Gaussian Distribution Curve

Gaussian Distribution

In machine learning, the Gaussian distribution, is also known as the normal distribution. It is a continuous probability distribution function that is symmetrical at the mean, and the majority of data falls within one standard deviation of the mean. It is characterized by its bell-shaped curve....

Gaussian Distribution Curve

The curve is symmetric and bell-shaped, and it mathematically represents the probability distribution of a continuous random variable. The Gaussian distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ), which determine the location and the spread of the curve....

Gaussian Distribution Table

A Gaussian distribution table, also known as a standard normal distribution table or z-table, is a tabulated form that provides values of the cumulative distribution function (CDF) for the standard normal distribution. The standard normal distribution has a mean(central value) of 0 and a standard deviation of 1.Normally , the table consists of two columns namely Z-value and their Cumulative probability . Z-value is the number of standard deviations away from the mean. It ranges from negative infinity to positive infinity. Cumulative probability represents the probability that a standard normal random variable is less than or equal to the corresponding z-value....

Properties of Gaussian Distribution

Some of the important properties are...

Machine Learning Methods that uses Gaussian Distribution

Likelihood Modeling: In algorithms, such as linear regression, logistic regression, and Gaussian mixture models, it is often assumed that the observed data is generated from a Gaussian distribution. It simplifies the model and allows for efficient parameter estimation.Bayesian Inference: In Bayesian machine learning, the Gaussian distribution is commonly used as a prior distribution over model parameters. This prior distribution reflects about the parameters before observing any data and is updated to a posterior distribution using Bayes’ theorem.Clustering: Gaussian mixture models (GMMs) can model complex data distributions and are often used in image segmentation and data compression.Anomaly Detection: Gaussian distribution is often used in anomaly detection algorithms, where the goal is to identify rare events or outliers in the data. Anomalies are detected based on the likelihood of the data under the Gaussian distribution.Dimensionality Reduction: Principal Component Analysis (PCA), it finds the directions of maximum variance in the data, which correspond to the principal components.Kernel Methods: Gaussian kernel is commonly used in kernelized machine learning algorithms, such as Support Vector Machines (SVMs) and Gaussian Processes (GPs), to define the similarity between data points....

Implementation of Gaussian Distribution in Machine Learning

Consider the famous Iris dataset consists of 150 samples of iris flowers, each with four features: sepal length, sepal width, petal length, and petal width. We can examine the distribution of one of these features, such as sepal length, using a histogram to see if it approximately follows a Gaussian distribution....