GMM binary search refers to a binary search algorithm that is used to find an approximate solution to the Gaussian Mixture Model (GMM) problem.
A Gaussian Mixture Model is a probabilistic model that represents a probability distribution as a combination of multiple Gaussian distributions. The GMM problem involves estimating the parameters of these Gaussian components given a set of observed data points.
In GMM binary search, the goal is to find the optimal number of Gaussian components (also known as clusters) that best represent the underlying data distribution. This is done by iteratively applying a binary search algorithm to narrow down the range of possible cluster numbers.
The basic idea is as follows:
Start with an initial range of possible cluster numbers, such as [min_clusters, max_clusters]. Compute the GMM for the mid-point of the range, let's say mid_clusters = (min_clusters + max_clusters) / 2. Evaluate the quality of the GMM fit using a criterion such as the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC). If the quality of the fit is better than a threshold (e.g., AIC or BIC decreases), update the range to [min_clusters, mid_clusters - 1] and go to step 2. If the quality of the fit is not satisfactory (e.g., AIC or BIC increases), update the range to [mid_clusters + 1, max_clusters] and go to step 2. Repeat steps 2-5 until the range is narrowed down to a single cluster number or until a desired convergence criterion is met. The resulting cluster number at the end of the binary search is considered an approximate optimal solution to the GMM problem for the given data.