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This paper introduces a Variational Neural Stochastic Differential Equation (V-NSDE) model to capture complex and noisy time-series data, specifically socioeconomic factors across districts in Odisha, India. V-NSDE combines Neural SDEs for expressive dynamics with VAEs for generative capabilities, using an encoder to map initial observations and district embeddings to a latent Gaussian distribution that initializes the Neural SDE. Experiments demonstrate that V-NSDE effectively learns complex temporal patterns, capturing both trends and random fluctuations across different districts, as evidenced by improvements in the ELBO training loss.
Achieve realistic modeling of complex, noisy time-series data by combining Neural SDEs and VAEs, outperforming traditional methods in capturing both trends and random fluctuations.
This study examines the challenges of modeling complex and noisy data related to socioeconomic factors over time, with a focus on data from various districts in Odisha, India. Traditional time-series models struggle to capture both trends and variations together in this type of data. To tackle this, a Variational Neural Stochastic Differential Equation (V-NSDE) model is designed that combines the expressive dynamics of Neural SDEs with the generative capabilities of Variational Autoencoders (VAEs). This model uses an encoder and a decoder. The encoder takes the initial observations and district embeddings and translates them into a Gaussian distribution, which determines the mean and log-variance of the first latent state. Then the obtained latent state initiates the Neural SDE, which utilize neural networks to determine the drift and diffusion functions that govern continuous-time latent dynamics. These governing functions depend on the time index, latent state, and district embedding, which help the model learn the unique characteristics specific to each district. After that, using a probabilistic decoder, the observations are reconstructed from the latent trajectory. The decoder outputs a mean and log-variance for each time step, which follows the Gaussian likelihood. The Evidence Lower Bound (ELBO) training loss improves by adding a KL-divergence regularization term to the negative log-likelihood (nll). The obtained results demonstrate the effective learning of V-NSDE in recognizing complex patterns over time, yielding realistic outcomes that include clear trends and random fluctuations across different areas.