Spatio-temporal probabilistic forecast using MMAF-guided learning

• URL: http://arxiv.org/abs/2603.15055v1
• Date: Mon, 16 Mar 2026 10:07:40 GMT
• Title: Spatio-temporal probabilistic forecast using MMAF-guided learning
• Abstract summary: We use feed-forward neural networks with Gaussian-distributed weights to determine a probabilistic forecast for ensemble-guided datasets.<n>Networks are trained using MMAF-guided learning, a generalized methodology in which the observed data are preprocessed.<n>Experiments on both synthetic and real data demonstrate that our forecasts remain on horizons across multiple time horizons.
• Score: 0.618564539309103
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We employ stochastic feed-forward neural networks with Gaussian-distributed weights to determine a probabilistic forecast for spatio-temporal raster datasets. The networks are trained using MMAF-guided learning, a generalized Bayesian methodology in which the observed data are preprocessed using an embedding designed to produce a low-dimensional representation that captures their dependence and causal structure. The design of the embedding is theory-guided by the assumption that a spatio-temporal Ornstein-Uhlenbeck process with finite second-order moments generates the observed data. The trained networks, in inference mode, are then used to generate ensemble forecasts by applying different initial conditions at different horizons. Experiments conducted on both synthetic and real data demonstrate that our forecasts remain calibrated across multiple time horizons. Moreover, we show that on such data, simple feed-forward architectures can achieve performance comparable to, and in some cases better than, convolutional or diffusion deep learning architectures used in probabilistic forecasting tasks.

Related papers

• Demystifying Data-Driven Probabilistic Medium-Range Weather Forecasting [63.8116386935854]
  We demonstrate that state-of-the-art probabilistic skill requires neither intricate architectural constraints nor specialized trainings.<n>We introduce a scalable framework for learning multi-scale atmospheric dynamics by combining a directly downsampled latent space with a history-conditioned local projector.<n>We find that our framework design is robust to the choice of probabilistic estimators, seamlessly supporting interpolants, diffusion models, and CRPS-based ensemble training.
  arXiv  Detail & Related papers  (2026-01-26T03:52:16Z)
• When Rigidity Hurts: Soft Consistency Regularization for Probabilistic Hierarchical Time Series Forecasting [69.30930115236228]
  Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting. Most methods focus on point predictions and do not provide well-calibrated probabilistic forecasts distributions. We propose PROFHiT, a fully probabilistic hierarchical forecasting model that jointly models forecast distribution of entire hierarchy.
  arXiv  Detail & Related papers  (2023-10-17T20:30:16Z)
• TempSAL -- Uncovering Temporal Information for Deep Saliency Prediction [64.63645677568384]
  We introduce a novel saliency prediction model that learns to output saliency maps in sequential time intervals. Our approach locally modulates the saliency predictions by combining the learned temporal maps. Our code will be publicly available on GitHub.
  arXiv  Detail & Related papers  (2023-01-05T22:10:16Z)
• Mixed moving average field guided learning for spatio-temporal data [0.0]
  We define a novel Bayesian-temporal embedding and a theory-guided machine learning approach to make ensemble forecasts. We use Lipschitz predictors to determine fixed-time and any-time PAC in the batch learning setting. We then test the performance of our learning methodology by using linear predictors and data sets simulated from a dependence- Ornstein-Uhlenbeck process.
  arXiv  Detail & Related papers  (2023-01-02T16:11:05Z)
• TACTiS: Transformer-Attentional Copulas for Time Series [76.71406465526454]
  estimation of time-varying quantities is a fundamental component of decision making in fields such as healthcare and finance. We propose a versatile method that estimates joint distributions using an attention-based decoder. We show that our model produces state-of-the-art predictions on several real-world datasets.
  arXiv  Detail & Related papers  (2022-02-07T21:37:29Z)
• Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization [5.5643498845134545]
  We use generative neural networks to parametrize distributions on high-dimensional spaces by transforming draws from a latent variable. We train generative networks to minimize a predictive-sequential (or prequential) scoring rule on a recorded temporal sequence of the phenomenon of interest. Our method outperforms state-of-the-art adversarial approaches, especially in probabilistic calibration.
  arXiv  Detail & Related papers  (2021-12-15T15:51:12Z)
• Probabilistic Time Series Forecasting with Implicit Quantile Networks [0.7249731529275341]
  We combine an autoregressive recurrent neural network to model temporal dynamics with Implicit Quantile Networks to learn a large class of distributions over a time-series target. Our approach is favorable in terms of point-wise prediction accuracy as well as on estimating the underlying temporal distribution.
  arXiv  Detail & Related papers  (2021-07-08T10:37:24Z)
• Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithms [2.266704469122763]
  This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. We establish the existence and well-posedness of the associated posterior moments under easily verifiable conditions. A model accuracy analysis suggests that the Bayesian probability probabilities reported by the data-driven models are also remarkably accurate under a frequentist definition.
  arXiv  Detail & Related papers  (2021-03-18T11:34:08Z)
• Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting [98.57851612518758]
  Probabilistic time series forecasting involves estimating the distribution of future based on its history. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks. We show in experiments that our model produces accurate and sharp probabilistic forecasts.
  arXiv  Detail & Related papers  (2021-01-31T06:49:33Z)
• Learned Factor Graphs for Inference from Stationary Time Sequences [107.63351413549992]
  We propose a framework that combines model-based algorithms and data-driven ML tools for stationary time sequences. neural networks are developed to separately learn specific components of a factor graph describing the distribution of the time sequence. We present an inference algorithm based on learned stationary factor graphs, which learns to implement the sum-product scheme from labeled data.
  arXiv  Detail & Related papers  (2020-06-05T07:06:19Z)
• A machine learning approach for forecasting hierarchical time series [4.157415305926584]
  We propose a machine learning approach for forecasting hierarchical time series. Forecast reconciliation is the process of adjusting forecasts to make them coherent across the hierarchy. We exploit the ability of a deep neural network to extract information capturing the structure of the hierarchy.
  arXiv  Detail & Related papers  (2020-05-31T22:26:16Z)

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.