Estimation of Copulas via Maximum Mean Discrepancy

Alquier, Pierre; Chérief-Abdellatif, Badr-Eddine; Derumigny, Alexis; Fermanian, Jean‐David

doi:10.1080/01621459.2021.2024836

Cited by 4 publications

(5 citation statements)

References 39 publications

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“…The unbiased estimate of the energy score, obtained from samples 2 with varying θ value from the same Gaussian spatial copula, is illustrated in Figure 1a, depicting an estimate in accordance with the true parameter value θ = 450. This shows the effectiveness of our approach for inference of parameters of spatial Gaussian copulas, in addition to the existing theoretical consistency results in Alquier et al [2022].…”

Section: Inference On Simulated Datasupporting

confidence: 72%

“…Building on Janke et al [2021], Alquier et al [2022], to circumvent the problematic unavailable likelihood expression, we develop a methodology using minimum scoring rules estimation [Dawid et al, 2016] for the inference of parameters of Gaussian copulas, applicable also to our case of censored latent Gaussian copulas.…”

Section: Infeasibility Of Maximum Likelihood Estimationmentioning

confidence: 99%

“…Recent advances in likelihood-free inference have led to the development of alternative methods for copulas inference. Alquier et al [2022] use the maximum mean discrepancy (MMD) as a function to minimise in order to learn the parameters of copulas, obtaining a covariance estimator robust to miss-specification. Similarly, Janke et al [2021] employ the energy distance (a possible instance of the MMD) as a loss function in the training of a generative network to approximate a copula distribution, avoiding the necessity for hyperparameters for the MMD.…”

Section: Copula Estimation Problemsmentioning

confidence: 99%

See 2 more Smart Citations

Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

Huk

Adewoyin

Dutta

2023

Preprint

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<p>This work develops a novel method for generating conditional probabilistic rainfall forecasts with temporal and spatial dependence. A two-step procedure is employed. Firstly, marginal location-specific distributions are modelled independently of one another. Secondly, a spatial dependency structure is learned in order to make these marginal distributions spatially coherent. <br />To learn marginal distributions over rainfall values, we propose a class of models termed Joint Generalised Neural Models (JGNMs). These models expand the linear part of generalised linear models with a deep neural network allowing them to take into account non-linear trends of the data while learning the parameters for a distribution over the outcome space.<br />In order to understand the spatial dependency structure of the data, a model based on censored copulas is presented. It is designed for the particularities of rainfall data and incorporates the spatial aspect into our approach. Uniting our two contributions, namely the JGNM and the Censored Spatial Copulas into a single model, we get a probabilistic model capable of generating possible scenarios on short to long-term timescales, able to be evaluated at any given location, seen or unseen. We show an application of it to a precipitation downscaling problem on a large UK rainfall dataset and compare it to existing methods.</p>

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Section: Inference On Simulated Datasupporting

confidence: 72%

Section: Infeasibility Of Maximum Likelihood Estimationmentioning

confidence: 99%

Section: Copula Estimation Problemsmentioning

confidence: 99%

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Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

Huk

Adewoyin

Dutta

2023

Preprint

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“…For example, choosing a copula to fit the data is an important but difficult problem. A robust approach to estimate copulae has been investigated recently by [Alquier et al, 2020] using Maximum Mean Discrepancy. In link with our example, semiparametric estimation of copulae with missing data could be of great interest as proposed by [Hamori et al, 2019].…”

Section: Discussionmentioning

confidence: 99%

Sample from copula: a COPPY module

Boulin¹

2022

Preprint

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The modeling of dependence between random variables is an important subject in several applied fields of science. To this aim the copula function can be used as a margin-free description of the dependence structure. Several copulae belong to specific families such as Archimedean, Elliptical or Extreme. While software implementation of copulae has been thoroughly explored in R software, methods to work with copula in Python are still in their infancy. To promote the dependence modeling with copula in Python, we have developed COPPY, a library that provides a range of random vector generation vector for copulae.

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“…The larger the value of the variance inflation factor, the more troublesome ( Schenck, 2021 ). As a rule of thumb, if the variance inflation factor of a variable exceeds 10 (this will happen if Ri 2 exceeds 0.95), that variable is said to be highly collinear ( Alquier et al, 2022 ). The variance inflation factor is given as:

Where, R

is the coefficient of determination, X j is regressed on the other explanatory variables.…”

Section: Methodsmentioning

confidence: 99%

Determents of sustainable charcoal production in AWI zone; the case of Fagita Lekoma district, Ethiopia

Bekele¹,

Kemal²

2022

Heliyon

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Estimation of Copulas via Maximum Mean Discrepancy

Cited by 4 publications

References 39 publications

Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

Sample from copula: a COPPY module

Determents of sustainable charcoal production in AWI zone; the case of Fagita Lekoma district, Ethiopia

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