The random forest classifier (Breiman, 2001) is
based on an ensemble of K classification trees. Sup-
pose the training set T has N samples. The training
set for each tree is formed by drawing N samples with
replacement from T . At each node, a subset of the in-
put variables is randomly picked for splitting. After
training, an input vector is presented to all K trees.
The majority among the K decisions is the overall de-
cision of the random forest classifier. The parameter
of the random forest is K, the number of trees in the
ensemble.
An artificial feedforward neural network has neu-
rons organized as three layers, viz. the input, the
hidden, and the output layers. Each neuron forms a
weighted sum of the inputs and a bias. The sum is
then passed through a nonlinearity, typically a tanh
function, to form the intput to the next layer or as the
output. Training is performed using the entire training
set T through the backpropagation algorithm. The pa-
rameter of the neural network is the number of neu-
rons in the hidden layer.
The Naive Bayes classifier uses a maximum a pos-
teriori rule, with the assumption that the input vari-
ables are independent, so that the joint class density is
the product of individual class densities. The training
set is used to estimate the individual class densities.
The support vector machine (Cortes and Vapnik,
1995) finds a separating hyperplane between the two
classes by balancing the classification error, weighted
by a cost term C, and the complexity of the hyper-
plane. To solve non-separable cases, the input vec-
tors are mapped to a higher dimensional space, often
via a kernel function such as a radial basis function
parameterized by γ, which controls the spread of the
function.
3 EXPERIMENTAL RESULTS
We have a set of 10 positive feedback features X =
{x
i
: i = 1,·· · ,10} and a set of 10 negative feedback
features Y = {y
i
: i = 1,··· ,10}. We have two pre-
diction problems: (i) to predict a hospital that is “bet-
ter” than the national benchmark; and (ii) to predict a
hospital that is “worse” than the national benchmark.
Using different combinations of input, there can be 6
experiments:
0. Use X to predict “better” hospitals;
1. Use Y to predict “better” hospitals;
2. Use X ∪Y to predict “better” hospitals;
3. Use X to predict “worse” hospitals;
4. Use Y to predict “worse” hospitals;
5. Use X ∪Y to predict “better” hospitals.
For each prediction task, corresponding to the six in-
fections we assemble six data sets, each with ten or
twenty input features and one target output. We use
the hospital ID to match the input HCAHPS response
vector with the target derived from the HAI perfor-
mance label. For each of the experiments, we use the
same protocol as follows. Each input feature is cen-
tered around 0 and scaled to have unit variance. Our
goal is to predict, for a hospital, whether it is better (or
worse) than the U.S. benchmark given the 10 (or 20)
HCAHPS-derived input features. We assign the target
value “+1” when the hospital has a label “better than
U.S. national benchmark” and the target value “−1”
otherwise when predicting a “better” hospital. Simi-
larly, we assign the target value “+1” when the hospi-
tal has a label “worse than U.S. national benchmark”
and the target value “−1” otherwise when predicting
a “worse” hospital. A hospital with a label “similar to
the U.S. national benchmark” will therefore have the
target value “−1” in both cases.
Experiment (0) was previously reported in (Pratt
and Chu, 2016) and the results are not repeated here.
We describe our results for experiments (1) through
(5) in the following. We partition the data set using
75% for training and 25% for test. From the train-
ing set, we use 50% to tune the classifier parameters.
This smaller set is partitioned into 75% for training
and 25% for test to obtain the best set of parameters.
The parameter for the neural network is the number of
hidden units. We use the radial basis function in the
support vector machine. The parameters for it are the
cost parameter and γ of the radial basis function. We
note that when we use 20 input variables, some larger
classifiers such as a neural network with 17 hidden
units or a random forest with 875 trees are deployed.
The prediction accuracies for each classifier for
each infection for the five experiments are shown in
Tables 1, 2, 3, 4, and 5. We show the bar plots of the
accuracies of two cases, both for predicting whether
a hospital is worse than the U.S. national benchmark.
We show the results for CAUTI, which has somewhat
balanced “better” and “worse” counts, in Fig. 1. In
Fig. 2, we show the results for C.diff, which has al-
most twice as many We show a third case, this time for
predicting whether a hospital is better than the U.S.
national benchmark when the HAI is CAUTI. Com-
paring Fig. 1 and Fig. 3, we see that while the accura-
cies are comparable, those for predicting a better hos-
pital are better for this infection. The performances of
the four classifiers relative to each other are consistent
for the two predictions.
We can see that the smallest data set (viz. “SSI:
Hysterectomy”) has the highest prediction accuracies
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