The impact of missing data on quantitative research can be serious,
leading to biased estimates of parameters, loss of information, increased
standard errors, weakened generalizability etc.
In this paper, we discuss and apply to a real-world data set a regression-
based data imputation method when data is a sequence (time series) of
multidimensional measurements

Computational models are central and data based modeling has become increasingly important over the last years. Sufficient amount of data has to be collected to build accurate data based models. Data collection can be time and labor intensive and sometimes even safety critical. Safe Active Learning is a sequential experimental design that selects highly informative measurements and learns to cope with safety considerations on the fly. This presentation will show the mathematical core of the algorithm as well as its impact on automation of data collection.

This contribution is based on previous publications.

We present a new method for combining (or aggregating or ensembling) multivariate probabilistic forecasts, considering dependencies between quantiles and marginals through a smoothing procedure that allows for online learning. We discuss two smoothing methods: dimensionality reduction using Basis matrices and penalized smoothing. The new online learning algorithm generalizes the standard CRPS learning framework into multivariate dimensions. It is based on Bernstein Online Aggregation (BOA) and yields optimal asymptotic learning properties. The procedure uses horizontal aggregation, i.e., aggregation across quantiles. We provide an in-depth discussion on possible extensions of the algorithm and several nested cases related to the existing literature on online forecast combination. We apply the proposed methodology to forecasting day-ahead electricity prices, which are 24-dimensional distributional forecasts. The proposed method yields significant improvements over uniform combination in terms of continuous ranked probability score (CRPS). We discuss the temporal evolution of the weights and hyperparameters and present the results of reduced versions of the preferred model. A fast C++ implementation of the proposed algorithm will be made available in connection with this contribution as an open-source R-Package on CRAN.

References: Berrisch, J., & Ziel, F. (2023). CRPS learning. Journal of Econometrics, 237(2), 105221.

Semi-structured regression (SSR) jointly learn interpretable structured effects of tabular data and additional unstructured effects modeled through a (deep) neural network. These two parts are embedded and trained together in one unifying network architecture. The structured part allows for an interpretation as in common statistical regression models whereas the remaining variation in the data can be explained by the more powerful (unstructured) neural network part. SSR also open up new ways of modeling multi-modal data, e.g., datasets with both tabular and image information, while preserving statistical model characteristics typically relied on in various fields such as medical research or psychology. In order to correctly interpret a SSR, an orthogonalization operation is used. There also exist various ways to perform statistical inference for SSR. By embedding statistical models in neural networks, SSR can be implemented in a generic software framework that leverages the full modularity of current deep learning platforms while also enabling many different statistical model specifications. This further allows classic statistical models themselves to be more flexible and scalable.

A method to forecast the demand and flexibility level of consumers of electricity is presented. The price-response model is defined by an optimization program whose defining parameters are represented by time series of prices, and minimum and maximum load flexibility levels. These parameters are, in turn, estimated from observational data by exploiting an approach based on duality theory. The proposed methodology is data-driven and exploits information from covariates via Kernel regression functions, such as price, and weather variables, to account the non-linearity for changes in the parameter estimates. The resulting estimation problem is a tractable mixed-integer linear program. Furthermore, we include a regularization term that is statistically adjusted by cross-validation and the estimated model is used to forecast the demand of customers and the flexibility level in a real dataset.