Mastering Forecasting Accuracy: A Probabilistic Approach Using VAEneu And CRPS

Neural Network 25/10/2024

3 main points
✔️ Development and proposal of a new probabilistic forecasting model, VAEneu, based on conditional variational autoencoders.
✔️ Introduction of a method that simultaneously optimizes the sharpness and calibration of the predictive distribution by utilizing continuous-rank probability scores (CRPS).
✔️ Demonstrated remarkable forecasting performance on 12 different data sets and comparisons with baseline models, laying the groundwork for further improvements and expanded applicability of probabilistic forecasting models in the future.

VAEneu: A New Avenue for VAE Application on Probabilistic Forecasting
written by Alireza Koochali, Ensiye Tahaei, Andreas Dengel, Sheraz Ahmed
(Submitted on 7 May 2024)
Comments: Published on arxiv.
Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

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The images used in this article are from the paper, the introductory slides, or were created based on them.

Summary

The world of probabilistic forecasting is undergoing a new revolution thanks to the latest research. This article takes a deep dive into VAEneu, a breakthrough in probabilistic forecasting, which is based on the Conditional Variational Autoencoder (CVAE) and has been proposed as a powerful tool to quantify future uncertainty. In particular, it uses the Continuous Rank Probability Score (CRPS) as a loss function to learn an acute and well-tuned precession distribution.

This technology further improves the accuracy and utility of probabilistic forecasting, especially in decision making in areas such as medicine, weather forecasting, and risk assessment, where accurate risk assessment is of critical importance. Through a comprehensive empirical study, VAEneu's superior forecasting performance was rigorously evaluated using 12 baseline models and 12 datasets. Let's take a closer look at the details of how this advanced model works.

Related Research

Research related to the development of VAEneu is closely related to the recent evolution of neural networks and their impact on probabilistic forecasting. In particular, architectures such as recurrent neural networks (RNNs), long short-term memory (LSTM), and gated recurrent units (GRUs) have proven capable of effectively processing time series data. In addition, WaveNet, which uses convolutional neural networks (CNNs), and Transformer, which incorporates a self-attention mechanism, represent innovative advances in this area.

Recently, new approaches to modeling predictive distributions using generative inverse networks (GANs) have emerged, allowing optimal scenarios to generate samples from real data distributions. However, the instability of adversarial objective functions makes training these networks challenging, and VAEneu has successfully overcome these challenges to learn sharp and well-tuned predictive distributions using CRPS.

This research also proposes new directions for models for probabilistic forecasting that do not rely on traditional probability distribution modeling, in particular, MQ-RNN, MQ-CNN, and Prophet as methods for modeling quantum prediction and important properties of predictive distributions. These models provide a quantum of probability distribution for prediction and aim to improve the accuracy and interpretability of probabilistic predictions.

Overall, these related studies have focused on the development of different methods and models to improve the accuracy of probabilistic forecasting, and VAEneu is a model that builds on this progress. It is hoped that this will open up new possibilities in the field of probabilistic forecasting.

Proposed Method

In this study, a new method for probabilistic forecasting, VAEneu, is proposed. The model is based on the conditional variational autoencoder (CVAE) and uses the continuous rank probability score (CRPS) as a loss function. The approach aims to learn more perceptive and calibrated forecast distributions.

Model Details (Figure 1)

VAEneu generates future data distributions conditional on past data in probabilistic forecasting of time series data. The modeluses theinput data ( _x0: t )as a condition and outputs the future data points (x _t+1) to be predicted. The encoder maps the input data to a latent variable z, which the decoder uses to form the predictive distribution.

Learning with CRPS

The CRPS is utilized as a loss function in training the model and is optimized so that the predictive distribution matches the true data distribution. Specifically, CRPS is used to shape the predictive distribution more closely to the true distribution and to improve the accuracy of the prediction (see Equations 6 and 7).

Implementation and Training (Figure 1)

The ability to understand the internal patterns of time series data is important for VAEneu to predict future data points based on past data. In the implementation, an encoder and decoder are designed to capture features of time-series data using a TCN (temporal convolutional network) or RNN (recurrent neural network). This structure provides the foundation for extracting higher-order features from the input data and making effective predictions.

Advantages of the Proposed Method

A major advantage of VAEneu over conventional methods is that it provides a better balance between the sharpness and calibration of the predictive distribution. In addition, the use of CRPS as a loss function improves forecasting performance by allowing the model to be better trained to fit real-world data distributions. This is expected to result in more reliable forecasts in a variety of practical scenarios.

Experiment

Extensive experiments with 12 different probabilistic forecasting models and 12 different datasets were conducted to validate VAEneu's performance. These datasets ranged from everyday life to scientific research. The main objective is to compare the accuracy of the predictions provided by VAEneu with other models.

Experimental Data Set

Datasets used include gold prices, household electricity consumption (HEPC), Internet traffic, mucky grass, Sogen River flow, sunspot numbers, US births, solar and wind power, and more. These data sets are collected at different frequencies and lengths, making them suitable for evaluating how well the model can adapt to different types of time series data.

Comparison with Baseline Model

Experiments compared VAEneu to existing probabilistic predictive models such as DeepAR, DeepState, DeepFactor, DRP, GPForecaster, MQ-RNN, MQ-CNN, Prophet, Wavenet, Transformer, TFT, and ForGAN. Through comparison with these models, the relative performance of VAEneu is evaluated.

Performance Evaluation (Table 1)

Model performance was quantitatively evaluated using the Continuous Rank Probability Score (CRPS), a measure of the accuracy of the predictive distribution, and the experiments show how accurately VAEneu predicts future data in each data set.In particular, Figure 4 shows the relative distribution of the model's CRPS across all data sets, which shows that VAEneu consistently performs well.

VAEneu is the best model or performs very close to the top model on many data sets. This demonstrates VAEneu's potential to become the new standard in the field of probabilistic forecasting. Its forecasting accuracy and consistency also represents an important advance, especially in areas where uncertainty needs to be accurately modeled.

Conclusion

The VAEneu model proposed in this study is based on a conditional variational autoencoder and uses CRPS as a loss function to provide perceptive and well-tuned probabilistic predictions. Through extensive experimentation, VAEneu has demonstrated its superior performance compared to 12 baseline models across 12 different data sets. The model has the potential to contribute to decision support, especially in areas where risk assessment and resource allocation are critical.

Future Outlook

Based on the success of VAEneu, the approach could be extended to more data types and forecast scenarios in the future. It would also be beneficial to explore different types of loss functions and optimization techniques to broaden the applicability of the model. In addition, implementing real-time stochastic forecasting and incorporating online learning capabilities to maintain its performance in dynamically changing environments are important research topics.

The application of VAEneu's approach to other machine learning models and algorithms is also expected to further improve the accuracy of forecasts. New research and improvements based on this model could make important contributions to the evolution of future forecasting techniques. In particular, the development of new algorithms to improve the accuracy of forecasts in areas of high uncertainty will be the next major step.