86,374 research outputs found
Large-scale Nonlinear Variable Selection via Kernel Random Features
We propose a new method for input variable selection in nonlinear regression.
The method is embedded into a kernel regression machine that can model general
nonlinear functions, not being a priori limited to additive models. This is the
first kernel-based variable selection method applicable to large datasets. It
sidesteps the typical poor scaling properties of kernel methods by mapping the
inputs into a relatively low-dimensional space of random features. The
algorithm discovers the variables relevant for the regression task together
with learning the prediction model through learning the appropriate nonlinear
random feature maps. We demonstrate the outstanding performance of our method
on a set of large-scale synthetic and real datasets.Comment: Final version for proceedings of ECML/PKDD 201
Alchemical and structural distribution based representation for improved QML
We introduce a representation of any atom in any chemical environment for the
generation of efficient quantum machine learning (QML) models of common
electronic ground-state properties. The representation is based on scaled
distribution functions explicitly accounting for elemental and structural
degrees of freedom. Resulting QML models afford very favorable learning curves
for properties of out-of-sample systems including organic molecules,
non-covalently bonded protein side-chains, (HO)-clusters, as well as
diverse crystals. The elemental components help to lower the learning curves,
and, through interpolation across the periodic table, even enable "alchemical
extrapolation" to covalent bonding between elements not part of training, as
evinced for single, double, and triple bonds among main-group elements
Alchemical and structural distribution based representation for improved QML
We introduce a representation of any atom in any chemical environment for the
generation of efficient quantum machine learning (QML) models of common
electronic ground-state properties. The representation is based on scaled
distribution functions explicitly accounting for elemental and structural
degrees of freedom. Resulting QML models afford very favorable learning curves
for properties of out-of-sample systems including organic molecules,
non-covalently bonded protein side-chains, (HO)-clusters, as well as
diverse crystals. The elemental components help to lower the learning curves,
and, through interpolation across the periodic table, even enable "alchemical
extrapolation" to covalent bonding between elements not part of training, as
evinced for single, double, and triple bonds among main-group elements
Feature Optimization for Atomistic Machine Learning Yields A Data-Driven Construction of the Periodic Table of the Elements
Machine-learning of atomic-scale properties amounts to extracting
correlations between structure, composition and the quantity that one wants to
predict. Representing the input structure in a way that best reflects such
correlations makes it possible to improve the accuracy of the model for a given
amount of reference data. When using a description of the structures that is
transparent and well-principled, optimizing the representation might reveal
insights into the chemistry of the data set. Here we show how one can
generalize the SOAP kernel to introduce a distance-dependent weight that
accounts for the multi-scale nature of the interactions, and a description of
correlations between chemical species. We show that this improves substantially
the performance of ML models of molecular and materials stability, while making
it easier to work with complex, multi-component systems and to extend SOAP to
coarse-grained intermolecular potentials. The element correlations that give
the best performing model show striking similarities with the conventional
periodic table of the elements, providing an inspiring example of how machine
learning can rediscover, and generalize, intuitive concepts that constitute the
foundations of chemistry.Comment: 9 pages, 4 figure
NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks
The graph Laplacian is a standard tool in data science, machine learning, and
image processing. The corresponding matrix inherits the complex structure of
the underlying network and is in certain applications densely populated. This
makes computations, in particular matrix-vector products, with the graph
Laplacian a hard task. A typical application is the computation of a number of
its eigenvalues and eigenvectors. Standard methods become infeasible as the
number of nodes in the graph is too large. We propose the use of the fast
summation based on the nonequispaced fast Fourier transform (NFFT) to perform
the dense matrix-vector product with the graph Laplacian fast without ever
forming the whole matrix. The enormous flexibility of the NFFT algorithm allows
us to embed the accelerated multiplication into Lanczos-based eigenvalues
routines or iterative linear system solvers and even consider other than the
standard Gaussian kernels. We illustrate the feasibility of our approach on a
number of test problems from image segmentation to semi-supervised learning
based on graph-based PDEs. In particular, we compare our approach with the
Nystr\"om method. Moreover, we present and test an enhanced, hybrid version of
the Nystr\"om method, which internally uses the NFFT.Comment: 28 pages, 9 figure
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