Direct interface to biglasso fitting, no preprocessing, path version

This function is intended for users who know exactly what they're doing and want complete control over the fitting process. It

does NOT add an intercept
does NOT standardize the design matrix both of the above are critical steps in data analysis. However, a direct API has been provided for use in situations where the lasso fitting process is an internal component of a more complicated algorithm and standardization must be handled externally.

biglasso_path(
  X,
  y,
  r,
  init = rep(0, ncol(X)),
  xtx,
  penalty = "lasso",
  lambda,
  alpha = 1,
  gamma,
  ncores = 1,
  max.iter = 1000,
  eps = 1e-05,
  dfmax = ncol(X) + 1,
  penalty.factor = rep(1, ncol(X)),
  warn = TRUE,
  output.time = FALSE,
  return.time = TRUE
)

Arguments

X: The design matrix, without an intercept. It must be a double type bigmemory::big.matrix() object.
y: The response vector
r: Residuals (length n vector) corresponding to init. WARNING: If you supply an incorrect value of r, the solution will be incorrect.
init: Initial values for beta. Default: zero (length p vector)
xtx: X scales: the jth element should equal crossprod(X[,j])/n. In particular, if X is standardized, one should pass xtx = rep(1, p). WARNING: If you supply an incorrect value of xtx, the solution will be incorrect. (length p vector)
penalty: String specifying which penalty to use. Default is 'lasso', Other options are 'SCAD' and 'MCP' (the latter are non-convex)
lambda: A vector of numeric values the lasso tuning parameter.
alpha: The elastic-net mixing parameter that controls the relative contribution from the lasso (l1) and the ridge (l2) penalty. The penalty is defined as: $$ \alpha||\beta||_1 + (1-\alpha)/2||\beta||_2^2.$$ alpha=1 is the lasso penalty, alpha=0 the ridge penalty, alpha in between 0 and 1 is the elastic-net ("enet") penalty.
gamma: Tuning parameter value for nonconvex penalty. Defaults are 3.7 for penalty = 'SCAD' and 3 for penalty = 'MCP'
ncores: The number of OpenMP threads used for parallel computing.
max.iter: Maximum number of iterations. Default is 1000.
eps: Convergence threshold for inner coordinate descent. The algorithm iterates until the maximum change in the objective after any coefficient update is less than eps times the null deviance. Default value is 1e-7.
dfmax: Upper bound for the number of nonzero coefficients. Default is no upper bound. However, for large data sets, computational burden may be heavy for models with a large number of nonzero coefficients.
penalty.factor: A multiplicative factor for the penalty applied to each coefficient. If supplied, penalty.factor must be a numeric vector of length equal to the number of columns of X.
warn: Return warning messages for failures to converge and model saturation? Default is TRUE.
output.time: Whether to print out the start and end time of the model fitting. Default is FALSE.
return.time: Whether to return the computing time of the model fitting. Default is TRUE.

Value

An object with S3 class "biglasso" with following variables.

beta: A sparse matrix where rows are estimates a given coefficient across all values of lambda
iter: A vector of length nlambda containing the number of iterations until convergence
resid: Vector of residuals calculated from estimated coefficients.
lambda: The sequence of regularization parameter values in the path.
alpha: Same as in biglasso()
loss: A vector containing either the residual sum of squares of the fitted model at each value of lambda.
penalty.factor: Same as in biglasso().
n: The number of observations used in the model fitting.
y: The response vector used in the model fitting.

Details

biglasso_path() works identically to biglasso_fit() except it offers the additional option of fitting models across a path of tuning parameter values.

Note:

Hybrid safe-strong rules are turned off for biglasso_fit(), as these rely on standardization
Currently, the function only works with linear regression (family = 'gaussian').

Author

Tabitha Peter and Patrick Breheny

Examples

data(Prostate)
X <- cbind(1, Prostate$X)
xtx <- apply(X, 2, crossprod)/nrow(X)
y <- Prostate$y
X.bm <- as.big.matrix(X)
init <- rep(0, ncol(X))
fit <- biglasso_path(X = X.bm, y = y, r = y, init = init, xtx = xtx,
  lambda = c(0.5, 0.1, 0.05, 0.01, 0.001), 
  penalty.factor=c(0, rep(1, ncol(X)-1)), max.iter=2000)
fit$beta
#> 9 x 5 sparse Matrix of class "dgCMatrix"
#>                                                                      
#>         1.86789798  1.726547654  1.105241004  0.62236552  0.237779016
#> lcavol  0.22521668  0.577920344  0.559394365  0.55854063  0.563967682
#> lweight .           0.042348062  0.334244868  0.55897485  0.615294573
#> age     .          -0.005532399 -0.012370678 -0.01887351 -0.020994791
#> lbph    .           0.076396177  0.083246962  0.09416931  0.096496944
#> svi     .           .            0.255311017  0.63017098  0.748190547
#> lcp     .           .            .           -0.06349802 -0.101736983
#> gleason .           .            .            .           0.042445101
#> pgg45   0.01256831  0.006710624  0.005389947  0.00498825  0.004541638
  
fit <- biglasso_path(X = X.bm, y = y, r = y, init = init, xtx = xtx,
  lambda = c(0.5, 0.1, 0.05, 0.01, 0.001), penalty='MCP',
  penalty.factor=c(0, rep(1, ncol(X)-1)), max.iter = 2000)
fit$beta
#> 9 x 5 sparse Matrix of class "dgCMatrix"
#>                                                                         
#>          1.648298073 -0.115420660  0.494158018  0.187554573  0.187527451
#> lcavol   0.667634641  0.600386232  0.569551761  0.564445466  0.564444994
#> lweight  .            0.753123645  0.613981343  0.621790535  0.621791579
#> age     -0.003182706 -0.017330406 -0.020888578 -0.021242328 -0.021242354
#> lbph     .            0.007112865  0.097369534  0.096738824  0.096738703
#> svi      .            .            0.752459039  0.761518580  0.761519278
#> lcp      .            .           -0.104951529 -0.106015242 -0.106015402
#> gleason  .            .            .            0.048346251  0.048350230
#> pgg45    0.005416757  0.006411446  0.005322958  0.004471521  0.004471458