise Kernelized Lasso
The goal of supervised feature selection is to find a subset of input
features that are responsible for predicting output values. The least absolute
shrinkage and selection operator (Lasso) allows computationally efficient
feature selection based on linear dependency between input features and output
values. In this paper, we consider a feature-wise kernelized Lasso for
capturing non-linear input-output dependency. We first show that, with
particular choices of kernel functions, non-redundant features with strong
statistical dependence on output values can be found in terms of kernel-based
independence measures. We then show that the globally optimal solution can be
efficiently computed; this makes the approach scalable to high-dimensional
problems. The effectiveness of the proposed method is demonstrated through
feature selection experiments with thousands of features.Comment: 18 page
Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods
Feature extraction and dimensionality reduction are important tasks in many
fields of science dealing with signal processing and analysis. The relevance of
these techniques is increasing as current sensory devices are developed with
ever higher resolution, and problems involving multimodal data sources become
more common. A plethora of feature extraction methods are available in the
literature collectively grouped under the field of Multivariate Analysis (MVA).
This paper provides a uniform treatment of several methods: Principal Component
Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis
(CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions
derived by means of the theory of reproducing kernel Hilbert spaces. We also
review their connections to other methods for classification and statistical
dependence estimation, and introduce some recent developments to deal with the
extreme cases of large-scale and low-sized problems. To illustrate the wide
applicability of these methods in both classification and regression problems,
we analyze their performance in a benchmark of publicly available data sets,
and pay special attention to specific real applications involving audio
processing for music genre prediction and hyperspectral satellite images for
Earth and climate monitoring
A low variance consistent test of relative dependency
We describe a novel non-parametric statistical hypothesis test of relative
dependence between a source variable and two candidate target variables. Such a
test enables us to determine whether one source variable is significantly more
dependent on a first target variable or a second. Dependence is measured via
the Hilbert-Schmidt Independence Criterion (HSIC), resulting in a pair of
empirical dependence measures (source-target 1, source-target 2). We test
whether the first dependence measure is significantly larger than the second.
Modeling the covariance between these HSIC statistics leads to a provably more
powerful test than the construction of independent HSIC statistics by
sub-sampling. The resulting test is consistent and unbiased, and (being based
on U-statistics) has favorable convergence properties. The test can be computed
in quadratic time, matching the computational complexity of standard empirical
HSIC estimators. The effectiveness of the test is demonstrated on several
real-world problems: we identify language groups from a multilingual corpus,
and we prove that tumor location is more dependent on gene expression than
chromosomal imbalances. Source code is available for download at
https://github.com/wbounliphone/reldep.Comment: International Conference on Machine Learning, Jul 2015, Lille, Franc
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