Deep autoencoder for low dimensionality for high dimensional data in regression models and direct inverse analysis of models.

In constructing machine learning models between features X and output variables Y in molecular, material, and process designs, and process control, when the number of X is huge, models are likely to overfit, and it takes time to construct models. Deep autoencoder (DAE) was focused on, and reduction of dimensions in the huge number X with DAE was investigated. Spectral data, profile data, and time-series data were used to virtually generate data whose number of X was 10,000, 100,000, and 1,000,000. For each dataset, DAE model was constructed with training data, and then test data of X was reconstructed by transforming X into latent variables Z and Z into X, and then, it was confirmed that DAE could reconstruct X with high reproducibility regardless of the number of X in all the datasets. In addition, regression models were constructed with Gaussian mixture regression (GMR), which could perform direct inverse analysis of model, between Z and Y, and then, Y could be predicted accurately regardless of the number of X. It was confirmed that DAE could appropriately reduce the dimension even when X was as large as 1 million. Furthermore, by combining DAE with GMR, it became possible to directly predict X values from target Y values by calculating Z from Y with GMR and transforming Z into X with DAE.