The {dglm} package provide “deep” versions of (generalized) linear
models with an interface that is designed to follow those of standard
regression routines (lm(), glm(), and coxph()) as closely as
possible while providing the ability to fit non-linear relationships
among data. The package implements these model fitting routines through
two functions that prepend a “d” in front of their linear-model
analogues.
dglm()regress variables onto count, continuous, or categorical variables.dcoxph()regress variables onto survival data.
In addition common associated methods including summary(), update(),
and predict() are implemented along with others to facilitate the
validating, examining, characterizing, updating, and predicting with
these models.
Deep learners, regressing tensors of order two (matrics) onto tensors of order one (vectors), can be thought of as non-linear generalizations of linear models. For example, consider the linear model:
yi = xi1 β1 + xi2 β2 + xi3 β3+ ...
We can rewrite this as
yi = f0( xi⋅ )
where f0 is a linear combination of the values in the vector xi⋅ – a deep learner with no hidden layers. Likewise, a logistic regression can be written as:
log ( yi / (1−yi) ) = f0( xi⋅ )
where yi is a zero-one variable. Any generalized linear model, including survival models, fits into a similar construction and we can extend these models to capture non-linear predictive information with respect to the dependent variable.
The package is not currently available on CRAN but you can install the development version of this package from GitHub with the following code
devtools::install_github("kaneplusplus/dlm")
library(keras)
library(dlrm)
# Regress iris variables onto Species (categorical) and get the accuracy.
fit_dlmcat <- dlr(iris, Species ~ ., hidden_layers = 16, epochs = 100)
sum(iris$Species == dlr_predict(iris, fit_dlmcat)) / nrow(iris)
#> [1] 0.6933333
# Regress iris variables onto Sepal.Length using a linear model and get the
# in-sample prediction accuracy.
fit_linear <- lm(Sepal.Length ~ ., iris)
sd(predict(fit_linear, iris))
#> [1] 0.7711747
# Perform the same operation with a deep learner with two hidden layers
# with 24 and 2 nodes respectively.
fit_dlmc <- dlr(iris, Sepal.Length ~., hidden_layers = c(24, 2))
sd(iris$Sepal.Length - dlr_predict(iris, fit_dlmc))
#> [1] 0.3086302
library(survival)
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
data(lung)
# Handle the categorical variables in lung
lung <- lung %>%
mutate(status = status - 1,
sex = as.factor(sex),
ph.ecog = as.factor(ph.ecog))
# Fit the deep survival model.
dc_fit <- dlcp(
lung,
Surv(time, status) ~ sex + age + meal.cal + wt.loss + ph.ecog,
epochs = 150,
validation_split = .2)
dl_weights <- get_weights(dc_fit$model)[[1]]
# Compare the deep survival model coefficients to coxph.
cfit <- summary(coxph(Surv(time, status) ~ sex + age + meal.cal + wt.loss + ph.ecog, lung))$conf.int
comp <- round(cbind(dl_weights, log(cfit)[,-2]), 3)
colnames(comp) <- c("Deep Learner Coefs", "Cox Coef", "Cox Lower .95", "Cox Upper .95")
comp
#> Deep Learner Coefs Cox Coef Cox Lower .95 Cox Upper .95
#> sex2 -0.115 -0.535 -0.926 -0.143
#> age -0.072 0.008 -0.015 0.030
#> meal.cal -0.003 0.000 -0.001 0.000
#> wt.loss -0.041 -0.012 -0.027 0.003
#> ph.ecog1 -0.055 0.336 -0.122 0.793
#> ph.ecog2 0.059 1.002 0.429 1.576
#> ph.ecog3 0.227 2.086 0.030 4.141
# Plot the training history.
plot_training_history(dc_fit)
#> `geom_smooth()` using formula 'y ~ x'
