multiview: Perform cooperative learning using the direct algorithm for...

In multiview: Cooperative Learning for Multi-View Analysis

Perform cooperative learning using the direct algorithm for two or more views.

Description

multiview uses glmnet::glmnet() to do most of its work and therefore takes many of the same parameters, but an intercept is always included and several other parameters do not apply. Such inapplicable arguments are overridden and warnings issued.

Usage

multiview(
  x_list,
  y,
  rho = 0,
  family = gaussian(),
  weights = NULL,
  offset = NULL,
  alpha = 1,
  nlambda = 100,
  lambda.min.ratio = ifelse(nobs < nvars, 0.01, 1e-04),
  lambda = NULL,
  standardize = TRUE,
  intercept = TRUE,
  thresh = 1e-07,
  maxit = 1e+05,
  penalty.factor = rep(1, nvars),
  exclude = list(),
  lower.limits = -Inf,
  upper.limits = Inf,
  trace.it = 0
)

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.
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.)
weights	observation weights. Can be total counts if responses are proportion matrices. Default is 1 for each observation
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.
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.
nlambda	The number of lambda values - default is 100.
lambda.min.ratio	Smallest value for lambda, as a fraction of lambda.max, the (data derived) entry value (i.e. the smallest value for which all coefficients are zero). The default depends on the sample size nobs relative to the number of variables nvars. If nobs > nvars, the default is 0.0001, close to zero. If nobs < nvars, the default is 0.01. A very small value of lambda.min.ratio will lead to a saturated fit in the nobs < nvars case. This is undefined for "binomial" and "multinomial" models, and glmnet will exit gracefully when the percentage deviance explained is almost 1.
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.
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.

Details

The current code can be slow for "large" data sets, e.g. when the number of features is larger than 1000. It can be helpful to see the progress of multiview as it runs; to do this, set trace.it = 1 in the call to multiview or cv.multiview. With this, multiview prints out its progress along the way. One can also pre-filter the features to a smaller set, using the exclude option, with a filter function.

If there are missing values in the feature matrices: we recommend that you center the columns of each feature matrix, and then fill in the missing values with 0.

For example,
x <- scale(x,TRUE,FALSE)
x[is.na(x)] <- 0
z <- scale(z,TRUE,FALSE)
z[is.na(z)] <- 0

Then run multiview in the usual way. It will exploit the assumed shared latent factors to make efficient use of the available data.

Value

An object with S3 class ⁠"multiview","*" ⁠, where "*" is "elnet", "lognet", "multnet", "fishnet" (poisson), "coxnet" or "mrelnet" for the various types of models.

call	the call that produced this object
a0	Intercept sequence of length length(lambda)
beta	For "elnet", "lognet", "fishnet" and "coxnet" models, a ⁠nvars x length(lambda)⁠ matrix of coefficients, stored in sparse column format ("CsparseMatrix"). For "multnet" and "mgaussian", a list of nc such matrices, one for each class.
lambda	The actual sequence of glmnet::glmnet() 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 (for "elnet", this is the R-square). 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, except for the Cox, where it is the 0 model.
df	The number of nonzero coefficients for each value of lambda. For "multnet", this is the number of variables with a nonzero coefficient for any class.
dfmat	For "multnet" and "mrelnet" only. A matrix consisting of the number of nonzero coefficients per class
dim	dimension of coefficient matrix (ices)
nobs	number of observations
npasses	total passes over the data summed over all lambda values
offset	a logical variable indicating whether an offset was included in the model
jerr	error flag, for warnings and errors (largely for internal debugging).

See Also

print, coef, coef_ordered, predict, and plot methods for "multiview", and the "cv.multiview" function.

Examples

# Gaussian
x = matrix(rnorm(100 * 20), 100, 20)
z = matrix(rnorm(100 * 10), 100, 10)
y = rnorm(100)
fit1 = multiview(list(x=x,z=z), y, rho = 0)
print(fit1)

# extract coefficients at a single value of lambda
coef(fit1, s = 0.01) 

# extract ordered (standardized) coefficients at a single value of lambda
coef_ordered(fit1, s = 0.01) 

# make predictions
predict(fit1, newx = list(x[1:10, ],z[1:10, ]), s = c(0.01, 0.005))

# make a path plot of features for the fit
plot(fit1, label=TRUE)

# Binomial
by = sample(c(0,1), 100, replace = TRUE)
fit2 = multiview(list(x=x,z=z), by, family = binomial(), rho=0.5)
predict(fit2, newx = list(x[1:10, ],z[1:10, ]), s = c(0.01, 0.005), type="response")
coef_ordered(fit2, s = 0.01) 
plot(fit2, label=TRUE)

# Poisson
py = matrix(rpois(100, exp(y))) 
fit3 = multiview(list(x=x,z=z), py, family = poisson(), rho=0.5)
predict(fit3, newx = list(x[1:10, ],z[1:10, ]), s = c(0.01, 0.005), type="response")
coef_ordered(fit3, s = 0.01) 
plot(fit3, label=TRUE)

multiview documentation built on April 3, 2023, 5:20 p.m.