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NarrowChurnModel.Rmd
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NarrowChurnModel.Rmd
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```{r}
library(glmnet)
library(gbm)
library(ggplot2)
library(WVPlots) # package code at https://github.com/WinVector/WVPlots
```
**Modeling functions**
```{r functions}
# ridge logistic regression
# assuming xframe is entirely numeric
ridge_predict_function = function(model, varnames) {
# to get around the 'unfullfilled promise' leak. blech.
force(model)
function(xframe) {
as.numeric(predict(model, newx=as.matrix(xframe[,varnames]), type="response"))
}
}
# assuming the xframe is entirely numeric
# if there are categories, we would have to use
# model_matrix, or something
# assuming family is one of c("binomial", "gaussian")
# should have a check for that
ridge_model = function(xframe, y) {
model = glmnet(as.matrix(xframe), y, alpha=0,
lambda=0.001, family="binomial")
varnames = colnames(xframe)
list(coef = coef(model),
deviance = deviance(model),
predfun = ridge_predict_function(model, varnames)
)
}
# gradient boosting functions
gbm_predict_function = function(model, nTrees) {
force(model)
function(xframe) {
predict(model,newdata=xframe,type='response',
n.trees=nTrees)
}
}
gbm_model = function(dframe, formula, weights=NULL) {
if(is.null(weights)) {
nrows = dim(dframe)[1]
weights=numeric(nrows)+1 # all 1
}
modelGBM <- gbm(as.formula(formula),
data=dTrainS,
weights=weights,
distribution='bernoulli',
n.trees=400,
interaction.depth=1, # additive model, to make it compatible with ridge regression
shrinkage=0.05,
bag.fraction=0.5,
keep.data=FALSE,
cv.folds=5)
print(summary(modelGBM))
nTrees <- gbm.perf(modelGBM)
print(nTrees)
list(predfun = gbm_predict_function(modelGBM, nTrees),
varinfs = summary(modelGBM))
}
get_deviance = function(y, pred) {
-2*sum(y*log(pred) + (1-y)*log(1-pred))
}
null_deviance = function(y) {
get_deviance(y, mean(y))
}
# stepwise ridge regression
add_var = function(xframe, y, current_vars, current_dev, candidate_vars) {
best_dev = current_dev
newvar = NULL
for(var in candidate_vars) {
active=c(current_vars, var)
xf = xframe[,active]
if(length(active) > 1) {
model = glmnet(as.matrix(xf), y,
alpha=0, lambda=0.001, family="binomial")
} else {
model =glm.fit(xframe[,active], y, family=binomial(link="logit"))
}
moddev = deviance(model)
if(moddev < best_dev) {
newvar = var
best_dev = moddev
}
}
improvement = 1 - (best_dev/current_dev)
list(current_vars= c(current_vars, newvar),
current_dev = best_dev,
improvement = improvement)
}
# evaluate model on holdout
evaluate = function(model, data, y, label) {
pred = model$predfun(data)
deviance = get_deviance(y, pred)
predictedToLeave = pred>0.5
# confusion matrix
cmat = table(pred=predictedToLeave, actual=y)
recall = cmat[2,2]/sum(cmat[,2])
precision = cmat[2,2]/sum(cmat[2,])
accuracy = sum(diag(cmat))/sum(cmat)
data.frame(label=label, deviance=deviance, recall=recall, precision=precision, accuracy=accuracy)
}
# xvar is integral
dist_and_mean = function(frm, xvar, title, meanlabel) {
meanval = mean(frm[[xvar]])
mode = max(table(frm[[xvar]]))
print(paste("Mean days until exit:", meanval))
DiscreteDistribution(frm, xvar, title=title) +
geom_vline(xintercept=meanval, color="blue", linetype=2)+
annotate("text", x=meanval, y=mode,
hjust=0, vjust=0,
label=meanlabel,
color="blue")
}
# same as above, but I'm using the filters to identify the set of interest,
# and the baseline counts
dist_and_mean_with_comparison = function(frm, model_filter, base_filter, xvar, title, meanlabel) {
pmod = dist_and_mean(frm[model_filter, ], xvar, title, meanlabel)
pmod +stat_summary(data=frm[base_filter,], aes(x=daysToX, y=1, ymin=0),
fun.y=sum, fun.ymax=sum, geom="linerange", size=5, alpha=0.25, color="darkgreen")
}
# evaluate model on timeliness.
evaluate_timeliness = function(model, hdata, y, label) {
pred = model$predfun(hdata)
deviance = get_deviance(y, pred)
hdata$predictedToLeave = pred>0.5
# fix the Infs in the data
isInf = hdata$daysToX == Inf # shouldn't be many of them
maxfinite = max(hdata$daysToX[!isInf])
hdata$daysToX[isInf] = maxfinite
# how long on average until flagged customers leave?
posmean = mean(hdata[hdata$predictedToLeave, "daysToX"])
print(paste(label, ":Flagged customers leave in", posmean, "days on average"))
# how long on average until unflagged customers leave?
negmean = mean(hdata[!hdata$predictedToLeave, "daysToX"])
print(paste(label, ":Unflagged customers leave in", negmean, "days on average"))
# how long until identified true positives leave?
tpfilter = hdata$predictedToLeave & hdata[[yVar]]
tpmean = mean(hdata[tpfilter, "daysToX"])
print(paste(label, ":True positive flagged customers leave in", tpmean, "days on average"))
print(dist_and_mean_with_comparison(hdata, model_filter=tpfilter, base_filter=y, "daysToX",
paste(label, "Distribution of days til exit, true positives"),
"mean days til exit"))
print(ScatterBoxPlot(hdata, "predictedToLeave", "daysToX", pt_alpha=0.2,
title=paste(label, "Distribution of days til exit")))
}
gainplot = function(model, data, yvar, label) {
data$pred = model$predfun(data)
data$predictedToLeave = data$pred > 0.5
GainCurvePlot(data, "pred", yvar, title=label)
}
# returns final set of variables, along with improvements and deviances
# use the variables to refit the final model
stepwise_ridge = function(data, vars, yVar, min_improve=1e-6) {
current_vars=c()
candidate_vars = vars
devs = numeric(length(vars))
improvement = numeric(length(vars))
current_dev=null_deviance(data[[yVar]])
do_continue=TRUE
while(do_continue) {
iter = add_var(data, data[[yVar]], current_vars, current_dev, candidate_vars)
current_vars = iter$current_vars
current_dev = iter$current_dev
count = length(current_vars)
devs[count] = current_dev
improvement[count] = iter$improvement
candidate_vars = setdiff(vars, current_vars)
# print(current_vars)
do_continue = (length(candidate_vars) > 0) && (iter$improvement > min_improve)
}
list(current_vars = current_vars, deviances=devs, improvement=improvement)
}
```
**Modeling**
First, null model and wide ridge model
```{r basemodels}
# loads vars (names of vars), yVar (name of y column),
# dTrainS, dTestS
load("wideData.rData")
# number of candiate variables
length(vars)
# fix the Infs in the training data
isInf = dTrainS$daysToX == Inf # shouldn't be many of them
maxfinite = max(dTrainS$daysToX[!isInf])
dTrainS$daysToX[isInf] = maxfinite
# null deviance
null_deviance(dTrainS[[yVar]])
# model using all variables
allvar_model = ridge_model(dTrainS[,vars], dTrainS[[yVar]])
deviance(allvar_model)
```
Next, the greedy forward stepwise regression
```{r stepmodel}
modelparams = stepwise_ridge(dTrainS, vars, yVar)
current_vars = modelparams$current_vars
devs = modelparams$deviances
improvement=modelparams$improvement
# number of variables selected
length(current_vars)
# display the selected windows
current_vars
final_model = ridge_model(dTrainS[,current_vars], dTrainS[[yVar]])
final_model$deviance
```
Examine the incremental model performance
```{r stepexam}
numvars = length(current_vars)
plotframe = data.frame(nvars=1:numvars, deviance = devs[1:numvars], improvement = improvement[1:numvars])
ggplot(plotframe, aes(x=nvars, y=deviance)) + geom_point() + geom_line()
ggplot(plotframe, aes(x=nvars, y=improvement)) + geom_point() + geom_line()
```
Depending on how you interpret the improvement graph, you want 2 variables (the max), 4, or 6 variables (the "elbow").
```{r smallmodels}
final2_model = ridge_model(dTrainS[,current_vars[1:2]], dTrainS[[yVar]])
final4_model = ridge_model(dTrainS[,current_vars[1:4]], dTrainS[[yVar]])
final6_model = ridge_model(dTrainS[,current_vars[1:6]], dTrainS[[yVar]])
deviance(final2_model)
deviance(final4_model)
deviance(final6_model)
```
Compare all the (non-trivial) models.
```{r compare1}
rbind(evaluate(allvar_model, dTestS, dTestS[[yVar]], "all variables"),
evaluate(final_model, dTestS, dTestS[[yVar]], "stepwise run"),
evaluate(final2_model, dTestS, dTestS[[yVar]], "best 2 variables"),
evaluate(final4_model, dTestS, dTestS[[yVar]], "best 4 variables"),
evaluate(final6_model, dTestS, dTestS[[yVar]], "best 6 variables"))
```
**Evaluation**
Pick the best model, and evaluate it and its timeliness on hold-out data
```{r eval1}
bestridge_model = final6_model
bestn = 6
gainplot(bestridge_model, dTestS, yVar, paste("Stepwise ridge,", bestn, "best variables"))
evaluate_timeliness(final6_model, dTestS, dTestS[[yVar]], paste("Stepwise ridge,", bestn, "best variables"))
```
**Gradient Boosting**
Just for fun, lets look at the gradient boosting solution
```{r gbm}
set.seed(43534656) # just so this reproduces
formula = paste(yVar, "~", paste(vars, collapse="+"))
modelGBM = gbm_model(dTrainS, formula)
# compare to the best ridge model
rbind(evaluate(bestridge_model, dTestS, dTestS[[yVar]], "best stepwise model"),
evaluate(modelGBM, dTestS, dTestS[[yVar]], "gbm model, interaction=1"))
gainplot(modelGBM, dTestS, yVar, "GBM, interaction level=1")
evaluate_timeliness(modelGBM, dTestS, dTestS[[yVar]], "GBM, interaction level=1")
```
What did the gbm model miss?
```{r difference}
# the exiting customers that the ridge model identified
ridge_tp = (bestridge_model$predfun(dTestS) > 0.5) & dTestS[[yVar]]
# the exiting customers the gbm model identified
gbm_tp = (modelGBM$predfun(dTestS) > 0.5) & dTestS[[yVar]]
sum(ridge_tp)
sum(gbm_tp)
# what did gbm miss that ridge found?
not_gbm = ridge_tp &! gbm_tp
sum(not_gbm)
table(dTestS[not_gbm, "daysToX"])
# what did ridge miss that gbm found?
not_ridge = gbm_tp & !ridge_tp
sum(not_ridge)
table(dTestS[not_ridge, "daysToX"])
```
One last crazy experiment. What if we use the variables that gbm chose?
```{r gnm_varselect}
ggplot(modelGBM$varinfs[1:20,], aes(x=1:20, y=rel.inf)) + geom_point() + geom_line()
# the elbow is either at 3 or 7. Let's use 7
usevars = as.character(modelGBM$varinfs$var[1:7])
# build a logistic regression model with these variables
model_gbmvars = ridge_model(dTrainS[,usevars], dTrainS[[yVar]])
# build a gbm with these variables
fmla = paste(yVar, "~", paste(usevars, collapse="+"))
model_gbmsmall = gbm_model(dTrainS, fmla)
rbind(evaluate(bestridge_model, dTestS, dTestS[[yVar]], "best stepwise model"),
evaluate(modelGBM, dTestS, dTestS[[yVar]], "gbm model, interaction=1"),
evaluate(model_gbmvars, dTestS, dTestS[[yVar]], "ridge model with best gbm variables"),
evaluate(model_gbmsmall, dTestS, dTestS[[yVar]], "gbm model with best gbm variables"))
gainplot(model_gbmvars, dTestS, yVar, "ridge model with best gbm variables")
evaluate_timeliness(model_gbmvars, dTestS, dTestS[[yVar]], "ridge model with best gbm variables")
evaluate_timeliness(model_gbmsmall, dTestS, dTestS[[yVar]], "gbm model with best gbm variables")
```