Recent advances in differentiable structure learning have framed the combinatorial problem of learning directed acyclic graphs as a continuous optimization problem. Various aspects, including data standardization, have been studied to identify factors that influence the empirical performance of these methods. In this work, we investigate critical limitations in differentiable structure learning methods, focusing on settings where the true structure can be identified up to Markov equivalence classes, particularly in the linear Gaussian case. While recent work highlighted potential non-convexity issues in this setting, we demonstrate and explain why the use of L1-penalized likelihood in such cases is fundamentally inconsistent, even if the global optimum of the optimization problem can be found. To resolve this limitation, we develop a hybrid differentiable structure learning method based on L0-penalized likelihood with hard acyclicity constraint, where the L0 penalty can be approximated by different techniques including Gumbel-Softmax. Specifically, we first estimate the underlying moral graph, and use it to restrict the search space of the optimization problem, which helps alleviate the non-convexity issue. Experimental results show that the proposed method enhances empirical performance both before and after data standardization, providing a more reliable path for future advancements in differentiable structure learning, especially for learning Markov equivalence classes.

Abstract Crowdfunding plays a key role in financial technology to provide individuals and enterprises with funding opportunities to establish start-ups and/or new business ventures. It is mainly used to link projects’ creators and backers, collect money and plan fundraising projects via social networks. This paper proposes a machine learning-enabled approach to analyse Kickstarter numerical and textual data and predict the successful funding and delivery of crowdfunding projects. It offers crowdfunding stakeholders benefits including creator credibility assessment, project risk reduction, and backer confidence enhancement. This research proposes a data preprocessing approach to prepare the dataset and extract the relevant features for the predictions. Besides, it trains and compares five numerical machine learning classification models and three text-mining methods to find the best-fitted numerical and textual analysis approaches. According to the results, the proposed SVM model outperforms the numerical benchmarks in terms of Accuracy, Precision, Recall, F1 score, and model Training latency. Moreover, BERT gives the best results if the dataset is complex, while Word2vec works better with simple features in textual analysis.