Sparse Recurrent Mixture Density Network for Time Series Forecasting
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Solution Overview
Problem
Conventional time series prediction methods fail to accurately capture trend changes and high variability in high-dimensional data, particularly in applications like supply-chain management and load forecasting, and lack the ability to provide confidence estimates for forecasts.
Innovation Solution
The use of sparse recurrent mixture density networks (RMDN) that incorporate a feedforward layer with Lasso penalty for dimensionality reduction, a recurrent neural network (RNN) for temporal pattern capture, and a mixture of Gaussians for predicting time series parameters, including confidence estimates, to handle high-dimensional data and variability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional forecasting methods are used, then the model complexity is low, but the ability to capture trend changes and high variability in high-dimensional data is poor
Solution Approach 1:
The model segments the forecasting task into multiple components: a feedforward layer for feature extraction, an RNN component for temporal pattern capture, and a MDN component for distribution modeling. This segmentation allows each component to specialize in capturing specific aspects of trend changes and variability in high-dimensional data, thereby improving adaptability while managing complexity through modular design.
Solution Approach 2:
The patent combines multiple neural network architectures (feedforward networks, recurrent neural networks, and mixture density networks) into a composite hybrid model. This composite structure leverages the strengths of each component: feedforward layers for feature extraction, RNNs for temporal dependencies, and MDNs for modeling complex output distributions, enabling the system to capture both trend changes and high variability effectively.
2Loss of information
If high-dimensional time series data is used, then the information content increases, but the computational complexity and difficulty of processing increases
Solution Approach 1:
The feedforward layer extracts relevant features from high-dimensional time series data by transforming the input into a lower-dimensional latent representation. This extraction process selectively captures important information while discarding redundant dimensions, thereby retaining essential information content while reducing computational complexity for subsequent processing stages.
Solution Approach 2:
The model performs dimensionality transformation by mapping high-dimensional input data into a lower-dimensional latent space through the feedforward layer, while the RNN component then processes this transformed data across the temporal dimension. This dimensional change allows the system to handle high-dimensional data efficiently by operating in a compressed representation space.
3Reliability
If confidence estimates are added to forecasts, then the usefulness of the prediction increases, but the model complexity increases
Solution Approach 1:
The mixture density network component serves multiple functions simultaneously: it models the predictive distribution of the target variable, captures uncertainty through mixture components, and generates confidence estimates as a byproduct. This multi-functionality allows the model to provide both forecasts and confidence measures without requiring separate dedicated structures, thereby improving reliability while limiting the increase in complexity.
4Productivity
If dimensionality reduction is performed, then the processing efficiency improves, but the risk of losing important features increases
Solution Approach 1:
The model employs a differentiable loss function that provides feedback during training to guide the feedforward layer in preserving important features during dimensionality reduction. The loss function monitors the quality of predictions and adjusts the feature extraction process accordingly, ensuring that reduced dimensions retain the most informative features while improving processing efficiency.
Solution Approach 2:
The feedforward layer learns optimal transformation parameters through training, dynamically adjusting the dimensionality reduction mapping to preserve important features. By changing the parameters of the transformation function based on training data characteristics, the model adapts the reduction process to retain critical information while achieving efficient processing of high-dimensional data.
Data Source
AI summary
This disclosure relates generally to system and method for time series prediction using a sparse recurrent mixture density network (RMDN), such as sparse LSTM-MDN and a sparse ED-MDN, for accurate forecasting of a high variability time series. The disclosed sparse RMDN has the ability to handle high-dimensional input features, capture trend shifts and high variability present in the data, and provide a confidence estimate of the forecast. A high-dimensional time series data is passed through a feedforward layer, which performs dimensionality reduction in an unsupervised manner by inducing sparsity on weights of the feedforward layer. The resultant low-dimensional time series is fed through recurrent layers to capture temporal patterns. These recurrent layers also aid in learning latent representation of the input data. Thereafter, a mixture density network (MDN) is used to model the variability and trend shifts present in the input and it also estimates the confidence of the predictions.