The rsample package is used to create splits and folds from your data. Here I use initial_split() to create a testing and training dataset. The resulting object is called an rsplit object and contains the original data and information about whether a record goes to testing or training. This object is not a flat dataframe but rather a nested list. The functions testing() and training() are used to create the appropriate tibbles for fitting.

In recent years, deep-learning-based approaches have been introduced to solving time-series forecasting-related problems. These novel methods have demonstrated impressive performance in univariate and low-dimensional multivariate time-series forecasting tasks. However, when these novel methods are used to handle high-dimensional multivariate forecasting problems, their performance is highly restricted by a practical training time and a reasonable GPU memory configuration. In this paper, inspired by a change of basis in the Hilbert space, we propose a flexible data feature extraction technique that excels in high-dimensional multivariate forecasting tasks. Our approach was originally developed for the National Science Foundation (NSF) Algorithms for Threat Detection (ATD) 2022 Challenge. Implemented using the attention mechanism and Convolutional Neural Networks (CNN) architecture, our method demonstrates great performance and compatibility. Our models trained on the GDELT Dataset finished 1st and 2nd places in the ATD sprint series and hold promise for other datasets for time series forecasting.

The debate on AI ethics largely focuses on technical improve ments and stronger regulation to prevent accidents or misuse of AI, with soluti ons relying on holding individual actors accountable for responsible AI devel opment. While useful and necessary, we argue that this "agency" approach disrega rds more indirect and complex risks resulting from AI's interaction with the soci o-economic and political context. This paper calls for a "structural" approach to assessing AI's effects in order to understand and prevent such systemic risks where no individual can be held accountable for the broader negative impacts. This i s particularly relevant for AI applied to systemic issues such as climate change and f ood security which require political solutions and global cooperation. To pro perly address the wide range of AI risks and ensure'AI for social good', agency-foc used policies must be complemented by policies informed by a structural approa ch.

We consider the question of learning in general topological vector spaces. By exploiting known (or parametrized) covariance structures, our Main Theorem demonstrates that any continuous linear map corresponds to a certain isomorphism of embedded Hilbert spaces. By inverting this isomorphism and extending continuously, we construct a version of the Ordinary Least Squares estimator in absolute generality. Our Gauss-Markov theorem demonstrates that OLS is a "best linear unbiased estimator", extending the classical result. We construct a stochastic version of the OLS estimator, which is a continuous disintegration exactly for the class of "uncorrelated implies independent" (UII) measures. As a consequence, Gaussian measures always exhibit continuous disintegrations through continuous linear maps, extending a theorem of the first author. Applying this framework to some problems in machine learning, we prove a useful representation theorem for covariance tensors, and show that OLS defines a good kriging predictor for vector-valued arrays on general index spaces. We also construct a support-vector machine classifier in this setting. We hope that our article shines light on some deeper connections between probability theory, statistics and machine learning, and may serve as a point of intersection for these three communities.