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Nonlinear Functional Output Regression: a Dictionary Approach [article]

Dimitri Bouche, Marianne Clausel, François Roueff, Florence d'Alché-Buc
2021 arXiv   pre-print
To address functional-output regression, we introduce projection learning (PL), a novel dictionary-based approach that learns to predict a function that is expanded on a dictionary while minimizing an  ...  Eventually, several robustness aspects of the proposed algorithms are highlighted on a toy dataset; and a study on two real datasets shows that they are competitive compared to other nonlinear approaches  ...  Abstract To address functional-output regression, we introduce projection learning (PL), a novel dictionary-based approach that learns to predict a function that is expanded on a dictionary while minimizing  ... 
arXiv:2003.01432v4 fatcat:3zi33q4y3bcnhckml2gcecrfs4

Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach [article]

Pawan Goyal, Peter Benner
2021 arXiv   pre-print
We utilize the fact that given a dictionary containing huge candidate nonlinear functions, dynamical models can often be described by a few appropriately chosen candidates.  ...  Additionally, we integrate a numerical integration framework with dictionary learning that yields differential equations without requiring or approximating derivative information at any stage.  ...  A compelling breakthrough towards discovering nonlinear governing equations appeared in [3, 37] , where an approach based on genetic programming or symbolic regression is developed to identify nonlinear  ... 
arXiv:2105.04869v1 fatcat:mmn7qsrmprbybjuafojyp5uk3u

A Geometric Dictionary Learning Based Approach for Fluorescence Spectroscopy Image Fusion

Zhiqin Zhu, Guanqiu Qi, Yi Chai, Penghua Li
2017 Applied Sciences  
Constructing an informative dictionary is a key step for sparsity-based image fusion method.  ...  In recent years, sparse representation approaches have been integrated into multi-focus image fusion methods.  ...  of the nonlinearity of the masking function [59, 60] .  ... 
doi:10.3390/app7020161 fatcat:3cf7f2vcmjcrveo4mjqsuh5cwq

A Sparse Nonlinear Bayesian Online Kernel Regression

Matthieu Geist, Olivier Pietquin, Gabriel Fricout
2008 2008 The Second International Conference on Advanced Engineering Computing and Applications in Sciences  
In this paper we propose a sparse nonlinear bayesian online kernel regression. Sparsity is achieved in a preprocessing step by using a dictionary method.  ...  First experiments on a cardinal sine regression show that our approach is promising.  ...  parameter ν outputs: a dictionary D Initialization; D 1 = {x 1 }; Dictionary computation; for k = 1, 2, . . .  ... 
doi:10.1109/advcomp.2008.7 fatcat:pc3vnmtlavcynctupioy2vqiq4

Online Bayesian kernel regression from nonlinear mapping of observations

Matthieu Geist, Olivier Pietquin, Gabriel Fricout
2008 2008 IEEE Workshop on Machine Learning for Signal Processing  
Several solutions can be envisioned among which regressing a family of parameterized functions so as to make it fit at best to the observed samples.  ...  In a large number of applications, engineers have to estimate a function linked to the state of a dynamic system.  ...  This approach is planned to be extended to stochastic transformation function (the observed part of nonlinearities) in order to solve a more general form of the Bellman equation.  ... 
doi:10.1109/mlsp.2008.4685498 fatcat:kvhqqe5sbjhuzadcencbjt7ymq

Learning Fast Approximations of Sparse Nonlinear Regression [article]

Yuhai Song, Zhong Cao, Kailun Wu, Ziang Yan, Changshui Zhang
2020 arXiv   pre-print
However, for sparse nonlinear regression problems, a similar idea is rarely exploited due to the complexity of nonlinearity.  ...  In this work, we bridge this gap by introducing the Nonlinear Learned Iterative Shrinkage Thresholding Algorithm (NLISTA), which can attain a linear convergence under suitable conditions.  ...  Learning Fast Approximations of Sparse Nonlinear Regression (Supplementary Material) A Proof of Lemma 2 Proof. Since f (·) is a element-wise function, the gradient of f (·) is a diagonal matrix.  ... 
arXiv:2010.13490v1 fatcat:cbivytoiwvc2ha7x3l2m2psi3e

Quantum Energy Regression using Scattering Transforms [article]

Matthew Hirn and Nicolas Poilvert and Stéphane Mallat
2016 arXiv   pre-print
We present a novel approach to the regression of quantum mechanical energies based on a scattering transform of an intermediate electron density representation.  ...  A scattering transform is a deep convolution network computed with a cascade of multiscale wavelet transforms.  ...  The modulus of the output functions from these convolutions are then averaged over the discrete spatial grid and the discrete sampling of [0, π) to obtain the wavelet dictionary functionals.  ... 
arXiv:1502.02077v3 fatcat:flz2vtsnunacfdpqfjh52alopi

Regression Analyses of Distributions using Quantile Functional Regression [article]

Hojin Yang, Veerabhadran Baladandayuthapani, Arvind U.K. Rao, and Jeffrey S. Morris
2018 arXiv   pre-print
We call this approach quantile functional regression, regressing subject-specific marginal distributions across repeated measurements on a set of covariates, allowing us to assess which covariates are  ...  We fit this model using a Bayesian framework that uses nonlinear shrinkage of quantlet coefficients to regularize the functional regression coefficients and provides fully Bayesian inference after fitting  ...  regression approach.  ... 
arXiv:1810.03496v1 fatcat:2xcodgbgujbj5bgnpnwp2nvwle

On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression [article]

Rajdip Nayek, Ramon Fuentes, Keith Worden, Elizabeth J. Cross
2020 arXiv   pre-print
The problem of discovering governing equations is cast as that of selecting relevant variables from a predetermined dictionary of basis variables and solved via sparse Bayesian linear regression.  ...  The results demonstrate the effectiveness of the SS priors in identifying the presence and type of nonlinearity in the system.  ...  In this approach, it is assumed that the function M consists of only a few terms, making it sparse in the space of possible functions.  ... 
arXiv:2012.01937v2 fatcat:5qpkyyof4zeo7gxb42tw7i4bm4

Weighted Direct Nonlinear Regression for Effective Image Interpolation

Jieying Zheng, Wanru Song, Yahong Wu, Feng Liu
2019 IEEE Access  
This paper proposes a learning-based image interpolation method based on weighted direct nonlinear regression.  ...  INDEX TERMS Image interpolation, image processing, super-resolution, anchored neighborhood, dictionary learning, nonlinear regression, training. 8646 2169-3536  ...  The most important part for the nonlinearity is the active function g(z), which is defined as the following sigmoid function: g(z) = 1 1 + e z (8) The function is a nonlinear continuous function that allows  ... 
doi:10.1109/access.2018.2890517 fatcat:4qssc5j56jet7ezruorssku6h4

Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality [article]

Vikas Sindhwani and Minh Ha Quang and Aurelie C. Lozano
2013 arXiv   pre-print
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems.  ...  As a key application enabled by our framework, we show how high-dimensional causal inference tasks can be naturally cast as sparse function estimation problems, leading to novel nonlinear extensions of  ...  We conducted 4 sets of experiments: with linear and nonlinear dictionaries (Gaussian kernels with 13 choices of bandwidths per group), and with or without output kernel learning.  ... 
arXiv:1210.4792v2 fatcat:xlorqn6djrc6jpfhhvy4ed7khm

An iterative orthogonal forward regression algorithm

Yuzhu Guo, L.Z. Guo, S.A. Billings, Hua-Liang Wei
2014 International Journal of Systems Science  
Index Terms: Iterative orthogonal forward regression, model structure detection, nonlinear system identification, orthogonal least squares  ...  A novel iterative learning algorithm is proposed to improve the classic orthogonal forward regression (OFR) algorithm in an attempt to produce an optimal solution under a purely OFR framework without using  ...  Terms i  are linear or nonlinear functions of the input, output and noise.  ... 
doi:10.1080/00207721.2014.981237 fatcat:ldxuncbkeff33cyt3tskjr24ga

Kernel Instrumental Variable Regression [article]

Rahul Singh, Maneesh Sahani, Arthur Gretton
2020 arXiv   pre-print
We propose kernel instrumental variable regression (KIV), a nonparametric generalization of 2SLS, modeling relations among X, Y, and Z as nonlinear functions in reproducing kernel Hilbert spaces (RKHSs  ...  Instrumental variable (IV) regression is a strategy for learning causal relationships in observational data.  ...  Basis function approximation [48, 17] is perhaps the closest prior IV approach, but we use infinite dictionaries of basis functions ψ and φ.  ... 
arXiv:1906.00232v6 fatcat:jqmcg6sp5vcabhaf7ey23fbwja

A Nonlinear Adaptive Beamforming Algorithm Based on Least Squares Support Vector Regression

Lutao Wang, Gang Jin, Zhengzhou Li, Hongbin Xu
2012 Sensors  
based on nonlinear least-square support vector regression machine (LS-SVR) is derived in this paper.  ...  In this approach, the conventional linearly constrained minimum variance cost function used by minimum variance distortionless response (MVDR) beamformer is replaced by a squared-loss function to increase  ...  Thus, the beamformer's output can be formulated as a linear regression in H.  ... 
doi:10.3390/s120912424 fatcat:niur3247rbcdfehtxeicjd2o2i

Image based regression using boosting method

Shaohua Kevin Zhou, B. Georgescu, Xiang Sean Zhou, D. Comaniciu
2005 Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1  
We formulate a multiple-output regression problem in such a way that overfitting is decreased and an analytic solution is admitted.  ...  We present a general algorithm of image based regression that is applicable to many vision problems. The proposed regressor that targets a multiple-output setting is learned using boosting method.  ...  Popular data-driven regression approaches include nonparameteric kernel regression (NPR), linear methods and their nonlinear kernel variants such as kernel ridge regression (KRR), support vector regression  ... 
doi:10.1109/iccv.2005.117 dblp:conf/iccv/ZhouGZC05 fatcat:2fldrocrbvegradvr5rfafcdom
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