Archive | Probability

A Gentle Introduction to Maximum Likelihood Estimation for Linear Regression

A Gentle Introduction to Linear Regression With Maximum Likelihood Estimation

Linear regression is a classical model for predicting a numerical quantity. The parameters of a linear regression model can be estimated using a least squares procedure or by a maximum likelihood estimation procedure. Maximum likelihood estimation is a probabilistic framework for automatically finding the probability distribution and parameters that best describe the observed data. Supervised […]

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A Gentle Introduction to Maximum Likelihood Estimation for Machine Learning

A Gentle Introduction to Maximum Likelihood Estimation for Machine Learning

Density estimation is the problem of estimating the probability distribution for a sample of observations from a problem domain. There are many techniques for solving density estimation, although a common framework used throughout the field of machine learning is maximum likelihood estimation. Maximum likelihood estimation involves defining a likelihood function for calculating the conditional probability […]

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Line Plot of Probability Distribution vs Cross-Entropy for a Binary Classification Task With Extreme Case Removed

A Gentle Introduction to Cross-Entropy for Machine Learning

Cross-entropy is commonly used in machine learning as a loss function. Cross-entropy is a measure from the field of information theory, building upon entropy and generally calculating the difference between two probability distributions. It is closely related to but is different from KL divergence that calculates the relative entropy between two probability distributions, whereas cross-entropy […]

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Histogram of Two Different Probability Distributions for the Same Random Variable

How to Calculate the KL Divergence for Machine Learning

It is often desirable to quantify the difference between probability distributions for a given random variable. This occurs frequently in machine learning, when we may be interested in calculating the difference between an actual and observed probability distribution. This can be achieved using techniques from information theory, such as the Kullback-Leibler Divergence (KL divergence), or […]

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Plot of Probability Distribution vs Entropy

A Gentle Introduction to Information Entropy

Information theory is a subfield of mathematics concerned with transmitting data across a noisy channel. A cornerstone of information theory is the idea of quantifying how much information there is in a message. More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated […]

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A Gentle Introduction to Bayesian Belief Networks

A Gentle Introduction to Bayesian Belief Networks

Probabilistic models can define relationships between variables and be used to calculate probabilities. For example, fully conditional models may require an enormous amount of data to cover all possible cases, and probabilities may be intractable to calculate in practice. Simplifying assumptions such as the conditional independence of all random variables can be effective, such as […]

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How to Develop a Naive Bayes Classifier from Scratch in Python

How to Develop a Naive Bayes Classifier from Scratch in Python

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 […]

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