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DMRnet (Delete or Merge Regressors) is a suit of algorithms for linear and logistic model selection with high-dimensional data (i.e. the number of regressors may exceed the number of observations). The predictors can be continuous or categorical. The selected model consists of a subset of numerical regressors and partitions of levels of factors.
For information on how to get started using DMRnet, see our getting started vignette.
DMRnet
packageTo install the development package version please execute
library(devtools)
devtools::install_github("SzymonNowakowski/DMRnet")Alternatively, to install the current stable CRAN version please execute
install.packages("DMRnet")After that, you can load the installed package into memory with a
call to library(DMRnet).
A new cross validation routine was introduced to improve the computed
model quality. It indexes models by GIC. The method was proposed and
first implemented for gaussian family by Piotr Pokarowski.
Since 0.3.1 version of the package it has been built into
DMRnet for both gaussian and binomial
families.
All in all, the cross validation features in the package are the following:
Models can be indexed by GIC or by model dimension. The relevant
setting is selected with, respectively,
indexation.mode="GIC" or
indexation.mode="dimension" parameter in a call to
cv.DMRnet(). The setting that indexes models by GIC has
been the default since 0.3.1 version of the package.
The net of lambda values is first calculated from the full data set and then this net is used for particular cross validation folds. The motivation behind this change is to stabilize the results.
Apart from df.min, which is the model with minimal
cross-validated error, the routines now return df.1se which
is the smallest model falling under the upper curve of a prediction
error plus one standard deviation. It can be used in
predict() for inference by passing md="df.1se"
instead of the default md="df.min".
Cross validation handles the mismatched factor levels in a way that minimizes incorrect behavior (see Section Handling of mismatched factor levels).
The new treatment of factors in cross validation/predict
and in DMRnet/predict pairs is based on the
following analysis:
Let us assume that - Xtr is training data in cross
validation or in a regular call via
DMRnet->model - Xte is test
data in cross validation or in a regular call via
model->predict
Without loss of generality, let us consider Xtr and
Xte to be one column only, with factors.
Let us also consider the following definitions: - A is a
true set of all factor levels in Xtr - B is a
true set of all factor levels in Xte -
C=levels(Xtr) is a set of factor levels in original data
that Xtr originates from, but it is still assigned to
Xtr via the levels() function. As a rule, when
taking subsets, R does not eliminate redundant factors, so
let us note that C is a superset of A.
There are 4 classes of problems:
C is a strict superset of A.
Then, if treated naively, DMRnet(...) when constructing
a model would throw an error, because we would end up with
NaN values in a column dedicated to this superfluous factor
level (to be exact, it would happen when columns get normalized).
The solution to that is straightforward. Before the model gets
constructed in DMRnet we recalculate the factor level set,
C_new. Then C_new=A.
SOLVED
B does not contain a level(s) present in
A.
(sample case: we did sample to Xtr the single Dutch
national from the Insurance
data set, and he is not present in Xte, because there
is only one instance of Dutch national in the whole Insurance data set).
As a result predict(...) would throw an error, because
expanded model-matrix dimensions would be conflicting.
The solution is simple here, too: in constructing a model make a note
about the true A set (technically, it gets stored into
levels.listed variable in a model) and then in
predict(...) assign the levels of Xte to be
equal to A. Only then create the model-matrix.
SOLVED
B contains a factor level(s) not present in
A, AND we are doing CV, so we have access to
Xtr.
The solution is to remove the rows with levels that are going to
cause problems later in predict(...) from Xte
before the prediction. The other solution would be to predict using
unknown.factor.levels=“NA” flag and then eliminate the NAs
from comparisons (this solution is NOT used at present)
SOLVED
B contains a factor level(s) not present in
A, AND we are NOT doing CV, so we have no access to
Xtr.
This case is problematic because this situation gets identified too
late - we are already in predict(...). At this point, only
the model created by DMRnet(...) function (which got passed
into predict(...) function) is known. We cannot perform
inference and we cannot perform any imputation for the problematic data
point, either (we don’t know Xtr and have no access to
it).
All that remains is to throw an error (when
unknown.factor.levels="error", the default) OR eliminate
the problematic rows, predict, and then replenish the result with
NAs in place of problematic values (when
unknown.factor.levels="NA").
None of this solutions is fully satisfactory, thus this case remains PROBLEMATIC.
Generally speaking, matrix rank in real world scenarios is more a
numerical concept than a mathematical concept and its value may differ
depending on a threshold. Thus various kinds of problems result from
data matrices close to singular. Since 0.3.1 version of the package, the
work has been devoted to improve stability of computations with such
ill-defined matrices. See NEWS.md for more information on
detailed stability improvements.
This remains to be introduced to PDMR, GLAMER and DMRnet algorithms in future versions.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.