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Probabilistic Matrix Factorization (PMF)
Bayesian approach to matrix factorization that models user-item preferences with probabilistic distributions, allowing to quantify and manage prediction uncertainty.
Latent Factor Matrix
Low-rank matrix representing unobserved latent characteristics (features) of users or items, whose entries are random variables in the PMF framework.
Posterior Distribution
Probabilistic distribution of latent factors after taking into account the observed data, representing the updated knowledge about the PMF model parameters.
Precision Matrix
Inverse of the covariance matrix, used in the definition of Gaussian distributions (prior and likelihood) to control confidence in observations and regularization of latent factors.
Three-Level Model
Extension of PMF where hyperparameters themselves are given a prior distribution, allowing automatic inference of optimal regularization and better handling of sparsity.
Observation Noise
Random variability inherent to observed data (e.g., imprecise ratings), modeled by the variance of the likelihood distribution in PMF to capture uncertainty in user preferences.
Automatic Regularization
Ability of the Bayesian PMF framework to automatically determine the optimal regularization level via inference on hyperparameters, avoiding costly manual tuning.
Posterior Mean Prediction
Point estimate of an unobserved rating calculated as the expectation of the posterior predictive distribution, integrating over the uncertainty of latent factors for a more robust prediction.
Variational Probabilistic Matrix Factorization
Alternative approach to MCMC sampling that approximates the posterior distribution by optimizing a lower bound on the log-likelihood, offering a speed-accuracy trade-off for large datasets.
User-Item Interaction Matrix
Sparse matrix of observed data (e.g., ratings, clicks) that the PMF model seeks to approximate by factorizing its observed entries to predict missing entries.