How to Develop an Intuition for Probability With Worked Examples

How to Develop an Intuition for Probability With Worked Examples

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 […]

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Probabilistic Model Selection Measures AIC, BIC, and MDL

How to Develop an Intuition for Joint, Marginal, and Conditional Probability

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 […]

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A Gentle Introduction to Joint, Marginal, and Conditional Probability

A Gentle Introduction to Joint, Marginal, and Conditional Probability

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 […]

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Histogram and Probability Density Function Plot Estimated via Kernel Density Estimation for a Bimodal Data Sample

A Gentle Introduction to Probability Density Estimation

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 […]

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Line Plot of Events vs Probability or the Probability Density Function for the Normal Distribution

Continuous Probability Distributions for Machine Learning

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 […]

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Discrete Probability Distributions for Machine Learning

Discrete Probability Distributions for Machine Learning

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 […]

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A Gentle Introduction to Probability Distributions

A Gentle Introduction to Probability Distributions

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 […]

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What Is Probability?

What Is Probability?

Uncertainty involves making decisions with incomplete information, and this is the way we generally operate in the world. Handling uncertainty is typically described using everyday words like chance, luck, and risk. Probability is a field of mathematics that gives us the language and tools to quantify the uncertainty of events and reason in a principled […]

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A Gentle Introduction to Uncertainty in Machine Learning

A Gentle Introduction to Uncertainty in Machine Learning

Applied machine learning requires managing uncertainty. There are many sources of uncertainty in a machine learning project, including variance in the specific data values, the sample of data collected from the domain, and in the imperfect nature of any models developed from such data. Managing the uncertainty that is inherent in machine learning for predictive […]

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