Statistical Downscaling via High-Dimensional Distribution Matching with Generative Models

• URL: http://arxiv.org/abs/2412.08079v1
• Date: Wed, 11 Dec 2024 03:52:17 GMT
• Title: Statistical Downscaling via High-Dimensional Distribution Matching with Generative Models
• Authors: Zhong Yi Wan, Ignacio Lopez-Gomez, Robert Carver, Tapio Schneider, John Anderson, Fei Sha, Leonardo Zepeda-Núñez,
• Abstract summary: We introduce Generative Bias Correction and Super-Resolution (GenBCSR), a two-stage probabilistic framework for statistical downscaling. By framing the downscaling problem as distribution matching, GenBCSR relaxes the constraints of supervised learning. We show that GenBCSR surpasses standard approaches in predictive accuracy of critical impact variables.
• Score: 12.737495484442443
• License:
• Abstract: Statistical downscaling is a technique used in climate modeling to increase the resolution of climate simulations. High-resolution climate information is essential for various high-impact applications, including natural hazard risk assessment. However, simulating climate at high resolution is intractable. Thus, climate simulations are often conducted at a coarse scale and then downscaled to the desired resolution. Existing downscaling techniques are either simulation-based methods with high computational costs, or statistical approaches with limitations in accuracy or application specificity. We introduce Generative Bias Correction and Super-Resolution (GenBCSR), a two-stage probabilistic framework for statistical downscaling that overcomes the limitations of previous methods. GenBCSR employs two transformations to match high-dimensional distributions at different resolutions: (i) the first stage, bias correction, aligns the distributions at coarse scale, (ii) the second stage, statistical super-resolution, lifts the corrected coarse distribution by introducing fine-grained details. Each stage is instantiated by a state-of-the-art generative model, resulting in an efficient and effective computational pipeline for the well-studied distribution matching problem. By framing the downscaling problem as distribution matching, GenBCSR relaxes the constraints of supervised learning, which requires samples to be aligned. Despite not requiring such correspondence, we show that GenBCSR surpasses standard approaches in predictive accuracy of critical impact variables, particularly in predicting the tails (99% percentile) of composite indexes composed of interacting variables, achieving up to 4-5 folds of error reduction.

Related papers

• Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms [31.42317398879432]
  Current inference approaches mainly fall into two categories: exact simulation and approximate methods such as $tau$-leaping. In this work, we advance the latter category by tailoring the first extension of high-order numerical inference schemes to discrete diffusion models. We rigorously analyze the proposed schemes and establish the second-order accuracy of the $theta$-trapezoidal method in KL divergence.
  arXiv  Detail & Related papers  (2025-02-01T00:25:21Z)
• Causal Invariance Learning via Efficient Optimization of a Nonconvex Objective [12.423111378195667]
  We propose a novel method for finding causal relationships among variables. We show that our method converges to a standard gradient method. Our algorithm avoids exhaustive searches, making it especially when the number of covariants is large.
  arXiv  Detail & Related papers  (2024-12-16T15:11:02Z)
• On conditional diffusion models for PDE simulations [53.01911265639582]
  We study score-based diffusion models for forecasting and assimilation of sparse observations. We propose an autoregressive sampling approach that significantly improves performance in forecasting. We also propose a new training strategy for conditional score-based models that achieves stable performance over a range of history lengths.
  arXiv  Detail & Related papers  (2024-10-21T18:31:04Z)
• Capturing Climatic Variability: Using Deep Learning for Stochastic Downscaling [0.0]
  Adapting to the changing climate requires accurate local climate information. Capturing variability while downscaling is crucial for estimating uncertainty and characterising extreme events. We propose approaches to improve the calibration of GANs in three ways.
  arXiv  Detail & Related papers  (2024-05-31T03:04:10Z)
• Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models [15.623456909553786]
  We introduce a two-stage probabilistic framework for statistical downscaling using unpaired data. We demonstrate the utility of the proposed approach on one- and two-dimensional fluid flow problems.
  arXiv  Detail & Related papers  (2023-05-24T23:40:23Z)
• Distributionally Robust Models with Parametric Likelihood Ratios [123.05074253513935]
  Three simple ideas allow us to train models with DRO using a broader class of parametric likelihood ratios. We find that models trained with the resulting parametric adversaries are consistently more robust to subpopulation shifts when compared to other DRO approaches.
  arXiv  Detail & Related papers  (2022-04-13T12:43:12Z)
• Increasing the accuracy and resolution of precipitation forecasts using deep generative models [3.8073142980733]
  We train a conditional Generative Adversarial Network -- coined CorrectorGAN -- to produce ensembles of high-resolution, bias-corrected forecasts. CorrectorGAN, once trained, produces predictions in seconds on a single machine. Results raise exciting questions about the necessity of regional models, and whether data-driven downscaling and correction methods can be transferred to data-poor regions.
  arXiv  Detail & Related papers  (2022-03-23T09:45:12Z)
• A Twin Neural Model for Uplift [59.38563723706796]
  Uplift is a particular case of conditional treatment effect modeling. We propose a new loss function defined by leveraging a connection with the Bayesian interpretation of the relative risk. We show our proposed method is competitive with the state-of-the-art in simulation setting and on real data from large scale randomized experiments.
  arXiv  Detail & Related papers  (2021-05-11T16:02:39Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)
• Improving Maximum Likelihood Training for Text Generation with Density Ratio Estimation [51.091890311312085]
  We propose a new training scheme for auto-regressive sequence generative models, which is effective and stable when operating at large sample space encountered in text generation. Our method stably outperforms Maximum Likelihood Estimation and other state-of-the-art sequence generative models in terms of both quality and diversity.
  arXiv  Detail & Related papers  (2020-07-12T15:31:24Z)
• Instability, Computational Efficiency and Statistical Accuracy [101.32305022521024]
  We develop a framework that yields statistical accuracy based on interplay between the deterministic convergence rate of the algorithm at the population level, and its degree of (instability) when applied to an empirical object based on $n$ samples. We provide applications of our general results to several concrete classes of models, including Gaussian mixture estimation, non-linear regression models, and informative non-response models.
  arXiv  Detail & Related papers  (2020-05-22T22:30:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.