Variational Autoencoders for Missing Data Imputation with Application to a Simulated Milling Circuit

Missing data values and differing sampling rates, particularly for important parameters such as particle size and stream composition, are a common problem in minerals processing plants. Missing data imputation is used to avoid information loss (due to downsampling or discarding incomplete records). A recent deep-learning technique, variational autoencoders (VAEs), has been used for missing data imputation in image data, and was compared here to imputation by mean replacement and by principal component analysis (PCA) imputation. The techniques were compared using a synthetic, nonlinear dataset, and a simulated milling circuit dataset, which included process disturbances, measurement noise, and feedback control. Each dataset was corrupted with missing values in 20% of records (lightly corrupted) and in 90% of records (heavily corrupted). For both lightly and heavily corrupted datasets, the root mean squared error of prediction for VAE imputation was lower than the traditional methods. Possibilities for the extension of missing data imputation to inferential sensing are discussed.