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The machine learning community often talks about over-fitting and other statistical issues. Are there any stats on how many models actually fail to reproduce good results after being deployed in actual use cases?

In many projects stakeholders might not even notice that deploying a ML model in fact hurt their business than whatever was used before. Or maybe the idea of marketing "Machine/Deep Learning or AI" as a companies flagship in itself helps get some more business (even if the intelligent part makes things worse).

In this regard, is there a paper that discusses how far applied machine learning has come?

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I don't think it would be possible to answer this question with respect to proprietary models used by private enterprise. But there is a vein of scholarship that focuses on flawed practices, such as in this paper.

Zachary C. Lipton, Jacob Steinhardt "Troubling Trends in Machine Learning Scholarship"

Collectively, machine learning (ML) researchers are engaged in the creation and dissemination of knowledge about data-driven algorithms. In a given paper, researchers might aspire to any subset of the following goals, among others: to theoretically characterize what is learnable, to obtain understanding through empirically rigorous experiments, or to build a working system that has high predictive accuracy. While determining which knowledge warrants inquiry may be subjective, once the topic is fixed, papers are most valuable to the community when they act in service of the reader, creating foundational knowledge and communicating as clearly as possible.

Recent progress in machine learning comes despite frequent departures from these ideals. In this paper, we focus on the following four patterns that appear to us to be trending in ML scholarship: (i) failure to distinguish between explanation and speculation; (ii) failure to identify the sources of empirical gains, e.g., emphasizing unnecessary modifications to neural architectures when gains actually stem from hyper-parameter tuning; (iii) mathiness: the use of mathematics that obfuscates or impresses rather than clarifies, e.g., by confusing technical and non-technical concepts; and (iv) misuse of language, e.g., by choosing terms of art with colloquial connotations or by overloading established technical terms. While the causes behind these patterns are uncertain, possibilities include the rapid expansion of the community, the consequent thinness of the reviewer pool, and the often-misaligned incentives between scholarship and short-term measures of success (e.g., bibliometrics, attention, and entrepreneurial opportunity). While each pattern offers a corresponding remedy (don't do it), we also discuss some speculative suggestions for how the community might combat these trends.

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