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As sequential neural architectures become deeper and more complex,uncertainty estimation is more and more challenging. Efforts in quantifyinguncertainty often rely on specific training procedures, and bear additionalcomputational costs due to the dimensionality of such models. In this paper, wepropose to decompose a classification or regression task in two steps: arepresentation learning stage to learn low-dimensional states, and a statespace model for uncertainty estimation. This approach allows to separaterepresentation learning and design of generative models. We demonstrate howpredictive distributions can be estimated on top of an existing and trainedneural network, by adding a state space-based last layer whose parameters areestimated with Sequential Monte Carlo methods. We apply our proposedmethodology to the hourly estimation of Electricity Transformer Oiltemperature, a publicly benchmarked dataset. Our model accounts for the noisydata structure, due to unknown or unavailable variables, and is able to provideconfidence intervals on predictions.

Last layer state space model for representation learning and uncertainty quantification