  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.
