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    • Update lars authored by Dean Samuel Schmitz's avatar Dean Samuel Schmitz
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    PrologMethods/Regression/lars.md
    View page @ 4fa022e6
    ......@@ -2,128 +2,77 @@
    An implementation of Least Angle Regression (Stagewise/laSso), also known as LARS.
    ```prolog
    :- use_module('path/to/.../src/methods/lars/lars.pl').
    %% usage example
    TrainData = [5.1,3.5,1.4, 4.9,3.0,1.4, 4.7,3.2,1.3, 4.6,3.1,1.5],
    TestData = [3,2,0, 5,1,4, 0,0,4, 3,3,5, 0,5,5, 2,5,5],
    lars_initAndTrainModel(0, 0.0, 0.0, 1.0e-16, TrainData, 3, [0,1,0,1], 0, _),
    lars_predict(TestData, 3, PredictList, 1).
    ```
    # Available Predicates
    * [initModelNoDataNoGram/4](/PrologMethods/Regression/lars#initmodelnodatanogram4)
    * [initModelNoDataWithGram/7](/PrologMethods/Regression/lars#initmodelnodatawithgram7)
    * [initModelWithDataNoGram/10](/PrologMethods/Regression/lars#initmodelwithdatanogram10)
    * [initModelWithDataWithGram/13](/PrologMethods/Regression/lars#initmodelwithdatawithgram13)
    * [activeSet/2](/PrologMethods/Regression/lars#activeset2)
    * [beta/2](/PrologMethods/Regression/lars#beta2)
    * [betaPath/3](/PrologMethods/Regression/lars#betapath3)
    * [computeError/7](/PrologMethods/Regression/lars#computeerror7)
    * [lambdaPath/2](/PrologMethods/Regression/lars#lambdapath2)
    * [matUtriCholFactor/3](/PrologMethods/Regression/lars#matutricholfactor3)
    * [predict/6](/PrologMethods/Regression/lars#predict6)
    * [train/9](/PrologMethods/Regression/lars#train9)
    * [lars_initAndTrainModel/9](/PrologMethods/Regression/lars#lars_initandtrainmodel9)
    * [lars_activeSet/2](/PrologMethods/Regression/lars#lars_activeset1)
    * [lars_beta/2](/PrologMethods/Regression/lars#lars_beta1)
    * [lars_betaPath/3](/PrologMethods/Regression/lars#lars_betapath2)
    * [lars_computeError/7](/PrologMethods/Regression/lars#lars_computeerror5)
    * [lars_lambdaPath/2](/PrologMethods/Regression/lars#lars_lambdapath1)
    * [lars_matUtriCholFactor/3](/PrologMethods/Regression/lars#lars_matutricholfactor2)
    * [lars_predict/6](/PrologMethods/Regression/lars#lars_predict4)
    ---
    [links/resources](/PrologMethods/Regression/lars#connected-linksresources)
    ## **_initModelNoDataNoGram/4_**
    ## **_lars_initAndTrainModel/9_**
    Only initialize the LARS model.
    ```prolog
    %% part of the predicate definition
    initModelNoDataNoGram( +integer,
    +float32, +float32, +float32).
    ```
    ### Parameters
    | Name | Type | Description | Default |
    |------|------|-------------|---------|
    | useCholesky | +integer(bool) | Whether or not to use Cholesky decomposition when solving linear system (as opposed to using the full Gram matrix). | (0)false |
    | lambda1 | +float | Regularization parameter for l1-norm penalty. | 0.0 |
    | lambda2 | +float | Regularization parameter for l2-norm penalty. | 0.0 |
    | tolerance | +float | Run until the maximum correlation of elements in (X^T y) is less than this. | 1e-16 |
    ---
    ## **_initModelNoDataWithGram/7_**
    Initialize LARS model, and pass in a precalculated Gram matrix but dont train the model.
    ```prolog
    %% part of the predicate definition
    initModelNoDataWithGram( +integer,
    %% predicate definition
    lars_initAndTrainModel(UseCholesky, Lambda1, Lambda2, Tolerance, DataList, DataPointsDim, ResponsesList, RowMajor, Error) :-
    Tolerance > 0,
    convert_list_to_float_array(DataList, DataPointsDim, array(Xsize, Xrownum, X)),
    convert_list_to_float_array(ResponsesList, array(Ysize, Y)),
    initAndTrainModelI(UseCholesky, Lambda1, Lambda2, Tolerance, X, Xsize, Xrownum, Y, Ysize, RowMajor, Error).
    %% foreign c++ predicate definition
    foreign(initAndTrainModel, c, initAndTrainModelI( +integer,
    +float32, +float32, +float32,
    +pointer(float_array), +integer, +integer,
    +float32, +float32, +float32).
    ```
    ### Parameters
    | Name | Type | Description | Default |
    |------|------|-------------|---------|
    | useCholesky | +integer(bool) | Whether or not to use Cholesky decomposition when solving linear system (as opposed to using the full Gram matrix). | (0)false |
    | gramMatrix | +matrix | Gram matrix. | - |
    | lambda1 | +float | Regularization parameter for l1-norm penalty. | 0.0 |
    | lambda2 | +float | Regularization parameter for l2-norm penalty. | 0.0 |
    | tolerance | +float | Run until the maximum correlation of elements in (X^T y) is less than this. | 1e-16 |
    ---
    ## **_initModelWithDataNoGram/10_**
    Initialize LARS model, and train the model.
    ```prolog
    %% part of the predicate definition
    initModelWithDataNoGram( +pointer(float_array), +integer, +integer,
    +pointer(float_array), +integer,
    +integer,
    +integer,
    +float32, +float32, +float32).
    +integer, -float32)).
    ```
    ### Parameters
    | Name | Type | Description | Default |
    |------|------|-------------|---------|
    | data | +matrix | Input data. | - |
    | responses | +vector | A vector of targets. | - |
    | transposeData | +integer(bool) | Should be true if the input data is column-major and false otherwise. | (1)true |
    | useCholesky | +integer(bool) | Whether or not to use Cholesky decomposition when solving linear system (as opposed to using the full Gram matrix). | (0)false |
    | lambda1 | +float | Regularization parameter for l1-norm penalty. | 0.0 |
    | lambda2 | +float | Regularization parameter for l2-norm penalty. | 0.0 |
    | tolerance | +float | Run until the maximum correlation of elements in (X^T y) is less than this. | 1e-16 |
    ---
    ## **_initModelWithDataWithGram/13_**
    Initialize LARS model, pass in a precalculated Gram matrix and train the model.
    ```prolog
    %% part of the predicate definition
    initModelWithDataWithGram( +pointer(float_array), +integer, +integer,
    +pointer(float_array), +integer,
    +integer,
    +integer,
    +pointer(float_array), +integer, +integer,
    +float32, +float32, +float32).
    ```
    ### Parameters
    | Name | Type | Description | Default |
    |------|------|-------------|---------|
    | data | +matrix | Input data. | - |
    | data | +matrix | Column-major input data (or row-major input data if rowMajor = true). | - |
    | responses | +vector | A vector of targets. | - |
    | transposeData | +integer(bool) | Should be true if the input data is column-major and false otherwise. | (1)true |
    | useCholesky | +integer(bool) | Whether or not to use Cholesky decomposition when solving linear system (as opposed to using the full Gram matrix). | (0)false |
    | gramMatrix | +matrix | Gram matrix. | - |
    | lambda1 | +float | Regularization parameter for l1-norm penalty. | 0.0 |
    | lambda2 | +float | Regularization parameter for l2-norm penalty. | 0.0 |
    | tolerance | +float | Run until the maximum correlation of elements in (X^T y) is less than this. | 1e-16 |
    | rowMajor | +integer(bool) | Set to false if the data is row-major. | (1)true |
    | error | -float | minimum cost error | - |
    ---
    ## **_activeSet/2_**
    ## **_lars_activeSet/1_**
    Get the set of active dimensions
    ```prolog
    %% part of the predicate definition
    activeSet(-pointer(float_array), -integer).
    %% predicate definition
    lars_activeSet(ActiveSetList) :-
    activeSetI(Y, Ysize),
    convert_float_array_to_list(Y, Ysize, ActiveSetList).
    %% foreign c++ predicate definition
    foreign(activeSet, c, activeSetI(-pointer(float_array), -integer)).
    ```
    ### Parameters
    ......@@ -133,13 +82,18 @@ activeSet(-pointer(float_array), -integer).
    ---
    ## **_beta/2_**
    ## **_lars_beta/1_**
    Get the solution coefficients.
    ```prolog
    %% part of the predicate definition
    beta(-pointer(float_array), -integer).
    %% predicate definition
    lars_beta(BetaList) :-
    betaI(Y, Ysize),
    convert_float_array_to_list(Y, Ysize, BetaList).
    %% foreign c++ predicate definition
    foreign(beta, c, betaI(-pointer(float_array), -integer)).
    ```
    ### Parameters
    ......@@ -149,13 +103,18 @@ beta(-pointer(float_array), -integer).
    ---
    ## **_betaPath/3_**
    ## **_lars_betaPath/2_**
    Get the set of coefficients after each iteration. The solution is the last element.
    ```prolog
    %% part of the predicate definition
    betaPath(-pointer(float_array), -integer, -integer).
    %% predicate definition
    lars_betaPath(BetaList, XCols) :-
    betaPathI(X, XCols, XRows),
    convert_float_array_to_2d_list(X, XCols, XRows, BetaList).
    %% foreign c++ predicate definition
    foreign(betaPath, c, betaPathI(-pointer(float_array), -integer, -integer)).
    ```
    ### Parameters
    ......@@ -165,18 +124,24 @@ betaPath(-pointer(float_array), -integer, -integer).
    ---
    ## **_computeError/7_**
    ## **_lars_computeError/5_**
    Compute cost error of the given data matrix using the currently-trained LARS model.
    Only ||y-beta\*X||2 is used to calculate cost error.
    ```prolog
    %% part of the predicate definition
    computeError( +pointer(float_array), +integer, +integer,
    %% predicate definition
    lars_computeError(DataList, DataRows, ResponsesList, RowMajor, Error) :-
    convert_list_to_float_array(DataList, DataRows, array(Xsize, Xrownum, X)),
    convert_list_to_float_array(ResponsesList, array(Ysize, Y)),
    computeErrorI(X, Xsize, Xrownum, Y, Ysize, RowMajor, Error).
    %% foreign c++ predicate definition
    foreign(computeError, c, computeErrorI( +pointer(float_array), +integer, +integer,
    +pointer(float_array), +integer,
    +integer,
    [-float32]).
    [-float32])).
    ```
    ### Parameters
    ......@@ -189,13 +154,18 @@ computeError( +pointer(float_array), +integer, +integer,
    ---
    ## **_lambdaPath/2_**
    ## **_lars_lambdaPath/1_**
    Get the set of values for lambda1 after each iteration; the solution is the last element.
    ```prolog
    %% part of the predicate definition
    lambdaPath(-pointer(float_array), -integer).
    %% predicate definition
    lars_lambdaPath(LambdaPathList) :-
    lambdaPathI(Y, Ysize),
    convert_float_array_to_list(Y, Ysize, LambdaPathList).
    %% foreign c++ predicate definition
    foreign(lambdaPath, c, lambdaPathI(-pointer(float_array), -integer)).
    ```
    ### Parameters
    ......@@ -205,13 +175,18 @@ lambdaPath(-pointer(float_array), -integer).
    ---
    ## **_matUtriCholFactor/3_**
    ## **_lars_matUtriCholFactor/2_**
    Get the upper triangular cholesky factor.
    ```prolog
    %% part of the predicate definition
    matUtriCholFactor(-pointer(float_array), -integer, -integer).
    %% predicate definition
    lars_matUtriCholFactor(FactorList, XCols) :-
    matUtriCholFactorI(X, XCols, XRows),
    convert_float_array_to_2d_list(X, XCols, XRows, FactorList).
    %% foreign c++ predicate definition
    foreign(matUtriCholFactor, c, matUtriCholFactorI(-pointer(float_array), -integer, -integer)).
    ```
    ### Parameters
    ......@@ -221,15 +196,21 @@ matUtriCholFactor(-pointer(float_array), -integer, -integer).
    ---
    ## **_predict/6_**
    ## **_lars_predict/4_**
    Predict y_i for each data point in the given data matrix using the currently-trained LARS model.
    ```prolog
    %% part of the predicate definition
    predict( +pointer(float_array), +integer, +integer,
    %% predicate definition
    lars_predict(PointsList, PointsRows, PredicList, RowMajor) :-
    convert_list_to_float_array(PointsList, PointsRows, array(Xsize, Xrownum, X)),
    predictI(X, Xsize, Xrownum, Y, Ysize, RowMajor),
    convert_float_array_to_list(Y, Ysize, PredicList).
    %% foreign c++ predicate definition
    foreign(predict, c, predictI( +pointer(float_array), +integer, +integer,
    -pointer(float_array), -integer,
    +integer).
    +integer)).
    ```
    ### Parameters
    ......@@ -241,38 +222,12 @@ predict( +pointer(float_array), +integer, +integer,
    ---
    ## **_train/9_**
    Train the LARS model with the given data.
    The input matrix (like all mlpack matrices) should be column-major – each column is an observation and each row is a dimension. However, because LARS is more efficient on a row-major matrix, this method will (internally) transpose the matrix. If this transposition is not necessary (i.e., you want to pass in a row-major matrix), pass 'false' for the transposeData parameter.
    ```prolog
    %% part of the predicate definition
    train( +pointer(float_array), +integer, +integer,
    +pointer(float_array), +integer,
    -pointer(float_array), -integer,
    +integer,
    [-float32]).
    ```
    ### Parameters
    | Name | Type | Description | Default |
    |------|------|-------------|---------|
    | data | +matrix | Column-major input data (or row-major input data if rowMajor = true). | - |
    | responses | +vector | A vector of targets. | - |
    | beta | -vector | Vector to store the solution (the coefficients) in. | - |
    | transposeData | +integer(bool) | Set to false if the data is row-major. | (1)true |
    | error | -float | minimum cost error( | |
    ---
    # Connected Links/Resources
    If you want a more detailed explanation, then go to the python documentation. There is most of the time a good explanation on how the methods work and what the parameters do.
    * [**MLpack::lars_C++\_documentation**](https://www.mlpack.org/doc/stable/doxygen/classmlpack_1_1regression_1_1LARS.html)
    * [**MLpack::lars_Python_documentation**](https://www.mlpack.org/doc/stable/python_documentation.html#lars)
    * [**MLpack::lars_C++\_documentation**](https://www.mlpack.org/doc/mlpack-3.4.2/doxygen/classmlpack_1_1regression_1_1LARS.html)
    * [**MLpack::lars_Python_documentation**](https://www.mlpack.org/doc/mlpack-3.4.2/python_documentation.html#lars)
    added some of the links from the python documentation
    ......