Gaussian mixture model
A Gaussian mixture model is a probabilistic model representing a distribution as a weighted combination of multiple Gaussian component distributions.
Math and Architectures of Deep Learning
A probabilistic model representing a distribution as a weighted combination of Gaussian components.
- How it is used
- Models unlabeled multiclass point clouds as clustered probability distributions for sampling and classification.
- How deep it goes
- Defines component parameters and latent selection, then develops posterior classification and iterative maximum-likelihood fitting.
- Examples
- Uses unlabeled height and weight data for adult females, adult males, and children, plus parameter-varied density plots.
- What you can do after
- Apply it via PyTorch distributions to construct mixtures, classify inputs by posterior component probability, and fit parameters iteratively.
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Outlier Detection in Python
A Gaussian mixture model represents a probability distribution as a weighted combination of multiple Gaussian component distributions.
- How it is used
- Uses Gaussian components to model multiple clusters for outlier detection and to generate synthetic tabular records.
- How deep it goes
- Explains component shapes, density interpretation, clustering, BIC-based selection, and sampling through practical procedures rather than a mathematical derivation.
- Examples
- Illustrates detection with three synthetic clusters and data generation with baseball records and expanded component covariances.
- What you can do after
- Apply it via scikit-learn’s GaussianMixture to model clusters, support outlier scoring, and sample synthetic records.
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Data Without Labels
A probabilistic model that represents data as a weighted combination of Gaussian probability distributions.
- How it is used
- Groups overlapping data through soft, probabilistic cluster assignments.
- How deep it goes
- Explains Gaussian parameters and the iterative EM procedure, then points toward Python implementation without specifying a library here.
- Examples
- Uses changing Gaussian curves and a point that could come from two distributions to illustrate shape and uncertain membership.
- What you can do after
- Evaluate/understand GMM as a clustering option for overlapping data and interpret its probabilistic assignments.
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Related concepts
- soft clusteringuses · Soft clustering is a clustering technique that assigns each item graded or probabilistic membership across multiple clusters rather than exclusive membership in one.
- generative modelingkind of · Generative modeling is a machine-learning approach that learns patterns or a data distribution to generate new samples resembling the data.
- normal distributionuses · A normal distribution is a continuous probability distribution with a symmetric, bell-shaped density determined by its mean and variance.
- expectation maximizationused by · Expectation maximization is an iterative algorithm for estimating model parameters with latent or unobserved variables by alternating latent-variable estimation with parameter optimization.
- K-means clusteringcontrasts with · K-means clustering partitions data into a specified number of groups by assigning observations to representative centers and iteratively updating those centers to reduce within-group distances.
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