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Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems and add a penalty term to the objective, but the augmented Lagrangian method adds yet another term designed to mimic a Lagrange multiplier.
The Lagrange multiplier theorem states that at any local maximum (or minimum) of the function evaluated under the equality constraints, if constraint qualification applies (explained below), then the gradient of the function (at that point) can be expressed as a linear combination of the gradients of the constraints (at that point), with the ...
Programming with Big Data in R (pbdR) [1] is a series of R packages and an environment for statistical computing with big data by using high-performance statistical computation. [ 2 ] [ 3 ] The pbdR uses the same programming language as R with S3/S4 classes and methods which is used among statisticians and data miners for developing statistical ...
It was proven in 2014 that the elastic net can be reduced to the linear support vector machine. [7] A similar reduction was previously proven for the LASSO in 2014. [8] The authors showed that for every instance of the elastic net, an artificial binary classification problem can be constructed such that the hyper-plane solution of a linear support vector machine (SVM) is identical to the ...
Lambda architecture depends on a data model with an append-only, immutable data source that serves as a system of record. [2]: 32 It is intended for ingesting and processing timestamped events that are appended to existing events rather than overwriting them. State is determined from the natural time-based ordering of the data.
In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator) [1]: p.26 is a higher-order function (i.e. a function which takes a function as argument) that returns some fixed point (a value that is mapped to itself) of its argument function, if one exists.
[7]: 132 Denote the equality constraints h i (x)=0 as Ax=b, where A has n columns. If Ax=b is infeasible, then of course the original problem is infeasible. Otherwise, it has some solution x 0, and the set of all solutions can be presented as: Fz+x 0, where z is in R k, k=n-rank(A), and F is an n-by-k matrix.
In statistics and machine learning, lasso (least absolute shrinkage and selection operator; also Lasso, LASSO or L1 regularization) [1] is a regression analysis method that performs both variable selection and regularization in order to enhance the prediction accuracy and interpretability of the resulting statistical model.