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[D] Chances on getting into a ML PhD without engineering background

Hi, I have a unusual background and I am looking at getting into a PhD in machine learning. Do you think it is possible to get into a ML PhD without an engineering background? I studied business in my bachelor in Europe, and since it had a relatively decent amount of math I got into a master specialising in financial engineering. The master was particularly quantitative. I am now working as a trader, doing a mix of quant/non-quant trading. And some of it is ML-based. For the last 2 years I really got into ML, taking classes on my free time (Learning from Data, reading Deep Learning book and other ML books, and now the David Silver RL class). And I found it so interesting that I want to spend more time on it and do research. Given how competitive PhD applications are, do I stand any chances, since my background is not pure engineering? If yes, any advices on how to start?

Note: While I am interested in many applications, I would be interested to research RL in trading too and I guess my profile would fit nicely there. But unfortunately it is not a developed area of research so it is difficult to point myself in that direction during applications.

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