What probabilistic model represents a data set as a mixture of multiple Gaussian distributions?

The Gaussian mixture model (GMM) is a powerful probabilistic model that represents a data set as a mixture of multiple Gaussian distributions, also known as normal distributions. In practice, GMMs are utilized to capture data that are more complex than what can be described by a single Gaussian distribution. Each Gaussian in the mixture is defined by its mean and variance, and the overall model is characterized by a weighted sum of these Gaussian components.

The GMM approach is particularly useful for clustering tasks because it allows for the modeling of different subpopulations within the overall data set. It effectively enables the identification of distinct groups that may not be linearly separable, making it an essential tool in various applications such as image processing and speech recognition.

Other probabilistic models listed serve different purposes. A Gaussian process is used primarily for regression tasks and provides a distribution over functions rather than a mixture of distributions. A hidden Markov model models sequences of observable events generated by an underlying process, typically employed in time-series data and not specifically for independent data points represented by Gaussian distributions. The multivariate Gaussian model describes a single Gaussian distribution across multiple dimensions but does not encompass a mixture of different distributions.

Therefore, the Gaussian mixture model (GMM) is the correct choice as