Preserving Seasonal and Trend Information: A Variational Autoencoder-Latent Space Arithmetic Based Approach for Non-stationary Learning

Abstract: AI models have garnered significant research attention towards predictive task automation. However, a stationary training environment is an underlying assumption for most models and such models simply do not work on non-stationary data since a stationary relationship is learned. The existing solutions propose making data stationary prior to model training and evaluation. This leads to loss of trend and seasonal patterns which are vital components for learning temporal dependencies of the system under study. This research aims to address this limitation by proposing a method for enforcing stationary behaviour within the latent space while preserving trend and seasonal information. The method deploys techniques including Differencing, Time-series decomposition, and Latent Space Arithmetic (LSA), to learn information vital for efficient approximation of trend and seasonal information which is then stored as embeddings within the latent space of a Variational Autoencoder (VAE). The approach's ability to preserve trend and seasonal information was evaluated on two time-series non-stationary datasets. For predictive performance evaluation, four deep learning models were trained on the latent vector representations of the datasets after application of the proposed method and all models produced competitive results in comparison with state-of-the-art techniques using RMSE as the performance metric.

Preserving Seasonal and Trend Information in Non-stationary Learning Through VAE-Latent Space Arithmetic

The aforementioned paper addresses a fundamental challenge in the domain of machine learning—specifically, the applicability of predictive models to non-stationary datasets. While most AI models are designed to function optimally under stationary conditions, real-world data often exhibit non-stationary characteristics due to underlying trends and seasonal variations. This discrepancy results in a loss of predictive accuracy when models trained on transformed stationary datasets encounter non-stationary patterns during deployment. The paper proposes a novel method to preserve the essential seasonal and trend information within non-stationary datasets by utilizing a Variational Autoencoder (VAE) combined with Latent Space Arithmetic (LSA).

The proposed approach comprises a two-phase methodology designed to preserve temporal dependencies within time-series data. Initially, the high-dimensional non-stationary datasets undergo time-series decomposition to isolate seasonal, trend, and residual components. In this setup, only the seasonal component is used to train the VAE, thereby capturing periodic patterns into the latent space embeddings. This latent space encoding within the VAE facilitates the preservation of trend and seasonal data which are crucial for robust temporal analysis.

Building upon this foundation, the second phase involves projecting the datasets onto a low-dimensional latent space using the VAE encoder. Thereafter, time-series decomposition is applied within the latent space to derive refined seasonal latent vectors by calculating distances to stored seasonal embeddings. Subtracting these seasonal embeddings from the data results in a residual-trend representation. The application of differencing further renders the data stationary, allowing the reconstruction of trend and seasonal components through LSA, where specific coefficients determine how much seasonal and trend information to retain.

The empirical evaluation of the methodology involved two non-stationary datasets: the DJIA dataset and the NIFTY-50 dataset. Across these datasets, the methodology was tested by using the Augmented Dickey-Fuller (ADF) test to verify the non-stationarity before and after the application of the proposed method. The results showcased substantial improvement in achieving stationarity within the latent space, as indicated by reduced p-values post-application of the approach, thereby corroborating the efficacy of the technique in preserving crucial temporal patterns.

Furthermore, the paper evaluated predictive performance by training four deep learning models: a standard Deep Neural Network (DNN), Long Short-Term Memory (LSTM), Bidirectional LSTM (BLSTM), and Gated Recurrent Units (GRU), on latent representations from the proposed VAE framework. The results indicate that the inclusion of trend and seasonal data significantly improves the models' predictive capabilities, reduced RMSE values were observed, emphasizing the importance of temporal component preservation.

The implications of this work are notable in that they offer a robust framework for enhancing the predictive accuracy of learning models on non-stationary data without sacrificing essential temporal information. Practically, this approach could be employed in various fields such as finance, climatology, and demand forecasting where trend and seasonal analysis are vital.

Looking ahead, future work could investigate extending this methodology to a broader range of time-series decomposition techniques and various non-linear transformation models within the latent space. Additionally, integrating this approach with real-time data analytics could significantly enhance its utility, enabling dynamic adjustments to predictive models in rapidly changing environments. Moreover, exploring integration with other deep learning architectures could potentially enhance the computational efficiency and scalability of the proposed solution.