Probabilistic Functional Neural Networks

• URL: http://arxiv.org/abs/2503.21585v1
• Date: Thu, 27 Mar 2025 15:01:37 GMT
• Title: Probabilistic Functional Neural Networks
• Authors: Haixu Wang, Jiguo Cao,
• Abstract summary: High-dimensional functional time series (HDFTS) are often characterized by nonlinear trends and high spatial dimensions.<n>We propose a novel probabilistic functional neural network (ProFnet) to address these challenges.<n>ProFnet integrates the strengths of feedforward and deep neural networks with probabilistic modeling.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: High-dimensional functional time series (HDFTS) are often characterized by nonlinear trends and high spatial dimensions. Such data poses unique challenges for modeling and forecasting due to the nonlinearity, nonstationarity, and high dimensionality. We propose a novel probabilistic functional neural network (ProFnet) to address these challenges. ProFnet integrates the strengths of feedforward and deep neural networks with probabilistic modeling. The model generates probabilistic forecasts using Monte Carlo sampling and also enables the quantification of uncertainty in predictions. While capturing both temporal and spatial dependencies across multiple regions, ProFnet offers a scalable and unified solution for large datasets. Applications to Japan's mortality rates demonstrate superior performance. This approach enhances predictive accuracy and provides interpretable uncertainty estimates, making it a valuable tool for forecasting complex high-dimensional functional data and HDFTS.

Related papers

• A data augmentation strategy for deep neural networks with application to epidemic modelling [2.4537195774258556]
  We present a proof of concept demonstrating the application of data-driven methods and deep neural networks to a recently introduced SIR-type model. Our results show that a robust data augmentation strategy trough suitable data-driven models can improve the reliability of Feed-Forward Neural Networks (FNNs) and Autoregressive Networks (NARs) This approach enhances the ability to handle nonlinear dynamics and offers scalable, data-driven solutions for epidemic forecasting.
  arXiv  Detail & Related papers  (2025-02-28T13:24:49Z)
• ST-FiT: Inductive Spatial-Temporal Forecasting with Limited Training Data [59.78770412981611]
  In real-world applications, most nodes may not possess any available temporal data during training.<n>We propose a principled framework named ST-FiT to handle this problem.
  arXiv  Detail & Related papers  (2024-12-14T17:51:29Z)
• Recurrent Interpolants for Probabilistic Time Series Prediction [10.422645245061899]
  Sequential models like recurrent neural networks and transformers have become standard for probabilistic time series forecasting. Recent work explores generative approaches using diffusion or flow-based models, extending to time series imputation and forecasting. This work proposes a novel method combining recurrent neural networks' efficiency with diffusion models' probabilistic modeling, based on interpolants and conditional generation with control features.
  arXiv  Detail & Related papers  (2024-09-18T03:52:48Z)
• SFANet: Spatial-Frequency Attention Network for Weather Forecasting [54.470205739015434]
  Weather forecasting plays a critical role in various sectors, driving decision-making and risk management. Traditional methods often struggle to capture the complex dynamics of meteorological systems. We propose a novel framework designed to address these challenges and enhance the accuracy of weather prediction.
  arXiv  Detail & Related papers  (2024-05-29T08:00:15Z)
• Tractable Function-Space Variational Inference in Bayesian Neural Networks [72.97620734290139]
  A popular approach for estimating the predictive uncertainty of neural networks is to define a prior distribution over the network parameters. We propose a scalable function-space variational inference method that allows incorporating prior information. We show that the proposed method leads to state-of-the-art uncertainty estimation and predictive performance on a range of prediction tasks.
  arXiv  Detail & Related papers  (2023-12-28T18:33:26Z)
• Uncertainty Quantification of Sparse Travel Demand Prediction with Spatial-Temporal Graph Neural Networks [4.488583779590991]
  We develop a spatial-temporal zero-inflated negative Binomial Graph Neural Network (STZINB-GNN) to quantify the uncertainty of the sparse travel demand. It analyzes spatial and temporal correlations using diffusion and temporal convolution networks, which are then fused to parameterize the probabilistic distributions of travel demand. The results demonstrate the superiority of STZINB-GNN over benchmark models, especially under high spatial-temporal resolutions.
  arXiv  Detail & Related papers  (2022-08-11T16:21:10Z)
• Probabilistic AutoRegressive Neural Networks for Accurate Long-range Forecasting [6.295157260756792]
  We introduce the Probabilistic AutoRegressive Neural Networks (PARNN) PARNN is capable of handling complex time series data exhibiting non-stationarity, nonlinearity, non-seasonality, long-range dependence, and chaotic patterns. We evaluate the performance of PARNN against standard statistical, machine learning, and deep learning models, including Transformers, NBeats, and DeepAR.
  arXiv  Detail & Related papers  (2022-04-01T17:57:36Z)
• Bilinear Input Normalization for Neural Networks in Financial Forecasting [101.89872650510074]
  We propose a novel data-driven normalization method for deep neural networks that handle high-frequency financial time-series. The proposed normalization scheme takes into account the bimodal characteristic of financial time-series. Our experiments, conducted with state-of-the-arts neural networks and high-frequency data, show significant improvements over other normalization techniques.
  arXiv  Detail & Related papers  (2021-09-01T07:52:03Z)
• Spatiotemporal convolutional network for time-series prediction and causal inference [21.895413699349966]
  A neural network computing framework, i.N.N., was developed to efficiently and accurately render a multistep-ahead prediction of a time series. The framework has great potential in practical applications in artificial intelligence (AI) or machine learning fields.
  arXiv  Detail & Related papers  (2021-07-03T06:20:43Z)
• RNN with Particle Flow for Probabilistic Spatio-temporal Forecasting [30.277213545837924]
  Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. In this work, we consider the time-series data as a random realization from a nonlinear state-space model. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings.
  arXiv  Detail & Related papers  (2021-06-10T21:49:23Z)
• Improving Uncertainty Calibration via Prior Augmented Data [56.88185136509654]
  Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. They are often overconfident in their predictions, which leads to inaccurate and miscalibrated probabilistic predictions. We propose a solution by seeking out regions of feature space where the model is unjustifiably overconfident, and conditionally raising the entropy of those predictions towards that of the prior distribution of the labels.
  arXiv  Detail & Related papers  (2021-02-22T07:02:37Z)
• 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)

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.