Accurate time series forecasting is critical for a wide range of problems with temporal data. Ensemble modeling is a well-established technique for leveraging multiple predictive models to increase accuracy and robustness, as the performance of a single predictor can be highly variable due to shifts in the underlying data distribution. This paper proposes a new methodology for building robust ensembles of time series forecasting models. Our approach utilizes Adaptive Robust Optimization (ARO) to construct a linear regression ensemble in which the models' weights can adapt over time. We demonstrate the effectiveness of our method through a series of synthetic experiments and real-world applications, including air pollution management, energy consumption forecasting, and tropical cyclone intensity forecasting. Our results show that our adaptive ensembles outperform the best ensemble member in hindsight by 16-26% in root mean square error and 14-28% in conditional value at risk and improve over competitive ensemble techniques.

Adaptive Ridge is a special form of Ridge regression, balancing the quadratic penalization on each parameter of the model. It was shown to be equivalent to Lasso (least absolute shrinkage and selection operator), in the sense that both procedures produce the same estimate. Lasso can thus be viewed as a particular quadratic penalizer. From this observation, we derive a fixed point algorithm to compute the Lasso solution. The analogy provides also a new hyper-parameter for tun(cid:173) ing effectively the model complexity. We finally present a series ofpossi(cid:173) ble extensions oflasso performing sparse regression in kernel smoothing, additive modeling and neural net training.

In supervised learning, we have a set of explicative variables x from which we wish to predict a response variable y.

In supervised learning, we have a set of explicative variables x from which we wish to predict a response variable y.

In supervised learning, we have a set of explicative variables x from which we wish to predict aresponse variable y.