Mathematics and Machine learning

As Arthur C. Clarke says, “any sufficiently advanced technology is indistinguishable from magic.” 

Two decades ago, machine learning(ML) would have been considered nothing less than magic. But, with the advent of big data and an increase in computing power along with storage capacity, ML has come a long way and brought the “magic” to everyone’s hand. Mathematics(statistics, algebra, calculus, matrix, and much more) forms the basis of the simple[yet complicated enough to give one nightmare] ML algorithms. While ML forms a tiny part of what continues to grow into the most mind-bending development of the current time- Artificial Intelligence[in short, a technique used to help machines mimic human behavior.] There lies a great surprise in knowing how some naïve concepts from Mathematics such as Bayes’ Theorem come in handy while explaining seemingly not so evident facts. 

 Consider a medical test result. Say that you are worried that you have a rare disease experienced by 1 percent of the population. You take the test, and the results are positive. Medical tests are never perfectly accurate, and the laboratory tells you that the test is positive in 99 percent of the cases when you are ill. In contrast, when you are healthy, the test will be negative in 99 percent of the cases. Now, using these figures, you immediately believe that you are undoubtedly ill, given the high percentage of positive tests when a person is ill (99 percent). However, the reality is quite different. In this case, the figures to plug into the Bayes’ theorem are as follows:

 Probability of getting diagnosed with the disease given you are actually ill: P(E|B) = 0.99 

Probability of being actually ill: P(B) = 0.01

Probability of getting diagnosed with the disease: P(E) = 0.01 * 0.99 + 0.99 *0.01 = 0.0198

 Using the general framework for Bayes’ formula : P(B|E) = P(E|B)*P(B) / P(E). 

We get that P(B|E), i.e., the probability of actually having the disease given you are diagnosed ill = 0.50.

Only 50%. Your chances of not being ill are more than you expected.

Is not this amazing!! Mathematics just relieved you of a lot of pain. :)

This is generally referred to as "Conditional probabilities" and this forms a very powerful tool for machine learning. Knowing the possible circumstances can boost your chances of correctly predicting an event by observing examples — exactly what machine learning is intended to do. In fact, the Naïve Bayes algorithm can really take advantage of boosting the chance of making a correct prediction by knowing the circumstances surrounding the prediction.