multiview.fit: Fit a GLM with elastic net regularization for a single value...
In multiview: Cooperative Learning for Multi-View Analysis

multiview.fit

R Documentation

Fit a GLM with elastic net regularization for a single value of lambda

Description

Fit a generalized linear model via penalized maximum likelihood for a single value of lambda. Can deal with any GLM family.

Usage

multiview.fit(
  x_list,
  x,
  y,
  rho,
  weights,
  lambda,
  alpha = 1,
  offset = rep(0, nobs),
  family = gaussian(),
  intercept = TRUE,
  thresh = 1e-07,
  maxit = 1e+05,
  penalty.factor = rep(1, nvars),
  exclude = c(),
  lower.limits = -Inf,
  upper.limits = Inf,
  warm = NULL,
  from.multiview.path = FALSE,
  save.fit = FALSE,
  trace.it = 0,
  user_lambda = FALSE
)

Arguments

`x_list`	a list of `x` matrices with same number of rows `nobs`
`x`	the column-binded entries of `x_list`
`y`	the quantitative response with length equal to `nobs`, the (same) number of rows in each `x` matrix
`rho`	the weight on the agreement penalty, default 0. `rho=0` is a form of early fusion, and `rho=1` is a form of late fusion. We recommend trying a few values of `rho` including 0, 0.1, 0.25, 0.5, and 1 first; sometimes `rho` larger than 1 can also be helpful.
`weights`	observation weights. Can be total counts if responses are proportion matrices. Default is 1 for each observation
`lambda`	A single value for the `lambda` hyperparameter.
`alpha`	The elasticnet mixing parameter, with `0\le\alpha\le 1`. The penalty is defined as `(1-\alpha)/2\|\|\beta\|\|_2^2+\alpha\|\|\beta\|\|_1.` `alpha=1` is the lasso penalty, and `alpha=0` the ridge penalty.
`offset`	A vector of length `nobs` that is included in the linear predictor (a `nobs x nc` matrix for the `"multinomial"` family). Useful for the `"poisson"` family (e.g. log of exposure time), or for refining a model by starting at a current fit. Default is `NULL`. If supplied, then values must also be supplied to the `predict` function.
`family`	A description of the error distribution and link function to be used in the model. This is the result of a call to a family function. Default is stats::gaussian. (See stats::family for details on family functions.)
`intercept`	Should intercept(s) be fitted (default `TRUE`)
`thresh`	Convergence threshold for coordinate descent. Each inner coordinate-descent loop continues until the maximum change in the objective after any coefficient update is less than `thresh` times the null deviance. Defaults value is `1E-7`.
`maxit`	Maximum number of passes over the data; default is `10^5`. (If a warm start object is provided, the number of passes the warm start object performed is included.)
`penalty.factor`	Separate penalty factors can be applied to each coefficient. This is a number that multiplies `lambda` to allow differential shrinkage. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in the model. Default is 1 for all variables (and implicitly infinity for variables listed in `exclude`). Note: the penalty factors are internally rescaled to sum to nvars, and the lambda sequence will reflect this change.
`exclude`	Indices of variables to be excluded from the model. Default is none. Equivalent to an infinite penalty factor for the variables excluded (next item). Users can supply instead an `exclude` function that generates the list of indices. This function is most generally defined as `⁠function(x_list, y, ...)⁠`, and is called inside `multiview` to generate the indices for excluded variables. The `...` argument is required, the others are optional. This is useful for filtering wide data, and works correctly with `cv.multiview`. See the vignette 'Introduction' for examples.
`lower.limits`	Vector of lower limits for each coefficient; default `-Inf`. Each of these must be non-positive. Can be presented as a single value (which will then be replicated), else a vector of length `nvars`
`upper.limits`	Vector of upper limits for each coefficient; default `Inf`. See `lower.limits`
`warm`	Either a `multiview` object or a list (with names `beta` and `a0` containing coefficients and intercept respectively) which can be used as a warm start. Default is `NULL`, indicating no warm start. For internal use only.
`from.multiview.path`	Was `multiview.fit()` called from `multiview.path()`? Default is `FALSE`.This has implications for computation of the penalty factors.
`save.fit`	Return the warm start object? Default is `FALSE`.
`trace.it`	Controls how much information is printed to screen. If `trace.it = 2`, some information about the fitting procedure is printed to the console as the model is being fitted. Default is `trace.it = 0` (no information printed). (`trace.it = 1` not used for compatibility with `multiview.path`.)
`user_lambda`	a flag indicating if user supplied the lambda sequence

Details

WARNING: Users should not call multiview.fit directly. Higher-level functions in this package call multiview.fit as a subroutine. If a warm start object is provided, some of the other arguments in the function may be overriden.

multiview.fit solves the elastic net problem for a single, user-specified value of lambda. multiview.fit works for any GLM family. It solves the problem using iteratively reweighted least squares (IRLS). For each IRLS iteration, multiview.fit makes a quadratic (Newton) approximation of the log-likelihood, then calls elnet.fit to minimize the resulting approximation.

In terms of standardization: multiview.fit does not standardize x and weights. penalty.factor is standardized so that to sum to nvars.

Value

An object with class "multiview". The list returned contains more keys than that of a "multiview" object.

`a0`	Intercept value.
`beta`	A `nvars` by `1` matrix of coefficients, stored in sparse matrix format.
`df`	The number of nonzero coefficients.
`dim`	Dimension of coefficient matrix.
`lambda`	Lambda value used.
`lambda_scale`	The multiview lambda scale factor
`dev.ratio`	The fraction of (null) deviance explained. The deviance calculations incorporate weights if present in the model. The deviance is defined to be 2*(loglike_sat - loglike), where loglike_sat is the log-likelihood for the saturated model (a model with a free parameter per observation). Hence dev.ratio=1-dev/nulldev.
`nulldev`	Null deviance (per observation). This is defined to be 2*(loglike_sat -loglike(Null)). The null model refers to the intercept model.
`npasses`	Total passes over the data.
`jerr`	Error flag, for warnings and errors (largely for internal debugging).
`offset`	A logical variable indicating whether an offset was included in the model.
`call`	The call that produced this object.
`nobs`	Number of observations.
`warm_fit`	If `save.fit = TRUE`, output of C++ routine, used for warm starts. For internal use only.
`family`	Family used for the model.
`converged`	A logical variable: was the algorithm judged to have converged?
`boundary`	A logical variable: is the fitted value on the boundary of the attainable values?
`obj_function`	Objective function value at the solution.