What type of machine learning are able to return feature importance?
You can calculate a feature importance for any classifier. Take a look at lime or shap
Shap unifies seven different methods (cited from the shap GitHub page):

1 LIME: Ribeiro, Marco Tulio, Sameer Singh, and Carlos Guestrin. &quot;Why should i trust you?: Explaining the predictions of any classifier.&quot; Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 2016.


2  Shapley sampling values: Strumbelj, Erik, and Igor Kononenko. &quot;Explaining prediction models and individual predictions with feature contributions.&quot; Knowledge and information systems 41.3 (2014): 647-665.


3  DeepLIFT: Shrikumar, Avanti, Peyton Greenside, and Anshul Kundaje. &quot;Learning important features through propagating activation differences.&quot; arXiv preprint arXiv:1704.02685 (2017).
4 QII: Datta, Anupam, Shayak Sen, and Yair Zick. &quot;Algorithmic transparency via quantitative input influence: Theory and experiments with learning systems.&quot; Security and Privacy (SP), 2016 IEEE Symposium on. IEEE, 2016.


5  Layer-wise relevance propagation: Bach, Sebastian, et al. &quot;On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation.&quot; PloS one 10.7 (2015): e0130140.


6  Shapley regression values: Lipovetsky, Stan, and Michael Conklin. &quot;Analysis of regression in game theory approach.&quot; Applied Stochastic Models in Business and Industry 17.4 (2001): 319-330.


7  Tree interpreter: Saabas, Ando. Interpreting random forests. http://blog.datadive.net/interpreting-random-forests/

Depending on the classification algorithm you could calculate the feature importance by using Gini or gain based methods, too ..