Understanding uncertainty and the likelihood of events.
Probability theory is the branch of mathematics concerned with quantifying uncertainty, and it's absolutely fundamental to machine learning. ML models are rarely 100% certain about their predictions; instead, they often output probabilities. For example, a classification model might predict that an email has a 95% probability of being spam. Understanding probability allows you to interpret and work with this uncertainty. Key concepts include basic probability rules, like the rules of addition and multiplication for events. Conditional probability, expressed through Bayes' Theorem, is particularly important. It allows us to update our beliefs about an event based on new evidence. This is the foundation of powerful classification algorithms like Naive Bayes. You'll also need to understand probability distributions, which describe the likelihood of different outcomes. Common distributions include the Gaussian (or Normal) distribution, which describes many natural phenomena, and the Bernoulli distribution, which describes events with two outcomes (like a coin flip). These distributions are used to model the data and the uncertainty in model parameters. Concepts like expected value and variance are also crucial for understanding the behavior of random variables. In essence, probability gives us a formal framework for reasoning about uncertainty, making it a cornerstone for building models that can make robust predictions in a world full of randomness and incomplete information.