Gaussian mixture models (GMMs) are a type of machine learning algorithm. They are used to classify data into different categories based on the probability distribution. Gaussian mixture models can be used in many different areas, including finance, marketing and so much more! In this blog, an introduction to gaussian mixture models is provided along with real-world examples, what they do and when GMMs should be used.
What are Gaussian mixture models (GMM)?
The Gaussian mixture model is defined as a clustering algorithm that is used to discover the underlying groups of data. It can be understood as a probabilistic model where Gaussian distributions are assumed for each group and they have means and covariances which define their parameters. GMM consists of two parts – mean vectors (μ) & covariance matrices (Σ). A Gaussian distribution is defined as a continuous probability distribution that takes on a bell-shaped curve. Another name for Gaussian distribution is the normal distribution. Here is a picture of Gaussian mixture models:
What is expectation-maximization (EM) method in relation to GMM?
In Gaussian mixture models, expectation-maximization method is used to find the gaussian mixture model parameters. Expectation is termed as E and maximization is termed as M. Expectation is used to find the gaussian parameters which are used to represent each component of gaussian mixture models. Maximization is termed as M and it is involved in determining whether new data points can be added or not.
Expectation-maximization method is a two-step iterative algorithm that alternates between performing an expectation step, in which we compute expectations for each data point using current parameter estimates and then maximize these to produce new gaussian, followed by a maximization step where we update our gaussian means based on the maximum likelihood estimate. This iterative process is performed until the gaussians parameters converge. Here is a picture representing the two-step iterative aspect of algorithm:
What are the key steps of using Gaussian mixture models?
The following are three different steps to using gaussian mixture models:
- Determining a covariance matrix that defines how each Gaussian is related to one another. The more similar two Gaussians are, the closer their means will be and vice versa if they are far away from each other in terms of similarity. A gaussian mixture model can have a covariance matrix that is diagonal or symmetric.
- Determining the number of gaussians in each group defines how many clusters there are.
- Selecting the hyperparameters which define how to optimally separate data using gaussian mixture models as well as deciding on whether or not each gaussian’s covariance matrix is diagonal or symmetric.
What are the differences between Gaussian mixture models and other types of machine learning algorithms such as K-means, support vector machines (SVM)?
Gaussian mixture models are an unsupervised machine learning algorithm, while support vector machines (SVM) is a supervised learning algorithm. This means that gaussian mixture models can be used when there is no labeled data, however, the opposite requires labelled dataset for training the SVM models.
The Gaussian mixture model is different from K-means because Gaussian mixture models discover the underlying groups of data which is different than simply trying to divide data into different parts. Another difference is that Gaussian mixture models provide a probability for each category which can be used to make more accurate decisions and predictions about the data at hand. In addition, Gaussian mixture models have a higher chance of finding the right number of clusters in the data compared to k-means.
Gaussian mixture models have been found to outperform other machine learning algorithms such as artificial neural networks (ANN) when it comes to separating volatility from trend and noise.
What are the scenarios when gaussian mixture models can be used?
The following are different scenarios when GMMs can be used:
- In case of time series analysis, GMMs can be used tol discover how volatility is related to trend and noise which can help predict future stock prices. One cluster could consist of a trend in the time series while another can have noise and volatility from other factors such as seasonality or external events which affect the stock price. In order to separate out these clusters, GMMs can be used because they provide a probability for each category instead of simply dividing the data into two parts such as that in case of K-means.
- Another example is when there are different groups in a dataset and it’s hard to label them as belonging to one group or another which makes it difficult for other machine learning algorithms such as K-means clustering algorithm to separate out the data. GMMs can be used in this case because they find gaussian mixture models that best describe each group and provide a probability for each cluster which is helpful when labeling clusters.
- Another example where gaussian mixture model can be useful is when it is desired to discover underlying groups of categories such as types of cancer or risk factors associated with different types of cancer.
What are some real-world examples where Gaussian mixture models can be used?
There are many different real-world problems that can be solved with gaussian mixture models. Gaussian mixture models are very useful when there are large datasets and it is difficult to find clusters. This is where Gaussian mixture models help. It is able to find clusters of Gaussians more efficiently than other clustering algorithms such as k-means.
Here are some real-world problems which can be solved using Gaussian mixture models:
- Finding patterns in medical datasets: GMMs can be used for segmenting images into multiple categories based on their content or finding specific patterns in medical datasets.
- Modeling natural phenomena: GMM can be used to model natural phenomena where it has been found that noise follows gaussian distributions. This model of probabilistic modeling relies on the assumption that there exists some underlying continuum of unobserved entities or attributes and that each member is associated with measurements taken at equidistant points in multiple observation sessions.
- Customer behavior analysis: GMMs can be used for performing customer behavior analysis in marketing to make predictions about future purchases based on historical data.
- Stock price prediction: Another area Gaussian mixture models are used is in finance where they can be applied to a stock’s price time series. GMMs can be used to detect changepoints in time series data and help find turning points of stock prices or other market movements that are otherwise difficult to spot due to volatility and noise.
- Gene expression data analysis: Gaussian mixture models can be used for gene expression data analysis. In particular, GMMs can be used to detect differentially expressed genes between two conditions and identify which genes might contribute towards a certain phenotype or disease state.
Gaussian mixture models are a type of machine learning algorithm that is commonly used in data science. They can be applied to different scenarios, including when there are large datasets and it’s difficult to find clusters or groups of gaussians. Gaussian mixture models provide probability estimates for each cluster which allows you to label the clusters with less effort than k-means clustering algorithms would require. GMMs also offer some other benefits such as finding gaussian mixture models that best describe each group, helping identify underlying categories of data sets, and predicting future stock prices more accurately by considering volatility and noise factors. If you’re looking for an efficient way to find patterns within complicated datasets or need help modeling natural phenomena like natural disasters or customer behavior analysis in your marketing, gaussian mixture models could be the right choice.