Deep Learning and Machine Learning
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Simply put, a computer makes a guess as to how a problem might be solved to get a desired answer from some input values. The computer checks to see if the answer is, in fact, correct and if not, changes are made to the equations that the computer is using to determine the answer from the inputs. The process continues until the computer can reliably obtain the correct answer.
The trick lies in the method whereby the equations are corrected little by little over time. If the computer is allowed to make enough guesses it will be able to figure out how to compute the answer from the input.
There is a YouTube channel called Welch Labs that has a good series of videos explaining how a very simple implementation of machine learning would work. I also recall that MIT has some math lectures on YouTube that explain the basic mathematical approaches. The math at the heart of these processes is relatively approachable.
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