Machine learning of temporal data
A time series is a sequence of observations of the same variable, collected over time.
At IDSIA, we cover different research areas related to time series, such as forecasting, time series classification and anomaly detection. We are active both in methodological research with international publications and in applied projects with companies.

Forecasting is the problem of predicting how the time series will evolve in the future, estimating both the most probable development and its uncertainty. A few years ago, we developed an ad-hoc forecasting algorithm  (InnoSuisse project 14026: Board predictive analytics). Our algorithm was then included in the commercial software sold internationally by the company.
More recently, we published a novel algorithm based on Gaussian Processes, which obtains better results than the state-of-the-art competitors (including for instance Facebook’s Prophet) in a wide variety of problems. An important area of future research is the study of the relations between Gaussian Processes and deep neural networks, which are becoming an important method also in forecasting.
We also have expertise on the problem of hierarchical forecasting, which is common in business applications, for instance when it is required to forecast the sales of a certain product over a country and its sub-regions. We applied such techniques in project with major companies, from Big Pharma industries to Credit Card companies.
The problem of anomaly detection is to detect observations which are anomalous given the previous statistical patterns of the time series. We devised anomaly detection techniques in project with a world leader in the banking sector (aimed at detecting unusual financial transactions) and switch (aimed at detecting unusual patterns in the internet traffic).
The problem of time series classification is to assign an appropriate label to a given time series.  We predict the crop grown in each pixel of a certain area monitored via remote sensing, based on the images which are collected over time by the satellite (we extract for each pixel a sequence of signals over time, which constitute the time series).


  • Corani, G., Benavoli, A., Zaffalon, M. (2021). Time series forecasting with Gaussian Processes needs priors. Proc. European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 103–117.
  • Corani, G., Azzimonti, D., Augusto, J.P.S.C., Zaffalon, M. (2020). Probabilistic reconciliation of hierarchical forecast via Bayes’ rule. In Proceedings European Conference on Machine Learning and Knowledge Discovery in Databases pp 211-226
  • Benavoli, A., Corani, G. (2021). State Space approximation of Gaussian Processes for time-series forecasting. In Proc. Workshop on Advanced Analytics and Learning on Temporal Data, 6th ECML PKDD Workshop, AALTD 2021.