26,473 research outputs found
Highly efficient hierarchical online nonlinear regression using second order methods
We introduce highly efficient online nonlinear regression algorithms that are suitable for real life applications. We process the data in a truly online manner such that no storage is needed, i.e., the data is discarded after being used. For nonlinear modeling we use a hierarchical piecewise linear approach based on the notion of decision trees where the space of the regressor vectors is adaptively partitioned based on the performance. As the first time in the literature, we learn both the piecewise linear partitioning of the regressor space as well as the linear models in each region using highly effective second order methods, i.e., Newton–Raphson Methods. Hence, we avoid the well known over fitting issues by using piecewise linear models, however, since both the region boundaries as well as the linear models in each region are trained using the second order methods, we achieve substantial performance compared to the state of the art. We demonstrate our gains over the well known benchmark data sets and provide performance results in an individual sequence manner guaranteed to hold without any statistical assumptions. Hence, the introduced algorithms address computational complexity issues widely encountered in real life applications while providing superior guaranteed performance in a strong deterministic sense. © 2017 Elsevier B.V
Piecewise linear regression based on adaptive tree structure using second order methods
We introduce a highly efficient online nonlinear regression algorithm. We process the data in a truly online manner such that no storage is needed, i.e., the data is discarded after used. For nonlinear modeling we use a hierarchical piecewise linear approach based on the notion of decision trees, where the regressor space is adaptively partitioned based directly on the performance. As the first time in the literature, we learn both the piecewise linear partitioning of the regressor space as well as the linear models in each region using highly effective second order methods, i.e., Newton-Raphson Methods. Hence, we avoid the well known over fitting issues and achieve substantial performance compared to the state of the art. We demonstrate our gains over the well known benchmark data sets and provide performance results in an individual sequence manner guaranteed to hold without any statistical assumptions. © 2016 IEEE
On-the-fly adaptivity for nonlinear twoscale simulations using artificial neural networks and reduced order modeling
A multi-fidelity surrogate model for highly nonlinear multiscale problems is
proposed. It is based on the introduction of two different surrogate models and
an adaptive on-the-fly switching. The two concurrent surrogates are built
incrementally starting from a moderate set of evaluations of the full order
model. Therefore, a reduced order model (ROM) is generated. Using a hybrid
ROM-preconditioned FE solver, additional effective stress-strain data is
simulated while the number of samples is kept to a moderate level by using a
dedicated and physics-guided sampling technique. Machine learning (ML) is
subsequently used to build the second surrogate by means of artificial neural
networks (ANN). Different ANN architectures are explored and the features used
as inputs of the ANN are fine tuned in order to improve the overall quality of
the ML model. Additional ANN surrogates for the stress errors are generated.
Therefore, conservative design guidelines for error surrogates are presented by
adapting the loss functions of the ANN training in pure regression or pure
classification settings. The error surrogates can be used as quality indicators
in order to adaptively select the appropriate -- i.e. efficient yet accurate --
surrogate. Two strategies for the on-the-fly switching are investigated and a
practicable and robust algorithm is proposed that eliminates relevant technical
difficulties attributed to model switching. The provided algorithms and ANN
design guidelines can easily be adopted for different problem settings and,
thereby, they enable generalization of the used machine learning techniques for
a wide range of applications. The resulting hybrid surrogate is employed in
challenging multilevel FE simulations for a three-phase composite with
pseudo-plastic micro-constituents. Numerical examples highlight the performance
of the proposed approach
Integrated Inference and Learning of Neural Factors in Structural Support Vector Machines
Tackling pattern recognition problems in areas such as computer vision,
bioinformatics, speech or text recognition is often done best by taking into
account task-specific statistical relations between output variables. In
structured prediction, this internal structure is used to predict multiple
outputs simultaneously, leading to more accurate and coherent predictions.
Structural support vector machines (SSVMs) are nonprobabilistic models that
optimize a joint input-output function through margin-based learning. Because
SSVMs generally disregard the interplay between unary and interaction factors
during the training phase, final parameters are suboptimal. Moreover, its
factors are often restricted to linear combinations of input features, limiting
its generalization power. To improve prediction accuracy, this paper proposes:
(i) Joint inference and learning by integration of back-propagation and
loss-augmented inference in SSVM subgradient descent; (ii) Extending SSVM
factors to neural networks that form highly nonlinear functions of input
features. Image segmentation benchmark results demonstrate improvements over
conventional SSVM training methods in terms of accuracy, highlighting the
feasibility of end-to-end SSVM training with neural factors
Nonlinear Models Using Dirichlet Process Mixtures
We introduce a new nonlinear model for classification, in which we model the
joint distribution of response variable, y, and covariates, x,
non-parametrically using Dirichlet process mixtures. We keep the relationship
between y and x linear within each component of the mixture. The overall
relationship becomes nonlinear if the mixture contains more than one component.
We use simulated data to compare the performance of this new approach to a
simple multinomial logit (MNL) model, an MNL model with quadratic terms, and a
decision tree model. We also evaluate our approach on a protein fold
classification problem, and find that our model provides substantial
improvement over previous methods, which were based on Neural Networks (NN) and
Support Vector Machines (SVM). Folding classes of protein have a hierarchical
structure. We extend our method to classification problems where a class
hierarchy is available. We find that using the prior information regarding the
hierarchical structure of protein folds can result in higher predictive
accuracy
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