In selecting important features from complex datasets, a key challenge is balancing the control of false positives with the power to make new discoveries. Current methods are often overly cautious, leading to fewer findings than desired. We introduce a machine learning-driven improvement to the T-Rex Selector, a current state of the art variable selector for high dimensional data, that closes this gap. Our technique uses a neural network, trained entirely on simulated data, to more accurately predict the proportion of false discoveries. This allows our procedure to operate much closer to the target error rate, significantly boosting its ability to identify true variables while maintaining reliable error control. Through extensive simulations, including a challenging synthetic genomics study, we demonstrate that our method outperforms existing approaches in detecting genuine features.

In recent years, generative deep learning techniques have seen widespread use, particularly in image and text generation. These methods have also shown promise in generating time series data, even in continuous domains. However, they struggle to capture certain probability distributions, such as the heavy-tailed distributions commonly observed in financial asset returns. This limitation arises from the Lipschitz continuity of the generator neural networks, which prevents the generation of distributions with heavier tails than the prior noise used in these methods. Simply using a heavier prior noise leads to stability and extrapolation issues. To address this challenge, our work proposes a novel approach. We reduce time series training data to the parameter space of a heavy-tailed cumulative distribution function, where the parameters evolve over time. Deep learning techniques are then employed to generate this parameter evolution, leveraging the more favourable probability distribution of the transformed data. Finally, time series on the sample space are generated by inversely transforming the parameter space using the quantile function, resulting in a more accurate modelling of the tail distribution.