Math
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Introduction

Lesson 1 Chapter 1

Probability theory is the branch of mathematics involved with probability. The notion of probability is used to measure the level of uncertainty. Probability theory aims to represent uncertain phenomena in terms of a set of axioms. Long story short, when we cannot be exact about the possible outcomes of a system, we try to represent the situation using the likelihood of different outcomes and scenarios.

The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the calculus
of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man’s mind.

James Clerk Maxwell

The probability theory is of great importance in many different branches of science. Let's focus on Artificial Intelligence empowered by Machine Learning. The question is, "how knowing probability is going to help us in Artificial Intelligence?" In AI applications, we aim to design an intelligent machine to do the task. First, the model should get a sense of the environment via modeling. As there is ambiguity regarding the possible outcomes, the model works based on estimation and approximation, which are done via probability. Second, as the machine tries to learn from the data (environment), it must reason about the process of learning and decision making. Such reasoning is not possible without considering all possible states, scenarios, and their likelihood. Third, to measure and assess the machine capabilities, we must utilize probability theory as well.

In this course, the goal is to provide sufficient background in probability theory so a practitioner has no problem following the Machine Learning concepts that requires an understanding of the probability. In case you are interested to know more about the probability, I recommend checking the associated references [1, 2, 3].

References

[1] Jaynes, Edwin T. Probability theory: The logic of science. Cambridge university press, 2003.

[2] Feller, Willliam. An introduction to probability theory and its applications. Vol. 2. John Wiley & Sons, 2008.

[3] Sheldon, Ross. A first course in probability. Pearson Education India, 2002.

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