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In statistics, the precision matrix or concentration matrix is the matrix inverse of the covariance matrix or dispersion matrix, =. [ 1 ] [ 2 ] [ 3 ] For univariate distributions , the precision matrix degenerates into a scalar precision , defined as the reciprocal of the variance , p = 1 σ 2 {\displaystyle p={\frac {1}{\sigma ^{2}}}} .
In a classification task, the precision for a class is the number of true positives (i.e. the number of items correctly labelled as belonging to the positive class) divided by the total number of elements labelled as belonging to the positive class (i.e. the sum of true positives and false positives, which are items incorrectly labelled as belonging to the class).
For example, in medicine sensitivity and specificity are often used, while in computer science precision and recall are preferred. An important distinction is between metrics that are independent of the prevalence or skew (how often each class occurs in the population), and metrics that depend on the prevalence – both types are useful, but ...
^ = = (¯) (¯) = [′ ()] (matrix form; is the identity matrix, J is a matrix of ones; the term in parentheses is thus the centering matrix) The Fisher information matrix for estimating the parameters of a multivariate normal distribution has a closed form expression.
These independence relations can be alternatively expressed using graphical models and there exist theorems linking graph structure and vertex ordering with zeros in the Cholesky factor. In particular, it is known [3] that independencies that are encoded in a moral graph lead to Cholesky factors of the precision matrix that have no fill-in.
In statistics and machine learning, Gaussian process approximation is a computational method that accelerates inference tasks in the context of a Gaussian process model, most commonly likelihood evaluation and prediction. Like approximations of other models, they can often be expressed as additional assumptions imposed on the model, which do ...
This topic, which concerns the task of filling in the missing entries of a partially observed matrix, became popular owing in large part to the Netflix prize for predicting user ratings for films. High-dimensional classification. Linear discriminant analysis cannot be used when >, because the sample covariance matrix is singular.
In statistics, the graphical lasso [1] is a sparse penalized maximum likelihood estimator for the concentration or precision matrix (inverse of covariance matrix) of a multivariate elliptical distribution.