greedy.fit: Greedy search for tuning penalty parameters
In smimodel: Sparse Multiple Index Models for Nonparametric Forecasting

greedy.fit

R Documentation

Greedy search for tuning penalty parameters

Description

Function to perform a greedy search over a given grid of penalty parameter combinations (lambda0, lambda2), and fits a single SMI model with the best (lowest validation set MSE) penalty parameter combination. If the optimal combination lies on the edge of the grid, the penalty parameters are adjusted by ±10%, and a second round of grid search is performed.This is a helper function designed to be called from greedy_smimodel.

Usage

greedy.fit(
  data,
  val.data,
  yvar,
  neighbour = 0,
  family = gaussian(),
  index.vars,
  initialise = c("ppr", "additive", "linear", "multiple", "userInput"),
  num_ind = 5,
  num_models = 5,
  seed = 123,
  index.ind = NULL,
  index.coefs = NULL,
  s.vars = NULL,
  linear.vars = NULL,
  nlambda = 100,
  lambda.min.ratio = 1e-04,
  refit = TRUE,
  M = 10,
  max.iter = 50,
  tol = 0.001,
  tolCoefs = 0.001,
  TimeLimit = Inf,
  MIPGap = 1e-04,
  NonConvex = -1,
  verbose = list(solver = FALSE, progress = FALSE),
  parallel = FALSE,
  workers = NULL,
  exclude.trunc = NULL,
  recursive = FALSE,
  recursive_colRange = NULL
)

Arguments

`data`	Training data set on which models will be trained. Must be a data set of class `tsibble`.(Make sure there are no additional date or time related variables except for the `index` of the `tsibble`).
`val.data`	Validation data set. (The data set on which the penalty parameter selection will be performed.) Must be a data set of class `tsibble`. (Once the penalty parameter selection is completed, the best model will be re-fitted for the combined data set `data + val.data`.)
`yvar`	Name of the response variable as a character string.
`neighbour`	`neighbour` argument passed from the outer function.
`family`	A description of the error distribution and link function to be used in the model (see `glm` and `family`).
`index.vars`	A `character` vector of names of the predictor variables for which indices should be estimated.
`initialise`	The model structure with which the estimation process should be initialised. The default is `"ppr"`, where the initial model is derived from projection pursuit regression. The other options are `"additive"` - nonparametric additive model, `"linear"` - linear regression model (i.e. a special case single-index model, where the initial values of the index coefficients are obtained through a linear regression), `"multiple"` - multiple models are fitted starting with different initial models (number of indices = `num_ind`; `num_models` random instances of the model (i.e. the predictor assignment to indices and initial index coefficients are generated randomly) are considered), and the final optimal model with the lowest loss is returned, and `"userInput"` - user specifies the initial model structure (i.e. the number of indices and the placement of index variables among indices) and the initial index coefficients through `index.ind` and `index.coefs` arguments respectively.
`num_ind`	If `initialise = "ppr"` or `"multiple"`: an `integer` that specifies the number of indices to be used in the model(s). The default is `num_ind = 5`.
`num_models`	If `initialise = "multiple"`: an `integer` that specifies the number of starting models to be checked. The default is `num_models = 5`.
`seed`	If `initialise = "multiple"`: the seed to be set when generating random starting points.
`index.ind`	If `initialise = "userInput"`: an `integer` vector that assigns group index for each predictor in `index.vars`.
`index.coefs`	If `initialise = "userInput"`: a `numeric` vector of index coefficients.
`s.vars`	A `character` vector of names of the predictor variables for which splines should be fitted individually (rather than considering as part of an index).
`linear.vars`	A `character` vector of names of the predictor variables that should be included linearly into the model.
`nlambda`	The number of values for lambda0 (penalty parameter for L0 penalty) - default is 100.
`lambda.min.ratio`	Smallest value for lambda0, as a fraction of lambda0.max (data derived).
`refit`	Whether to refit the model combining training and validation sets after parameter tuning. If `FALSE`, the final model will be estimated only on the training set.
`M`	Big-M value used in MIP.
`max.iter`	Maximum number of MIP iterations performed to update index coefficients for a given model.
`tol`	Tolerance for the objective function value (loss) of MIP.
`tolCoefs`	Tolerance for coefficients.
`TimeLimit`	A limit for the total time (in seconds) expended in a single MIP iteration.
`MIPGap`	Relative MIP optimality gap.
`NonConvex`	The strategy for handling non-convex quadratic objectives or non-convex quadratic constraints in Gurobi solver.
`verbose`	A named list controlling verbosity options. Defaults to `list(solver = FALSE, progress = FALSE)`. solver Logical. If TRUE, print detailed solver output. progress Logical. If TRUE, print optimisation algorithm progress messages.
`parallel`	The option to use parallel processing in fitting SMI models for different penalty parameter combinations.
`workers`	If `parallel = TRUE`: Number of cores to use.
`exclude.trunc`	The names of the predictor variables that should not be truncated for stable predictions as a character string. (Since the nonlinear functions are estimated using splines, extrapolation is not desirable. Hence, if any predictor variable in `val.data` that is treated non-linearly in the estimated model, will be truncated to be in the in-sample range before obtaining predictions. If any variables are listed here will be excluded from such truncation.)
`recursive`	Whether to obtain recursive forecasts or not (default - `FALSE`).
`recursive_colRange`	If `recursive = TRUE`, the range of column numbers in `val.data` to be filled with forecasts. Recursive/autoregressive forecasting is required when the lags of the response variable itself are used as predictor variables into the model. Make sure such lagged variables are positioned together in increasing lag order (i.e. `lag_1, lag_2, ..., lag_m`, `lag_m =` maximum lag used) in `val.data`, with no break in the lagged variable sequence even if some of the intermediate lags are not used as predictors.

Value

A list that contains six elements:

`initial`	A list of information of the model initialisation. (For descriptions of the list elements see `make_smimodelFit`).
`best`	A list of information of the final optimised model. (For descriptions of the list elements see `make_smimodelFit`).
`best_lambdas`	Selected penalty parameter combination.
`lambda0_seq`	Sequence of values for lambda0 used to construct the initial grid.
`lambda2_seq`	Sequence of values for lambda2 used to construct the initial grid.
`searched`	A `tibble` containing the penalty parameter combinations searched during the two-step greedy search and the corresponding validation set MSEs.