# Recursive input and state estimation: A general framework for learning from time series with missing data

arXiv: https://arxiv.org/abs/2104.08556 · HTML: https://mlsanity.com/paper/2104.08556/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 28 references that are in the map.
- First posted on arXiv 17 Apr 2021.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Time2Vec: Learning a Vector Representation of Time](https://mlsanity.com/paper/1907.05321/) (2019)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [Modeling Missing Data in Clinical Time Series with RNNs](https://mlsanity.com/paper/1606.04130/) (2016)
- [Embedding Multimodal Relational Data for Knowledge Base Completion](https://mlsanity.com/paper/1809.01341/) (2018)
- [Deep Multi-Output Forecasting: Learning to Accurately Predict Blood Glucose Trajectories](https://mlsanity.com/paper/1806.05357/) (2018)
- [Time-Dependent Representation for Neural Event Sequence Prediction](https://mlsanity.com/paper/1708.00065/) (2017)
- [A deep learning approach to diabetic blood glucose prediction](https://mlsanity.com/paper/1707.05828/) (2017)

## Abstract (arXiv)

Time series with missing data are signals encountered in important settings for machine learning. Some of the most successful prior approaches for modeling such time series are based on recurrent neural networks that transform the input and previous state to account for the missing observations, and then treat the transformed signal in a standard manner. In this paper, we introduce a single unifying framework, Recursive Input and State Estimation (RISE), for this general approach and reformulate existing models as specific instances of this framework. We then explore additional novel variations within the RISE framework to improve the performance of any instance. We exploit representation learning techniques to learn latent representations of the signals used by RISE instances. We discuss and develop various encoding techniques to learn latent signal representations. We benchmark instances of the framework with various encoding functions on three data imputation datasets, observing that RISE instances always benefit from encoders that learn representations for numerical values from the digits into which they can be decomposed.