878 research outputs found
Implicit Copulas from Bayesian Regularized Regression Smoothers
We show how to extract the implicit copula of a response vector from a
Bayesian regularized regression smoother with Gaussian disturbances. The copula
can be used to compare smoothers that employ different shrinkage priors and
function bases. We illustrate with three popular choices of shrinkage priors
--- a pairwise prior, the horseshoe prior and a g prior augmented with a point
mass as employed for Bayesian variable selection --- and both univariate and
multivariate function bases. The implicit copulas are high-dimensional, have
flexible dependence structures that are far from that of a Gaussian copula, and
are unavailable in closed form. However, we show how they can be evaluated by
first constructing a Gaussian copula conditional on the regularization
parameters, and then integrating over these. Combined with non-parametric
margins the regularized smoothers can be used to model the distribution of
non-Gaussian univariate responses conditional on the covariates. Efficient
Markov chain Monte Carlo schemes for evaluating the copula are given for this
case. Using both simulated and real data, we show how such copula smoothing
models can improve the quality of resulting function estimates and predictive
distributions
Copula-like Variational Inference
This paper considers a new family of variational distributions motivated by
Sklar's theorem. This family is based on new copula-like densities on the
hypercube with non-uniform marginals which can be sampled efficiently, i.e.
with a complexity linear in the dimension of state space. Then, the proposed
variational densities that we suggest can be seen as arising from these
copula-like densities used as base distributions on the hypercube with Gaussian
quantile functions and sparse rotation matrices as normalizing flows. The
latter correspond to a rotation of the marginals with complexity . We provide some empirical evidence that such a variational family can
also approximate non-Gaussian posteriors and can be beneficial compared to
Gaussian approximations. Our method performs largely comparably to
state-of-the-art variational approximations on standard regression and
classification benchmarks for Bayesian Neural Networks.Comment: 33rd Conference on Neural Information Processing Systems (NeurIPS
2019), Vancouver, Canad
Multi-task Sparse Structure Learning With Gaussian Copula Models
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. While sometimes the underlying task relationship structure is known, often the structure needs to be estimated from data at hand. In this paper, we present a novel family of models for MTL, applicable to regression and classification problems, capable of learning the structure of tasks relationship. In particular, we consider a joint estimation problem of the tasks relationship structure and the individual task parameters, which is solved using alternating minimization. The task relationship revealed by structure learning is founded on recent advances in Gaussian graphical models endowed with sparse estimators of the precision (inverse covariance) matrix. An extension to include flexible Gaussian copula models that relaxes the Gaussian marginal assumption is also proposed. We illustrate the e ff ectiveness of the proposed model on a variety of synthetic and benchmark data sets for regression and classi fi cation. We also consider the problem of combining Earth System Model (ESM) outputs for better projections of future climate, with focus on projections of temperature by combining ESMs in South and North America, and show that the proposed model outperforms several existing methods for the problem.17NSF [IIS-1029711, IIS-0916750, IIS-0953274, CNS-1314560, IIS-1422557, CCF-1451986, IIS-1447566]NASA [NNX12AQ39A]IBMYahooCNPqCNPq, BrazilConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq
Open TURNS: An industrial software for uncertainty quantification in simulation
The needs to assess robust performances for complex systems and to answer
tighter regulatory processes (security, safety, environmental control, and
health impacts, etc.) have led to the emergence of a new industrial simulation
challenge: to take uncertainties into account when dealing with complex
numerical simulation frameworks. Therefore, a generic methodology has emerged
from the joint effort of several industrial companies and academic
institutions. EDF R&D, Airbus Group and Phimeca Engineering started a
collaboration at the beginning of 2005, joined by IMACS in 2014, for the
development of an Open Source software platform dedicated to uncertainty
propagation by probabilistic methods, named OpenTURNS for Open source Treatment
of Uncertainty, Risk 'N Statistics. OpenTURNS addresses the specific industrial
challenges attached to uncertainties, which are transparency, genericity,
modularity and multi-accessibility. This paper focuses on OpenTURNS and
presents its main features: openTURNS is an open source software under the LGPL
license, that presents itself as a C++ library and a Python TUI, and which
works under Linux and Windows environment. All the methodological tools are
described in the different sections of this paper: uncertainty quantification,
uncertainty propagation, sensitivity analysis and metamodeling. A section also
explains the generic wrappers way to link openTURNS to any external code. The
paper illustrates as much as possible the methodological tools on an
educational example that simulates the height of a river and compares it to the
height of a dyke that protects industrial facilities. At last, it gives an
overview of the main developments planned for the next few years
Copula Ordinal Regression for Joint Estimation of Facial Action Unit Intensity
Joint modeling of the intensity of facial action units (AUs) from face images is challenging due to the large number of AUs (30+) and their intensity levels (6). This is in part due to the lack of suitable models that can efficiently handle such a large number of outputs/classes simultaneously, but also due to the lack of labelled target data. For this reason, majority of the methods proposed so far resort to independent classifiers for the AU intensity. This is suboptimal for at least two reasons: the facial appearance of some AUs changes depending on the intensity of other AUs, and some AUs co-occur more often than others. Encoding this is expected to improve the estimation of target AU intensities, especially in the case of noisy image features, head-pose variations and imbalanced training data. To this end, we introduce a novel modeling framework, Copula Ordinal Regression (COR), that leverages the power of copula functions and CRFs, to detangle the probabilistic modeling of AU dependencies from the marginal modeling of the AU intensity. Consequently, the COR model achieves the joint learning and inference of intensities of multiple AUs, while being computationally tractable. We show on two challenging datasets of naturalistic facial expressions that the proposed approach consistently outperforms (i) independent modeling of AU intensities, and (ii) the state-ofthe-art approach for the target task
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