Description Usage Arguments Details Value References See Also Examples

Computes a number of Lasso solution paths with increasing numbers of interactions present in the design matrices corresponding to each path. Previous paths are used to speed up computation of subsequent paths so the process is very fast.

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`x` |
input matrix of dimension nobs by nvars; each row is an observation vector. |

`y` |
response variable; shoud be a numeric vector. |

`nlambda` |
the number of lambda values. Must be at least 3. |

`iter_max` |
the number of iterations of the Backtracking algorithm to
run. |

`lambda.min.ratio` |
smallest value in |

`lambda` |
user supplied |

`thresh` |
convergence threshold for coordinate descent. Each inner
coordinate descent loop continues until either the maximum change in the
objective after any coefficient update is less than |

`verbose` |
if |

`inter_orig` |
an optional 2-row matrix with each column giving interactions that are to be added to the design matrix before the algorithm begins. |

The Lasso optimisations are performed using coordinate descent similarly to the glmnet package. An intercept term is always included. Variables are centred and scaled to have equal empirical variance. Interactions are constructed from these centred and scaled variables, and the interactions themselves are also centred and scaled. Note the coefficients are returned on the original scale of the variables. Coefficients returned for interactions are for simple pointwise products of the original variables with no scaling.

An object with S3 class "`BT`

".

`call`

the call that produced the object

`a0`

list of intercept vectors

`beta`

list of matrices of coefficients stored in sparse column format (

`CsparseMatrix`

)`fitted`

list of fitted values

`lambda`

the sequence of

`lambda`

values used`nobs`

the number of observations

`nvars`

the number of variables

`var_indices`

the indices of the non-constant columns of the design matrix

`interactions`

a 2-row matrix with columns giving the interactions that were added to the design matrix

`path_lookup`

a matrix with columns corresponding to iterations and rows to lambda values. Entry

*ij*gives the component of the`a0`

and`beta`

lists that gives the coefficients for the*i*th`lambda`

value and*j*th iteration`l_start`

a vector with component entries giving the minimimum

`lambda`

index in the corresponding copmonents of`beta`

and`a0`

Shah, R. D. (2016) *Modelling interactions in high-dimensional data with
Backtracking. JMLR, to appear.*
http://www.statslab.cam.ac.uk/~rds37/papers/shah16.pdf

`predict.BT`

, `coef.BT`

methods and the `cvLassoBT`

function.

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