gamlr {gamlr} | R Documentation |
Adaptive L1 penalized regression estimation.
gamlr(x, y, family=c("gaussian","binomial","poisson"), gamma=0,nlambda=100, lambda.start=Inf, lambda.min.ratio=0.01, free=NULL, standardize=TRUE, obsweight=NULL,varweight=NULL, prexx=(p<500), tol=1e-7,maxit=1e5,verb=FALSE, ...) ## S3 method for class 'gamlr' plot(x, against=c("pen","dev"), col=NULL, select=TRUE, df=TRUE, ...) ## S3 method for class 'gamlr' coef(object, select=NULL, k=2, corrected=TRUE, ...) ## S3 method for class 'gamlr' predict(object, newdata, type = c("link", "response"), ...) ## S3 method for class 'gamlr' logLik(object, ...)
x |
A dense |
y |
A vector of response values.
There is almost no argument checking,
so be careful to match |
family |
Response model type;
either "gaussian", "poisson", or "binomial".
Note that for "binomial", |
gamma |
Penalty concavity tuning parameter; see details. Zero (default) yields the lasso, and higher values correspond to a more concave penalty. |
nlambda |
Number of regularization path segments. |
lambda.start |
Initial penalty value. Default of |
lambda.min.ratio |
The smallest penalty weight
(expected L1 cost) as a ratio of the path start value.
Our default is always 0.01; note that this differs from |
free |
Free variables: indices of the columns of |
standardize |
Whether to standardize the coefficients to have standard deviation of one. This is equivalent to multiplying the L1 penalty by each coefficient standard deviation. |
obsweight |
For |
varweight |
Multipliers on the penalty associated with each covariate coefficient. Must be non-negative. These are further multiplied by sd(x_j) if |
prexx |
Only possible for |
tol |
Optimization convergence tolerance relative to the null model deviance for each inner coordinate-descent loop. This is measured against the maximum coordinate change times deviance curvature after full parameter-set update. |
maxit |
Max iterations for a single segment coordinate descent routine. |
verb |
Whether to print some output for each path segment. |
object |
A gamlr object. |
against |
Whether to plot paths against log penalty or deviance. |
select |
In In |
k |
If |
corrected |
A flag that swaps corrected (for high dimensional bias) |
newdata |
New |
type |
Either "link" for the linear equation,
or "response" for predictions transformed
to the same domain as |
col |
A single plot color,
or vector of length |
df |
Whether to add to the plot degrees of freedom along the top axis. |
... |
Extra arguments to each method. Most importantly, from
|
Finds posterior modes along a regularization path of adapted L1 penalties via coordinate descent.
Each path segment t minimizes the objective -(φ/n)logLHD(β_1
... β_p) + ∑ ω_jλ|β_j|, where φ is the
exponential family dispersion parameter (σ^2 for
family="gaussian"
, one otherwise). Weights ω_j are
set as 1/(1+γ|b_j^{t-1}|) where b_j^{t-1} is our estimate of β_j for the previous path segment (or zero if t=0). This adaptation is what makes the penalization ‘concave’; see Taddy (2013) for details.
plot.gamlr
can be used to graph the results: it
shows the regularization paths for penalized β, with degrees of freedom along the top axis and minimum AICc selection marked.
logLik.gamlr
returns log likelihood along the regularization path. It is based on the deviance
, and is correct only up to static constants;
e.g., for a Poisson it is off by ∑_i y_i(\log y_i-1) (the saturated log likelihood) and for a Gaussian it is off by likelihood constants (n/2)(1+\log2π).
lambda |
The path of fitted prior expected L1 penalties. |
nobs |
The number of observations. |
alpha |
Intercepts. |
beta |
Regression coefficients. |
df |
Approximate degrees of freedom. |
deviance |
Fitted deviance: (-2/φ)( logLHD.fitted - logLHD.saturated ). |
iter |
Number of optimization iterations by segment, broken into coordinate descent cycles and IRLS re-weightings for |
family |
The exponential family model. |
Under prexx=TRUE
(requires family="gaussian"
), weighted covariances (VX)'X and (VX)'y, weighted column sums of VX, and column means \bar{x} will be pre-calculated. Here V is the diagonal matrix of least squares weights (obsweights
, so V defaults to I). It is not necessary (they will be built by gamlr
otherwise), but you have the option to pre-calculate these sufficient statistics yourself as arguments vxx
(matrix
or dspMatrix
), vxy
, vxsum
, and xbar
(all vectors
) respectively. Search PREXX
in gamlr.R
to see the steps involved, and notice that there is very little argument checking – do at your own risk. Note that xbar
is an unweighted calculation, even if V \neq I. For really Big Data you can then run with x=NULL
(e.g., if these statistics were calculated on distributed machines and full design is unavailable). Beware: in this x=NULL
case our deviance (and df, if gamma>0
) calculations are incorrect and selection rules will always return the smallest-lambda model.
Matt Taddy mataddy@gmail.com
Taddy (2017 JCGS), One-Step Estimator Paths for Concave Regularization, http://arxiv.org/abs/1308.5623
cv.gamlr, AICc, hockey
### a low-D test (highly multi-collinear) n <- 1000 p <- 3 xvar <- matrix(0.9, nrow=p,ncol=p) diag(xvar) <- 1 x <- matrix(rnorm(p*n), nrow=n)%*%chol(xvar) y <- 4 + 3*x[,1] + -1*x[,2] + rnorm(n) ## run models to extra small lambda 1e-3xlambda.start fitlasso <- gamlr(x, y, gamma=0, lambda.min.ratio=1e-3) # lasso fitgl <- gamlr(x, y, gamma=2, lambda.min.ratio=1e-3) # small gamma fitglbv <- gamlr(x, y, gamma=10, lambda.min.ratio=1e-3) # big gamma par(mfrow=c(1,3)) ylim = range(c(fitglbv$beta@x)) plot(fitlasso, ylim=ylim, col="navy") plot(fitgl, ylim=ylim, col="maroon") plot(fitglbv, ylim=ylim, col="darkorange")