Merge branch 'release-0.3' of github.com:smartcorelib/smartcore into release-0.3

This commit is contained in:
Lorenzo (Mec-iS)
2022-11-08 12:22:06 +00:00
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//! set and then aggregate their individual predictions to form a final prediction. In classification setting the overall prediction is the most commonly
//! occurring majority class among the individual predictions.
//!
//! In smartcore you will find implementation of RandomForest - a popular averaging algorithms based on randomized [decision trees](../tree/index.html).
//! In `smartcore` you will find implementation of RandomForest - a popular averaging algorithms based on randomized [decision trees](../tree/index.html).
//! Random forests provide an improvement over bagged trees by way of a small tweak that decorrelates the trees. As in bagging, we build a number of
//! decision trees on bootstrapped training samples. But when building these decision trees, each time a split in a tree is considered,
//! a random sample of _m_ predictors is chosen as split candidates from the full set of _p_ predictors.
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//! \\[\hat{\beta} = (X^TX)^{-1}X^Ty \\]
//!
//! the \\((X^TX)^{-1}\\) term is both computationally expensive and numerically unstable. An alternative approach is to use a matrix decomposition to avoid this operation.
//! smartcore uses [SVD](../../linalg/svd/index.html) and [QR](../../linalg/qr/index.html) matrix decomposition to find estimates of \\(\hat{\beta}\\).
//! `smartcore` uses [SVD](../../linalg/svd/index.html) and [QR](../../linalg/qr/index.html) matrix decomposition to find estimates of \\(\hat{\beta}\\).
//! The QR decomposition is more computationally efficient and more numerically stable than calculating the normal equation directly,
//! but does not work for all data matrices. Unlike the QR decomposition, all matrices have an SVD decomposition.
//!
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//!
//! \\[ Pr(y=1) \approx \frac{e^{\beta_0 + \sum_{i=1}^n \beta_iX_i}}{1 + e^{\beta_0 + \sum_{i=1}^n \beta_iX_i}} \\]
//!
//! smartcore uses [limited memory BFGS](https://en.wikipedia.org/wiki/Limited-memory_BFGS) method to find estimates of regression coefficients, \\(\beta\\)
//! `smartcore` uses [limited memory BFGS](https://en.wikipedia.org/wiki/Limited-memory_BFGS) method to find estimates of regression coefficients, \\(\beta\\)
//!
//! Example:
//!
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//! where \\(\alpha \geq 0\\) is a tuning parameter that controls strength of regularization. When \\(\alpha = 0\\) the penalty term has no effect, and ridge regression will produce the least squares estimates.
//! However, as \\(\alpha \rightarrow \infty\\), the impact of the shrinkage penalty grows, and the ridge regression coefficient estimates will approach zero.
//!
//! smartcore uses [SVD](../../linalg/svd/index.html) and [Cholesky](../../linalg/cholesky/index.html) matrix decomposition to find estimates of \\(\hat{\beta}\\).
//! `smartcore` uses [SVD](../../linalg/svd/index.html) and [Cholesky](../../linalg/cholesky/index.html) matrix decomposition to find estimates of \\(\hat{\beta}\\).
//! The Cholesky decomposition is more computationally efficient and more numerically stable than calculating the normal equation directly,
//! but does not work for all data matrices. Unlike the Cholesky decomposition, all matrices have an SVD decomposition.
//!
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//! Computes the area under the receiver operating characteristic (ROC) curve that is equal to the probability that a classifier will rank a
//! randomly chosen positive instance higher than a randomly chosen negative one.
//!
//! smartcore calculates ROC AUC from Wilcoxon or Mann-Whitney U test.
//! `smartcore` calculates ROC AUC from Wilcoxon or Mann-Whitney U test.
//!
//! Example:
//! ```