# Last layer state space model for representation learning and uncertainty quantification

arXiv: https://arxiv.org/abs/2307.01566 · HTML: https://mlsanity.com/paper/2307.01566/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 43 references that are in the map.
- First posted on arXiv 4 Jul 2023.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning](https://mlsanity.com/paper/2002.06470/) (2020)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](https://mlsanity.com/paper/1512.05287/) (2015)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Bayesian Uncertainty Estimation for Batch Normalized Deep Networks](https://mlsanity.com/paper/1802.06455/) (2018)
- [Deep and Confident Prediction for Time Series at Uber](https://mlsanity.com/paper/1709.01907/) (2017)
- [Bayesian Recurrent Neural Networks](https://mlsanity.com/paper/1704.02798/) (2017)
- [On Last-Layer Algorithms for Classification: Decoupling Representation from Uncertainty Estimation](https://mlsanity.com/paper/2001.08049/) (2020)
- [The Monte Carlo Transformer: a stochastic self-attention model for sequence prediction](https://mlsanity.com/paper/2007.08620/) (2020)
- [Backward importance sampling for online estimation of state space models](https://mlsanity.com/paper/2002.05438/) (2020)
- [Variational latent discrete representation for time series modelling](https://mlsanity.com/paper/2306.15282/) (2023)

## Abstract (arXiv)

As sequential neural architectures become deeper and more complex, uncertainty estimation is more and more challenging. Efforts in quantifying uncertainty often rely on specific training procedures, and bear additional computational costs due to the dimensionality of such models. In this paper, we propose to decompose a classification or regression task in two steps: a representation learning stage to learn low-dimensional states, and a state space model for uncertainty estimation. This approach allows to separate representation learning and design of generative models. We demonstrate how predictive distributions can be estimated on top of an existing and trained neural network, by adding a state space-based last layer whose parameters are estimated with Sequential Monte Carlo methods. We apply our proposed methodology to the hourly estimation of Electricity Transformer Oil temperature, a publicly benchmarked dataset. Our model accounts for the noisy data structure, due to unknown or unavailable variables, and is able to provide confidence intervals on predictions.