Estimation of spatial processes using local scoring rules

Dawid, A. P.; Monachini, Monica

doi:10.1007/s10182-012-0191-8

Cited by 10 publications

(11 citation statements)

References 17 publications

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“…Indeed, evaluating (2.2) and computing the SME Q̂ requires no knowledge of the normalization constant, which is eliminated upon taking logarithmic derivatives with respect to x . Besides the imaging problems considered by Hyvärinen (2005), score matching has been applied to spatial statistics (Dawid and Musio, 2013) and neural networks (Köster and Hyvärinen, 2007; Vincent, 2011; Le et al, 2011). …”

Section: Score Matchingmentioning

confidence: 99%

Estimation of high-dimensional graphical models using regularized score matching

Lin¹,

Drton²,

Shojaie³

2016

Electron. J. Statist.

112

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Graphical models are widely used to model stochastic dependences among large collections of variables. We introduce a new method of estimating undirected conditional independence graphs based on the score matching loss, introduced by Hyvärinen (2005), and subsequently extended in Hyvärinen (2007). The regularized score matching method we propose applies to settings with continuous observations and allows for computationally efficient treatment of possibly non-Gaussian exponential family models. In the well-explored Gaussian setting, regularized score matching avoids issues of asymmetry that arise when applying the technique of neighborhood selection, and compared to existing methods that directly yield symmetric estimates, the score matching approach has the advantage that the considered loss is quadratic and gives piecewise linear solution paths under ℓ1 regularization. Under suitable irrepresentability conditions, we show that ℓ1-regularized score matching is consistent for graph estimation in sparse high-dimensional settings. Through numerical experiments and an application to RNAseq data, we confirm that regularized score matching achieves state-of-the-art performance in the Gaussian case and provides a valuable tool for computationally efficient estimation in non-Gaussian graphical models.

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Section: Score Matchingmentioning

confidence: 99%

Estimation of high-dimensional graphical models using regularized score matching

Lin¹,

Drton²,

Shojaie³

2016

Electron. J. Statist.

112

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“…For binary X v and S 0 the Brier score, it leads to the ratio matching method of Hyvärinen (2005). Some comparisons may be found in Dawid & Musio (2013).…”

Section: Composite Scoresmentioning

confidence: 99%

Minimum Scoring Rule Inference

Dawid

Monachini

Ventura

2015

Scandinavian J Statistics

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Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory of such equations can be applied to understand the properties of the associated estimator. In this paper we develop some basic scoring rule estimation theory, and explore robustness and interval estimation preoperties by means of theory and simulations.

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“…For binary X v , taking S 0 to be the Brier score forms the basis of the ratio matching method of Hyvärinen (2007). Some comparisons can be found in Dawid and Musio (2013).…”

Section: Pseudo Scorementioning

confidence: 99%