Uncertainty propagation through neural network bottleneck features

Any real world data will have some degree of uncertainty, coping with such uncertainty is one of the most important challenges faced by any Machine Learning system. Transforming the data in the high-dimensional space to a space of fewer dimensions has a long history as a method for data visualization, and for extracting key low dimensional features. Recently, the nonlinear dimensionality reduction methods, have shown surprising results. But propagating uncertainty of input data through such nonlinear transforms is a difficult and important problem. In this paper, we use a Gaussian approximation by unscented transform to propagate the uncertainty in input data through auto-encoders neural networks. Unscented transform is easier to implement than classic Monte-Carlo method and uses the same order of calculations as linearization. Moreover, we extract an approximate of uncertainty of bottleneck features. The performance of the proposed method is visualized graphically and also evaluated on a small speaker recognition task. The results indicate the effectiveness of our proposed method for propagating uncertainties of inputs through bottleneck features in the performance of classification task.