Hello friend,

You really cannot master absolutely anything in the world. All you can do is be good at it, gradually get better than the rest with discipline and rigorous practice and then try to improve yourself further.

Machine learning is applied in almost every field of work today. It mainly involves statistical methodologies, some discrete math and co-ordinate geometry, some optimization/operational research concepts, some game theory concepts if you are into AI programming etc. But all these are just for the entry level problems that you can solve with machine learning. But I would suggest not to give too much stress on the subsidiary fields of study and only study an associated topic if the algorithm demands so. Learn as you go is the best strategy to follow.

These concepts are intuitive. Several weeks to understand what the the top 10 algorithms like k-means, svm, randomforests, linear regression , association rules do. Mind you, just understand the concepts and their usage.

For more detailed examples, coding in R /python, using libraries yourself or products like weka 2-3 months easily, depending on the depth to which you need to immerse yourself. Another 2-3 months to learn and practice using machine learning libraries with varying types, size of data. Especially if you are applying it to Big data.

This still does not take into account understanding the mathematics and statistics behind complicated algorithms. That takes considerably more time and experience, perhaps upto a year.

In sum, anywhere from a few days/weeks to a year depending on depth.

If you are totally dedicated for it than it doesn't depends on your backgroung you must go for it.