Neural Networks for Parameter Estimation in Intractable Models

Lenzi, Amanda; Bessac, Julie; Rudi, Johann; Stein, Michael L.

doi:10.48550/arxiv.2107.14346

Cited by 4 publications

(7 citation statements)

References 30 publications

(34 reference statements)

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“…Gerber & Nychka (2021) showed that their CNN estimator was comparable to the maximum likelihood estimator in terms of bias and variance and, like Zammit-Mangion & Wikle (2020), reported a hundred-fold speed up in estimation. Lenzi et al (2021) considered a similar CNN framework for estimating parameters in models of spatial extremes. This approach to parameter estimation is still in its infancy in spatial statistics, but has seen wide use in a variety of related areas that require parameter estimation.…”

Section: Deep Learning For Parameter Estimation In Spatial and Spatio...mentioning

confidence: 99%

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Statistical Deep Learning for Spatial and Spatio-Temporal Data

Wikle¹,

Zammit‐Mangion²

2022

Preprint

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Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g., images) and time (e.g., sequences). Indeed, deep models have also been extensively used by the statistical community to model spatial and spatio-temporal data through, for example, the use of multi-level Bayesian hierarchical models and deep Gaussian processes. In this review, we first present an overview of traditional statistical and machine learning perspectives for modeling spatial and spatio-temporal data, and then focus on a variety of hybrid models that have recently been developed for latent process, data, and parameter specifications. These hybrid models integrate statistical modeling ideas with deep neural network models in order to take advantage of the strengths of each modeling paradigm. We conclude by giving an overview of computational technologies that have proven useful for these hybrid models, and with a brief discussion on future research directions.

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Section: Deep Learning For Parameter Estimation In Spatial and Spatio...mentioning

confidence: 99%

“…• Lenzi et al (2021) use deep learning to estimate parameters with statistical spatial models of extremes, whose likelihood is intractable or difficult to evaluate. They apply their methods for efficiently estimating parameters in a Brown-Resnick process fitted to surface temperature data.…”

Section: Introductionmentioning

confidence: 99%

Statistical Deep Learning for Spatial and Spatio-Temporal Data

Wikle¹,

Zammit‐Mangion²

2022

Preprint

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“…[3] provided universal approximation results for functions on finite dimensional topological spaces; that is, if F is dense in C(R n ; R m ), then {f • ϕ : f ∈ F } is dense in C(X ; R m ) when ϕ : X → R n is continuous and injective. [4] used distributional neural networks to estimate parameters for max-stable processes. [5] does density estimation using neural networks.…”

Section: Introductionmentioning

confidence: 99%

Universal Approximation and the Topological Neural Network

Kouritzin,

Richard

2023

IEEE Access

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A topological neural network (TNN), which takes input data from a Tychonoff topological space instead of the usual finite dimensional space, is introduced. As a consequence, a distributional neural network (DNN) that takes Borel measures as data is also introduced. Combined these new neural networks facilitate things like recognizing long range dependence, heavy tails and other properties in stochastic process paths or like acting on belief states produced by particle filtering or hidden Markov model algorithms. The veracity of the TNN and DNN are then established herein by a strong universal approximation theorem for Tychonoff spaces and its corollary for spaces of measures. These theorems show that neural networks can arbitrarily approximate uniformly continuous functions (with respect to the sup metric) associated with a unique uniformity. We also provide some discussion showing that neural networks on positive-finite measures are a generalization of the recent deep learning notion of deep sets.

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“…Huser et al (2022) have also applied the Vecchia approximation that requires only moderate-dimensional (say 10 or 15) joint distribution functions, which are available for some MSPs. Deep learning has been used to estimate parameters in spatial models (Gerber and Nychka, 2021;Lenzi et al, 2021) by simulating datasets with different parameter values and using deep learning to identify features of the simulated data that are indicative of particular parameter values. However, it is difficult to extend them to problems with many parameters such as the spatio-temporally varying coefficients (STVC) case that are crucial to our application.…”

Section: Introductionmentioning

confidence: 99%

Modeling Extremal Streamflow using Deep Learning Approximations and a Flexible Spatial Process

Majumder¹,

Reich²,

Shaby³

2022

Preprint

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Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly suited for modeling extreme events. Spatial extreme value models with more realistic tail dependence characteristics are under active development. They are theoretically justified, but give intractable likelihoods, making computation challenging for small datasets and prohibitive for continental-scale studies. We propose a process mixture model which specifies spatial dependence in extreme values as a convex combination of a Gaussian process and a max-stable process, yielding desirable tail dependence properties but intractable likelihoods. To address this, we employ a unique computational strategy where a feed-forward neural network is embedded in a density regression model to approximate the conditional distribution at one spatial location given a set of neighbors. We then use this univariate density function to approximate the joint likelihood for all locations by way of a Vecchia approximation. The process mixture model is used to analyze changes in annual maximum streamflow within the US over the last 50 years, and is able to detect areas which show increases in extreme streamflow over time.

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Neural Networks for Parameter Estimation in Intractable Models

Cited by 4 publications

References 30 publications

Statistical Deep Learning for Spatial and Spatio-Temporal Data

Statistical Deep Learning for Spatial and Spatio-Temporal Data

Universal Approximation and the Topological Neural Network

Modeling Extremal Streamflow using Deep Learning Approximations and a Flexible Spatial Process

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