Last Updated on November 14, 2019 Probability can be used for more than calculating the likelihood of one event; it can summarize the likelihood of all possible outcomes. A thing of interest in probability is called a random variable, and the relationship between each possible outcome for a random variable and their probabilities is called a probability distribution. Probability distributions are an important foundational concept in probability and the names and shapes of common probability distributions will be familiar. The […]

Last Updated on February 10, 2020 The probability for a discrete random variable can be summarized with a discrete probability distribution. Discrete probability distributions are used in machine learning, most notably in the modeling of binary and multi-class classification problems, but also in evaluating the performance for binary classification models, such as the calculation of confidence intervals, and in the modeling of the distribution of words in text for natural language processing. Knowledge of discrete probability distributions is also required […]

Last Updated on September 25, 2019 The probability for a continuous random variable can be summarized with a continuous probability distribution. Continuous probability distributions are encountered in machine learning, most notably in the distribution of numerical input and output variables for models and in the distribution of errors made by models. Knowledge of the normal continuous probability distribution is also required more generally in the density and parameter estimation performed by many machine learning models. As such, continuous probability distributions […]

Last Updated on July 24, 2020 Probability density is the relationship between observations and their probability. Some outcomes of a random variable will have low probability density and other outcomes will have a high probability density. The overall shape of the probability density is referred to as a probability distribution, and the calculation of probabilities for specific outcomes of a random variable is performed by a probability density function, or PDF for short. It is useful to know the probability […]

Last Updated on May 6, 2020 Probability quantifies the uncertainty of the outcomes of a random variable. It is relatively easy to understand and compute the probability for a single variable. Nevertheless, in machine learning, we often have many random variables that interact in often complex and unknown ways. There are specific techniques that can be used to quantify the probability for multiple random variables, such as the joint, marginal, and conditional probability. These techniques provide the basis for a […]

Last Updated on December 6, 2019 Probability for a single random variable is straight forward, although it can become complicated when considering two or more variables. With just two variables, we may be interested in the probability of two simultaneous events, called joint probability: the probability of one event given the occurrence of another event called the conditional probability, or just the probability of an event regardless of other variables, called the marginal probability. These types of probability are easy […]

Last Updated on November 1, 2019 Probability calculations are frustratingly unintuitive. Our brains are too eager to take shortcuts and get the wrong answer, instead of thinking through a problem and calculating the probability correctly. To make this issue obvious and aid in developing intuition, it can be useful to work through classical problems from applied probability. These problems, such as the birthday problem, boy or girl problem, and the Monty Hall problem trick us with the incorrect intuitive answer […]

Last Updated on January 10, 2020 Probability for Machine Learning Crash Course.Get on top of the probability used in machine learning in 7 days. Probability is a field of mathematics that is universally agreed to be the bedrock for machine learning. Although probability is a large field with many esoteric theories and findings, the nuts and bolts, tools and notations taken from the field are required for machine learning practitioners. With a solid foundation of what probability is, it is […]

Last Updated on December 4, 2019 Bayes Theorem provides a principled way for calculating a conditional probability. It is a deceptively simple calculation, although it can be used to easily calculate the conditional probability of events where intuition often fails. Although it is a powerful tool in the field of probability, Bayes Theorem is also widely used in the field of machine learning. Including its use in a probability framework for fitting a model to a training dataset, referred to […]

Last Updated on January 10, 2020 Classification is a predictive modeling problem that involves assigning a label to a given input data sample. The problem of classification predictive modeling can be framed as calculating the conditional probability of a class label given a data sample. Bayes Theorem provides a principled way for calculating this conditional probability, although in practice requires an enormous number of samples (very large-sized dataset) and is computationally expensive. Instead, the calculation of Bayes Theorem can be […]