# WTTE-RNN : Weibull Time To Event Recurrent Neural Network A model for sequential prediction of time-to-event in the case of discrete or continuous censored data, recurrent events or time-varying covariates

[Examensarbete på avancerad nivå]

In this thesis we propose a new model for predicting time to events: the Weibull Time To Event RNN. This is a simple framework for time-series prediction of the time to the next event applicable when we have any or all of the problems of continuous or discrete time, right censoring, recurrent events, temporal patterns, time varying covariates or time series of varying lengths. All these problems are frequently encountered in customer churn, remaining useful life, failure, spike-train and event prediction. The proposed model estimates the distribution of time to the next event as having a discrete or continuous Weibull distribution with parameters being the output of a recurrent neural network. The model is trained using a special objective function (log-likelihood-loss for censored data) commonly used in survival analysis. The Weibull distribution is simple enough to avoid sparsity and can easily be regularized to avoid overfitting but is still expressive enough to encode concepts like increasing, stationary or decreasing risk and can converge to a point-estimate if allowed. The predicted Weibull-parameters can be used to predict expected value and quantiles of the time to the next event. It also leads to a natural 2d-embedding of future risk which can be used for monitoring and exploratory analysis. We describe the WTTE-RNN using a general framework for censored data which can easily be extended with other distributions and adapted for multivariate prediction. We show that the common Proportional Hazards model and the Weibull Accelerated Failure time model are special cases of the WTTE-RNN. The proposed model is evaluated on simulated data with varying degrees of censoring and temporal resolution. We compared it to binary fixed window forecast models and naive ways of handling censored data. The model outperforms naive methods and is found to have many advantages and comparable performance to binary fixed-window RNNs without the need to specify window size and the ability to train on more data. Application to the CMAPSS-dataset for PHM-run-to-failure of simulated Jet-Engines gives promising results.

**Nyckelord: **Censored, censoring, Weibull, Waiting Time, Recurrent Neural Networks, churn, time varying covariates, failure, Machine Learning, Deep Learning.

Publikationen registrerades 2017-12-07. Den ändrades senast 2017-12-07

CPL ID: 253611

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