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Considering industrial process with high-dimensional, intrinsic nonlinearities and possibly abnormal observations, a robust deep learning soft sensor model is developed under the just-in-time learning framework. As an unsupervised deep learning approach, Variational Autoencoder (VAE) has been successfully applied to soft sensing problems owing to its ability to describe the latent representations by probability distributions. In this work, to construct high performance soft sensor model, mutual information (MI) is first introduced for input variable selection. By further incorporating MI as weights on variable of the traditional VAE model, a MI-based output-relevant VAE is developed. For each new sample that arrives, by utilizing Symmetric Kullback-Leibler (SKL) divergence, its relevance with historical samples is determined. Based on the SKL divergence, the input samples that are most relevant to the query sample can be collected. The selected historical input samples and corresponding output samples are employed to build a Gaussian process regression (GPR) local model. Expectation maximation (EM) algorithm is utilized to deal with the nonlinearity and abnormal output observations in GPR local model simultaneously for robustness of the soft sensors. Numerical simulations and a benchmark process are employed to validate the effectiveness of the proposed soft sensor, which demonstrates its superior performance over traditional approaches. • A MI-based output-relevant VAE is presented by incorporating MI as weights on variable of the traditional VAE model. • The selected historical samples through SKL divergence are employed to build a GPR local model. • The abnormal output observations in GPR local model for robustness of the soft sensors is dealt with the EM algorithm. • Numerical simulations and a benchmark process are employed to validate the effectiveness of the proposed soft sensor. [ABSTRACT FROM AUTHOR]