Diego Porras

Fernando Martínez-García, Álvaro Rubio-García, Samuel Fernández-Lorenzo et al.

We introduce SA-FDR, a novel algorithm for $\ell_0$-norm feature selection that considers this task as a combinatorial optimisation problem and solves it by using simulated annealing to perform a global search over the space of feature subsets. The optimisation is guided by the Fisher discriminant ratio, which we use as a computationally efficient proxy for model quality in classification tasks. Our experiments, conducted on datasets with up to hundreds of thousands of samples and hundreds of features, demonstrate that SA-FDR consistently selects more compact feature subsets while achieving a high predictive accuracy. This ability to recover informative yet minimal sets of features stems from its capacity to capture inter-feature dependencies often missed by greedy optimisation approaches. As a result, SA-FDR provides a flexible and effective solution for designing interpretable models in high-dimensional settings, particularly when model sparsity, interpretability, and performance are crucial.

Samuel Fernández-Lorenzo, Diego Porras, Juan José García-Ripoll

Tracking a financial index boils down to replicating its trajectory of returns for a well-defined time span by investing in a weighted subset of the securities included in the benchmark. Picking the optimal combination of assets becomes a challenging NP-hard problem even for moderately large indices consisting of dozens or hundreds of assets, thereby requiring heuristic methods to find approximate solutions. Hybrid quantum-classical optimization with variational gate-based quantum circuits arises as a plausible method to improve performance of current schemes. In this work we introduce a heuristic pruning algorithm to find weighted combinations of assets subject to cardinality constraints. We further consider different strategies to respect such constraints and compare the performance of relevant quantum ansätze and classical optimizers through numerical simulations.