multiview.path: Fit a GLM with elastic net regularization for a path of...
In multiview: Cooperative Learning for Multi-View Analysis

multiview.path

R Documentation

Fit a GLM with elastic net regularization for a path of lambda values

Description

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

Usage

multiview.path(
  x_list,
  y,
  rho = 0,
  weights = NULL,
  lambda,
  nlambda,
  user_lambda = FALSE,
  alpha = 1,
  offset = NULL,
  family = gaussian(),
  standardize = TRUE,
  intercept = TRUE,
  thresh = 1e-07,
  maxit = 1e+05,
  penalty.factor = rep(1, nvars),
  exclude = integer(0),
  lower.limits = -Inf,
  upper.limits = Inf,
  trace.it = 0,
  x,
  nvars,
  nobs,
  xm,
  xs,
  control,
  vp,
  vnames,
  start_val,
  is.offset
)

Arguments

`x_list`	a list of `x` matrices with same number of rows `nobs`
`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 user supplied `lambda` sequence, default `NULL`. Typical usage is to have the program compute its own `lambda` sequence. This sequence, in general, is different from that used in the `glmnet::glmnet()` call (named `lambda`) Supplying a value of `lambda` overrides this. WARNING: use with care. Avoid supplying a single value for `lambda` (for predictions after CV use `stats::predict()` instead. Supply instead a decreasing sequence of `lambda` values as `multiview` relies on its warms starts for speed, and its often faster to fit a whole path than compute a single fit.
`nlambda`	The number of `lambda` values - default is 100.
`user_lambda`	a flag indicating if user supplied the lambda sequence
`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.)
`standardize`	Logical flag for x variable standardization, prior to fitting the model sequence. The coefficients are always returned on the original scale. Default is `standardize=TRUE`. If variables are in the same units already, you might not wish to standardize. See details below for y standardization with `family="gaussian"`.
`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 for all lambda values; default is 10^5.
`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`
`trace.it`	If `trace.it=1`, then a progress bar is displayed; useful for big models that take a long time to fit.
`x`	the `cbind`ed matrices in `x_list`
`nvars`	the number of variables (total)
`nobs`	the number of observations
`xm`	the column means vector (could be zeros if `standardize = FALSE`)
`xs`	the column std dev vector (could be 1s if `standardize = FALSE`)
`control`	the multiview control object
`vp`	the variable penalities (processed)
`vnames`	the variable names
`start_val`	the result of first call to `get_start`
`is.offset`	a flag indicating if offset is supplied or not

Details

multiview.path solves the elastic net problem for a path of lambda values. It generalizes multiview::multiview in that it works for any GLM family.

Sometimes the sequence is truncated before nlam values of lambda have been used. This happens when multiview.path detects that the decrease in deviance is marginal (i.e. we are near a saturated fit).

Value

An object with class "multiview" "glmnetfit" and "glmnet"

`a0`	Intercept sequence of length `length(lambda)`.
`beta`	A `⁠nvars x length(lambda)⁠` matrix of coefficients, stored in sparse matrix format.
`df`	The number of nonzero coefficients for each value of lambda.
`dim`	Dimension of coefficient matrix.
`lambda`	The actual sequence of lambda values used. When alpha=0, the largest lambda reported does not quite give the zero coefficients reported (lambda=inf would in principle). Instead, the largest lambda for alpha=0.001 is used, and the sequence of lambda values is derived from this.
`lambda`	The sequence of lambda values
`mvlambda`	The corresponding sequence of multiview lambda values
`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 summed over all lambda values.
`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.
`family`	Family used for the model.
`nobs`	Number of observations.