Homological Convolutional Neural Networks
This addresses the problem of improving deep learning for tabular data, which is often less effective than classic methods, by introducing a more interpretable and scalable approach.
The authors tackled the challenge of applying deep learning to tabular data by proposing a novel architecture that uses topologically constrained network representations to capture relational information from sparse inputs, achieving state-of-the-art performance on 18 benchmark datasets.
Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine learning approaches being often computationally cheaper and equally effective than increasingly complex deep learning architectures. The challenge arises from the fact that, in tabular data, the correlation among features is weaker than the one from spatial or semantic relationships in images or natural language, and the dependency structures need to be modeled without any prior information. In this work, we propose a novel deep learning architecture that exploits the data structural organization through topologically constrained network representations to gain relational information from sparse tabular inputs. The resulting model leverages the power of convolution and is centered on a limited number of concepts from network topology to guarantee: (i) a data-centric and deterministic building pipeline; (ii) a high level of interpretability over the inference process; and (iii) an adequate room for scalability. We test our model on 18 benchmark datasets against 5 classic machine learning and 3 deep learning models, demonstrating that our approach reaches state-of-the-art performances on these challenging datasets. The code to reproduce all our experiments is provided at https://github.com/FinancialComputingUCL/HomologicalCNN.