7,455 research outputs found
Efficient construction of linear models in materials modeling and applications to force constant expansions
Linear models, such as force constant (FC) and cluster expansions, play a key
role in physics and materials science. While they can in principle be
parametrized using regression and feature selection approaches, the convergence
behavior of these techniques, in particular with respect to thermodynamic
properties is not well understood. Here, we therefore analyze the efficacy and
efficiency of several state-of-the-art regression and feature selection
methods, in particular in the context of FC extraction and the prediction of
different thermodynamic properties. Generic feature selection algorithms such
as recursive feature elimination with ordinary least-squares (OLS), automatic
relevance determination regression, and the adaptive least absolute shrinkage
and selection operator can yield physically sound models for systems with a
modest number of degrees of freedom. For large unit cells with low symmetry
and/or high-order expansions they come, however, with a non-negligible
computational cost that can be more than two orders of magnitude higher than
that of OLS. In such cases, OLS with cutoff selection provides a viable route
as demonstrated here for both second-order FCs in large low-symmetry unit cells
and high-order FCs in low-symmetry systems. While regression techniques are
thus very powerful, they require well-tuned protocols. Here, the present work
establishes guidelines for the design of protocols that are readily usable,
e.g., in high-throughput and materials discovery schemes. Since the underlying
algorithms are not specific to FC construction, the general conclusions drawn
here also have a bearing on the construction of other linear models in physics
and materials science.Comment: 15 pages, 12 figure
Foothill: A Quasiconvex Regularization for Edge Computing of Deep Neural Networks
Deep neural networks (DNNs) have demonstrated success for many supervised
learning tasks, ranging from voice recognition, object detection, to image
classification. However, their increasing complexity might yield poor
generalization error that make them hard to be deployed on edge devices.
Quantization is an effective approach to compress DNNs in order to meet these
constraints. Using a quasiconvex base function in order to construct a binary
quantizer helps training binary neural networks (BNNs) and adding noise to the
input data or using a concrete regularization function helps to improve
generalization error. Here we introduce foothill function, an infinitely
differentiable quasiconvex function. This regularizer is flexible enough to
deform towards and penalties. Foothill can be used as a binary
quantizer, as a regularizer, or as a loss. In particular, we show this
regularizer reduces the accuracy gap between BNNs and their full-precision
counterpart for image classification on ImageNet.Comment: Accepted in 16th International Conference of Image Analysis and
Recognition (ICIAR 2019
Extended Bayesian Information Criteria for Gaussian Graphical Models
Gaussian graphical models with sparsity in the inverse covariance matrix are
of significant interest in many modern applications. For the problem of
recovering the graphical structure, information criteria provide useful
optimization objectives for algorithms searching through sets of graphs or for
selection of tuning parameters of other methods such as the graphical lasso,
which is a likelihood penalization technique. In this paper we establish the
consistency of an extended Bayesian information criterion for Gaussian
graphical models in a scenario where both the number of variables p and the
sample size n grow. Compared to earlier work on the regression case, our
treatment allows for growth in the number of non-zero parameters in the true
model, which is necessary in order to cover connected graphs. We demonstrate
the performance of this criterion on simulated data when used in conjunction
with the graphical lasso, and verify that the criterion indeed performs better
than either cross-validation or the ordinary Bayesian information criterion
when p and the number of non-zero parameters q both scale with n
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