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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).
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More technically, general versions of the approximation lead to a sparse Cholesky factor of the precision matrix. Using the standard Cholesky factorization produces entries which can be interpreted [2] as conditional correlations with zeros indicating no independence (since the model is Gaussian). These independence relations can be ...
Because the variance of the estimator of a parameter vector is a matrix, the problem of "minimizing the variance" is complicated. Using statistical theory, statisticians compress the information-matrix using real-valued summary statistics; being real-valued functions, these "information criteria" can be maximized.
^ = = (¯) (¯) = [′ ()] (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.
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 ...
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.