Density estimation is a statistical technique used to estimate the probability distribution of a dataset in order to understand the underlying patterns and characteristics of the data. It involves modeling the distribution of data points across the feature space to capture how likely different values or combinations of values are.
Density estimation is commonly used in various fields, including data analysis, machine learning, anomaly detection, and data visualization. The goal is to gain insights into the data distribution and potentially use it for various tasks such as generating new data, identifying outliers, or understanding the relationships between variables.
Example methods…
Histograms: Histograms divide the data range into intervals (bins) and count the number of data points falling into each interval. The height of each bin represents the density of data points.
Kernel Density Estimation (KDE): KDE smooths the histogram by placing a kernel (usually a Gaussian function) on each data point and then summing up these kernels.
Parzen Windows: Similar to KDE, Parzen windows involve placing windows (often Gaussian) around each data point and summing them to estimate the density at different points.
Mixture Models: Mixture models assume that the data is a mixture of multiple probability distributions, such as from multiple subpopulations. Gaussian Mixture Models (GMMs) are a common example.
Expectation-Maximization (EM): EM estimates parameters of mixture models, where the algorithm iteratively alternates between estimating the latent variables and updating the model parameters.