AS10-3 SPAM or HAM
孟祥瑄 Kahlen
2018年8月19日
packages = c(
"dplyr","ggplot2","caTools","tm","SnowballC","ROCR","rpart",
"rpart.plot","randomForest")
existing = as.character(installed.packages()[,1])
for(pkg in packages[!(packages %in% existing)]) install.packages(pkg)rm(list=ls(all=TRUE))
Sys.setlocale("LC_ALL","C")## [1] "C"options(digits=5, scipen=10)
library(dplyr)
library(tm)
library(SnowballC)
library(ROCR)
library(caTools)
library(rpart)
library(rpart.plot)
library(randomForest)Problem 1 - Exploration
Begin by loading the dataset emails.csv into a data frame called emails. Remember to pass the stringsAsFactors=FALSE option when loading the data.
emails= read.csv("data/emails.csv", stringsAsFactors = F)1.1 How many emails are in the dataset?
- 5728
1.2 How many of the emails are spam?
table(emails$spam)##
## 0 1
## 4360 1368- 1368
1.3 Which word appears at the beginning of every email in the dataset?
substr(emails$text[1:5], 1, 60) #Extract or replace substrings in a character vector.## [1] "Subject: naturally irresistible your corporate identity lt "
## [2] "Subject: the stock trading gunslinger fanny is merrill but "
## [3] "Subject: unbelievable new homes made easy im wanting to sho"
## [4] "Subject: 4 color printing special request additional inform"
## [5] "Subject: do not have money , get software cds from here ! s"#head(emails$text)- subjects
1.4 Words in every document
【P1.4】Could a spam classifier potentially benefit from including the frequency of the word that appears in every email?
- Yes – the number of times the word appears might help us differentiate spam from ham.
1.5 How many characters are in the longest email?
nchar(emails$text) %>% max## [1] 439521.6 Which row contains the shortest email in the dataset?
nchar(emails$text) %>% which.min## [1] 1992Problem 2 - Preparing the Corpus
2.1 Corpus and DTM
Follow the standard steps to build and pre-process the corpus:
- Build a new corpus variable called corpus.
- Using tm_map, convert the text to lowercase.
- Using tm_map, remove all punctuation from the corpus.
- Using tm_map, remove all English stopwords from the corpus.
- Using tm_map, stem the words in the corpus.
- Build a document term matrix from the corpus, called dtm.
If the code length(stopwords(“english”)) does not return 174 for you, then please run the line of code in this file, which will store the standard stop words in a variable called sw. When removing stop words, use tm_map(corpus, removeWords, sw) instead of tm_map(corpus, removeWords, stopwords(“english”)).
corpus = Corpus(VectorSource(emails$text))
corpus = tm_map(corpus, content_transformer(tolower)) ## Warning in tm_map.SimpleCorpus(corpus, content_transformer(tolower)):
## transformation drops documentscorpus = tm_map(corpus, removePunctuation)## Warning in tm_map.SimpleCorpus(corpus, removePunctuation): transformation
## drops documentscorpus = tm_map(corpus, removeWords, stopwords("english"))## Warning in tm_map.SimpleCorpus(corpus, removeWords, stopwords("english")):
## transformation drops documentscorpus = tm_map(corpus, stemDocument)## Warning in tm_map.SimpleCorpus(corpus, stemDocument): transformation drops
## documentsdtm = DocumentTermMatrix(corpus)
dtm## <<DocumentTermMatrix (documents: 5728, terms: 28687)>>
## Non-/sparse entries: 481719/163837417
## Sparsity : 100%
## Maximal term length: 24
## Weighting : term frequency (tf)How many terms are in dtm?
- 28687
2.2 Remove less frequent words
To obtain a more reasonable number of terms, limit dtm to contain terms appearing in at least 5% of documents, and store this result as spdtm (don’t overwrite dtm, because we will use it in a later step of this homework).
spdtm= removeSparseTerms(dtm, 0.95)
spdtm## <<DocumentTermMatrix (documents: 5728, terms: 330)>>
## Non-/sparse entries: 213551/1676689
## Sparsity : 89%
## Maximal term length: 10
## Weighting : term frequency (tf)【P2.2】How many terms are in spdtm?
- 330
2.3 Build data frame
Build a data frame ems from spdtm
ems = as.data.frame(as.matrix(spdtm))【P2.3】What is the most frequent word in spdtm?
colSums(ems) %>% sort %>% tail## hou will vinc subject ect enron
## 5577 8252 8532 10202 11427 13388- enron
2.4 Most frequent words in HAM emalis
Add a variable called “spam” to emailsSparse containing the email spam labels. You can do this by copying over the “spam” variable from the original data frame (remember how we did this in the Twitter lecture).
Incorporate target variable spam
ems$spam = emails$spamHow many word stems appear at least 5000 times in the ham emails in the dataset? Hint: in this and the next question, remember not to count the dependent variable we just added.
# ham emails即選擇不是spam的，因此令spam==0
subset(ems, spam==0) %>% colSums %>% sort %>% tail(7)## 2000 hou will vinc subject ect enron
## 4935 5569 6802 8531 8625 11417 13388- 6
2.5 Most frequent words in SPAM emalis
【P2.5】How many word stems appear at least 1000 times in the spam emails in the dataset?
subset(ems, spam==1) %>% colSums %>% sort %>% tail()## mail com compani spam will subject
## 917 999 1065 1368 1450 1577- 3
- Note that the variable “spam” is the dependent variable and is not the frequency of a word stem.
2.6 Observation 1
【P2.6】The lists of most common words are significantly different between the spam and ham emails. What does this likely imply?
- The frequencies of these most common words are likely to help differentiate between spam and ham.
2.7 Observation 2
【P2.7】Several of the most common word stems from the ham documents, such as “enron”, “hou” (short for Houston), “vinc” (the word stem of “Vince”) and “kaminski”, are likely specific to Vincent Kaminski’s inbox. What does this mean about the applicability of the text analytics models we will train for the spam filtering problem?
- The models we build are personalized, and would need to be further tested before being used as a spam filter for another person.
- The ham dataset is certainly personalized to Vincent Kaminski, and therefore it might not generalize well to a general email user. Caution is definitely necessary before applying the filters derived in this problem to other email users. 資料顯然相當個人化，要注意此預測個人可能會有相當的準確度，但較缺乏一般性
Problem 3 - Building machine learning models
First, convert the dependent variable to a factor with “emailsSparse\(spam = as.factor(emailsSparse\)spam)”.
Next, set the random seed to 123 and use the sample.split function to split emailsSparse 70/30 into a training set called “train” and a testing set called “test”. Make sure to perform this step on emailsSparse instead of emails.
Split the data first
set.seed(123)
ems$spam = as.factor(ems$spam)
names(ems) = make.names(names(ems)) #不用這行跑不出random forest，why?
spl = sample.split(ems$spam, SplitRatio = 0.7)
tr = subset(ems, spl)
ts = subset(ems, !spl)and build
- A logistic regression model called spamLog. You may see a warning message here - we’ll discuss this more later.
A CART model called spamCART, using the default parameters to train the model (don’t worry about adding minbucket or cp). Remember to add the argument method=“class” since this is a binary classification problem.
A random forest model called spamRF, using the default parameters to train the model (don’t worry about specifying ntree or nodesize). Directly before training the random forest model,
set the random seed to 123(even though we’ve already done this earlier in the problem, it’s important to set the seed right before training the model so we all obtain the same results. Keep in mind though that on certain operating systems, your results might still be slightly different).
#1 GLM
glm = glm(spam~., tr, family = "binomial")## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred#2 CART
cart= rpart(spam~., tr, method = "class")
#3 random forest
set.seed(123)
rf= randomForest(spam~., data=tr)3.1 Prediction of Logistic Model
predglm = predict(glm, type="response")【P3.1a】 How many of the training set predicted probabilities from spamLog are less than 0.00001?
sum(predglm < 0.00001)## [1] 3046【P3.1b】 How many of the training set predicted probabilities from spamLog are more than 0.99999?
sum(predglm>0.99999)## [1] 954【P3.1c】 How many of the training set predicted probabilities from spamLog are between 0.00001 and 0.99999?
sum(predglm > 0.00001 & predglm < 0.99999)## [1] 103.2 Significant predictors in the GLM model
【P3.2】How many variables are labeled as significant (at the p=0.05 level) in the logistic regression summary output?
summary(glm)##
## Call:
## glm(formula = spam ~ ., family = "binomial", data = tr)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.01 0.00 0.00 0.00 1.35
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -30.8167 10548.7431 0.00 1.00
## busi -4.8029 10002.2892 0.00 1.00
## chang -27.1680 22152.8907 0.00 1.00
## compani 4.7813 9186.3255 0.00 1.00
## corpor -0.8286 28181.3478 0.00 1.00
## day -6.0998 5866.2876 0.00 1.00
## done 6.8284 18822.0500 0.00 1.00
## effect 19.4824 21002.4128 0.00 1.00
## effort 16.0582 56700.5791 0.00 1.00
## even -16.5389 22886.6379 0.00 1.00
## full 21.2510 21904.3401 0.00 1.00
## good 5.3994 16193.4281 0.00 1.00
## inform 20.7808 8549.0245 0.00 1.00
## interest 26.9804 11587.5921 0.00 1.00
## list -8.6921 2148.9795 0.00 1.00
## look -7.0307 15631.4459 0.00 1.00
## made 2.8205 27432.2618 0.00 1.00
## make 29.0054 15276.3527 0.00 1.00
## manag 6.0145 14452.5449 0.00 1.00
## market 7.8952 8012.2953 0.00 1.00
## much 0.3775 13921.5777 0.00 1.00
## order 6.5327 12424.0848 0.00 1.00
## origin 32.2628 38175.2472 0.00 1.00
## product 10.1584 13447.6403 0.00 1.00
## provid 0.2423 18589.0873 0.00 1.00
## realli -26.6685 46403.4563 0.00 1.00
## result -0.5002 31401.0516 0.00 1.00
## see -11.1990 12932.4679 0.00 1.00
## special 17.7707 27552.3644 0.00 1.00
## subject 30.4112 10548.7431 0.00 1.00
## system 3.7780 9148.6586 0.00 1.00
## use -13.8535 9381.7631 0.00 1.00
## websit -25.6266 18475.0280 0.00 1.00
## will -11.1938 5980.4800 0.00 1.00
## within 29.0029 21632.4965 0.00 1.00
## without 19.4198 17628.7430 0.00 1.00
## continu 14.8661 15351.2387 0.00 1.00
## group 0.5264 10371.4780 0.00 1.00
## like 5.6494 7659.8787 0.00 1.00
## trade -17.5502 14825.1007 0.00 1.00
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## home 5.9729 8964.8271 0.00 1.00
## new 1.0033 10091.5253 0.00 1.00
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## com 1.9363 4039.2049 0.00 1.00
## fax 3.5370 33855.8899 0.00 1.00
## mail 7.5837 10210.9569 0.00 1.00
## messag 17.1570 2561.5756 0.01 0.99
## now 37.8968 12190.2490 0.00 1.00
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## version -36.0636 29386.8036 0.00 1.00
## best -8.2005 1333.3866 -0.01 1.00
## end -13.1054 29380.6882 0.00 1.00
## get 5.1538 9737.0707 0.00 1.00
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## money 32.6355 13212.0683 0.00 1.00
## softwar 25.7485 10593.0947 0.00 1.00
## custom 18.2882 10079.0874 0.00 1.00
## hello 21.6555 13606.7312 0.00 1.00
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## assist -11.2827 24895.2579 0.00 1.00
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## believ 32.3259 21360.0825 0.00 1.00
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## can 3.7617 7673.8931 0.00 1.00
## cost -1.9376 18329.8873 0.00 1.00
## creat 13.3762 39460.0516 0.00 1.00
## current 3.6291 17066.2426 0.00 1.00
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## event 16.9419 18505.8473 0.00 1.00
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## invest 32.0125 23934.4148 0.00 1.00
## involv 38.1486 33152.6085 0.00 1.00
## just -10.2116 11140.8256 0.00 1.00
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## may -9.4339 13969.5651 0.00 1.00
## mean 0.6078 29518.7119 0.00 1.00
## mention -22.7859 27136.9157 0.00 1.00
## might 12.4416 17533.0051 0.00 1.00
## month -3.7267 11123.6690 0.00 1.00
## need 0.8437 12207.6171 0.00 1.00
## note 14.4603 22937.8916 0.00 1.00
## number -9.6218 15914.5979 0.00 1.00
## offic -13.4416 23114.7234 0.00 1.00
## oper -16.9570 27565.6010 0.00 1.00
## person 18.6976 9575.4766 0.00 1.00
## posit -15.4311 23155.9923 0.00 1.00
## possibl -13.6596 24918.1573 0.00 1.00
## present -6.1630 12775.0563 0.00 1.00
## price 3.4276 7849.8596 0.00 1.00
## problem 12.6202 9763.0319 0.00 1.00
## process -0.2957 11905.8484 0.00 1.00
## project 2.1733 14973.0515 0.00 1.00
## read -15.2745 21446.7493 0.00 1.00
## relat -51.1383 17926.4612 0.00 1.00
## report -14.8212 14769.9198 0.00 1.00
## requir 0.5004 29365.4547 0.00 1.00
## research -28.2590 15526.4663 0.00 1.00
## resourc -27.3489 35221.0605 0.00 1.00
## return 17.4510 18435.1876 0.00 1.00
## review -4.8245 10132.7968 0.00 1.00
## risk -4.0008 17177.9984 0.00 1.00
## secur -16.0368 2200.7143 -0.01 0.99
## servic -7.1643 12351.2210 0.00 1.00
## set -9.3532 26268.8952 0.00 1.00
## short -8.9735 17207.5148 0.00 1.00
## specif -23.3669 30834.2029 0.00 1.00
## state 12.2075 16772.1315 0.00 1.00
## term 20.1329 23031.5438 0.00 1.00
## thing 25.7860 13405.1719 0.00 1.00
## today -17.6156 19649.5746 0.00 1.00
## two -25.7267 18439.4399 0.00 1.00
## understand 9.3072 23416.6569 0.00 1.00
## unit -4.0205 30080.6466 0.00 1.00
## well -22.2193 9713.4012 0.00 1.00
## work -10.9874 11596.3171 0.00 1.00
## hour 2.4780 13334.9003 0.00 1.00
## lot -19.6368 13211.3752 0.00 1.00
## real 20.4591 23580.8524 0.00 1.00
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## X000 14.7384 10583.7959 0.00 1.00
## X2001 -32.1477 13177.6879 0.00 1.00
## follow 17.6578 3079.6809 0.01 1.00
## name 16.7214 13218.4481 0.00 1.00
## sent -14.8820 21953.7964 0.00 1.00
## last 1.0464 13724.4471 0.00 1.00
## avail 8.6511 17094.5716 0.00 1.00
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## http 25.2794 21071.1240 0.00 1.00
## join -38.2408 23338.6228 0.00 1.00
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## next. 14.9230 17244.6865 0.00 1.00
## remov 23.2545 24837.8658 0.00 1.00
## repli 15.3798 29155.6188 0.00 1.00
## wish 11.7309 31747.3794 0.00 1.00
## www -7.8672 22237.5989 0.00 1.00
## year -10.1029 10394.6904 0.00 1.00
## back -13.2347 22723.0238 0.00 1.00
## internet 8.7490 10999.9271 0.00 1.00
## member 13.8130 23429.9085 0.00 1.00
## receiv 0.5765 15848.4961 0.00 1.00
## site 8.6886 14955.3526 0.00 1.00
## anoth -8.7440 20316.9364 0.00 1.00
## associ 9.0494 19093.5413 0.00 1.00
## comment -3.2514 33870.0142 0.00 1.00
## corp 16.0550 27083.0385 0.00 1.00
## date -2.7862 16985.3060 0.00 1.00
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## free 6.1132 8121.0418 0.00 1.00
## issu -37.0837 33960.7079 0.00 1.00
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## move -38.3362 30112.4663 0.00 1.00
## particip -11.5427 17383.3058 0.00 1.00
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## respons -19.5960 36666.0058 0.00 1.00
## say 7.3662 22174.2442 0.00 1.00
## week -6.7950 10458.9864 0.00 1.00
## dear -2.3132 23063.8923 0.00 1.00
## regard -3.6681 15110.0149 0.00 1.00
## thank -38.9047 10586.9613 0.00 1.00
## address -4.6129 11134.3868 0.00 1.00
## contact 1.5300 12616.5255 0.00 1.00
## engin 26.6429 23936.0768 0.00 1.00
## etc 0.9470 15694.7652 0.00 1.00
## immedi 62.8533 33464.6929 0.00 1.00
## net 12.5616 21972.8129 0.00 1.00
## per 13.6749 12732.8339 0.00 1.00
## place 9.0053 36608.9650 0.00 1.00
## respond 29.7419 38879.3034 0.00 1.00
## sincer -20.7317 35145.2647 0.00 1.00
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## data -26.0909 22714.2774 0.00 1.00
## detail 11.9692 23008.8487 0.00 1.00
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## success 4.3436 27830.4737 0.00 1.00
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## help 17.3096 2790.8998 0.01 1.00
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## meet -1.0626 12633.5575 0.00 1.00
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## write 44.0618 28249.1186 0.00 1.00
## think -12.1812 20772.9999 0.00 1.00
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## run -51.6220 44337.5156 0.00 1.00
## shall 19.2987 30748.7761 0.00 1.00
## soon 23.4975 37313.2839 0.00 1.00
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## attach -10.3659 15343.2998 0.00 1.00
## abl -2.0485 20883.2671 0.00 1.00
## program 1.4441 11831.1619 0.00 1.00
## sorri 6.0356 22992.8231 0.00 1.00
## valu 0.9024 13599.5916 0.00 1.00
## check 1.4252 19631.4419 0.00 1.00
## feel 2.5959 23476.2770 0.00 1.00
## better 42.6315 23599.8879 0.00 1.00
## plan -18.3036 6320.4988 0.00 1.00
## experi 2.4597 22404.6552 0.00 1.00
## hope -14.3545 21794.8858 0.00 1.00
## begin 22.2801 29731.4126 0.00 1.00
## X2000 -36.3065 15559.7816 0.00 1.00
## case -33.7240 28804.2328 0.00 1.00
## depart -40.6847 25092.9541 0.00 1.00
## financi -9.7467 17271.8378 0.00 1.00
## houston -18.5450 7305.0368 0.00 1.00
## intern -7.9907 33512.7814 0.00 1.00
## john -0.5326 28562.0674 0.00 1.00
## juli -13.5778 30093.2708 0.00 1.00
## mark -33.5007 32080.8705 0.00 1.00
## open 21.1417 29613.7993 0.00 1.00
## public -52.4985 23410.5823 0.00 1.00
## sinc -3.4385 35455.9820 0.00 1.00
## still 3.8779 26222.2125 0.00 1.00
## thought 12.4329 30228.1125 0.00 1.00
## univers 12.2758 21969.4115 0.00 1.00
## appreci -21.4464 27616.2809 0.00 1.00
## keep 18.6660 27816.0700 0.00 1.00
## cours 16.6526 18338.3815 0.00 1.00
## direct -20.5061 31942.8882 0.00 1.00
## togeth -23.5481 18689.9723 0.00 1.00
## energi -16.1971 16457.8766 0.00 1.00
## london 6.7453 16419.7348 0.00 1.00
## updat -15.0978 14480.7185 0.00 1.00
## suggest -38.4217 44745.1860 0.00 1.00
## option -1.0852 9325.3243 0.00 1.00
## monday -1.0340 32330.8096 0.00 1.00
## kevin -37.7904 47379.7471 0.00 1.00
## book 4.3007 20235.7919 0.00 1.00
## deal -11.2937 14476.4873 0.00 1.00
## invit 4.3037 22150.2429 0.00 1.00
## tuesday -28.0830 39588.8687 0.00 1.00
## interview -16.4048 18733.9704 0.00 1.00
## schedul 1.9191 35796.8427 0.00 1.00
## school -3.8701 28823.4689 0.00 1.00
## model -22.9233 10487.3469 0.00 1.00
## financ -9.1224 7523.9504 0.00 1.00
## morn -26.4476 34027.8914 0.00 1.00
## attend -34.5055 32573.3227 0.00 1.00
## robert -20.9550 29071.4318 0.00 1.00
## student -18.1473 21856.4156 0.00 1.00
## april -26.2027 22080.5315 0.00 1.00
## talk -10.1057 20206.4181 0.00 1.00
## arrang 10.6947 21352.2139 0.00 1.00
## deriv -49.7106 35873.6724 0.00 1.00
## thursday -14.9135 32617.9203 0.00 1.00
## resum -9.2191 20996.1407 0.00 1.00
## doc -25.9712 26031.8370 0.00 1.00
## confer -0.7503 8557.3634 0.00 1.00
## wednesday -15.2636 26422.7645 0.00 1.00
## edu -0.2122 691.7410 0.00 1.00
## friday -11.4616 19964.7326 0.00 1.00
## ect 0.8685 5341.5129 0.00 1.00
## hou 6.8515 6436.8947 0.00 1.00
## vinc -37.3476 8647.1553 0.00 1.00
## X853 -1.2123 59416.8273 0.00 1.00
## shirley -71.3287 63289.3774 0.00 1.00
## enron -8.7888 5718.8782 0.00 1.00
## kaminski -18.1196 6029.0713 0.00 1.00
## X713 -24.2730 29138.3799 0.00 1.00
## crenshaw 99.9441 67692.0276 0.00 1.00
## vkamin -66.4898 57028.7697 0.00 1.00
## gibner 29.0119 24595.4818 0.00 1.00
## stinson -43.4535 26967.0175 0.00 1.00
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 4409.49 on 4009 degrees of freedom
## Residual deviance: 13.46 on 3679 degrees of freedom
## AIC: 675.5
##
## Number of Fisher Scoring iterations: 25- 0 (none)
3.3 Words in the Decision Tree
【P3.3】How many of the word stems “enron”, “hou”, “vinc”, and “kaminski” appear in the CART tree?
prp(cart)
- 2 (enrou, vinc) Recall that we suspect these word stems are specific to Vincent Kaminski and might affect the generalizability of a spam filter built with his ham data.
3.4 training accuracy
What is the training set accuracy of spamLog, using a threshold of 0.5 for predictions?
table(tr$spam, predglm>0.5) %>% {sum(diag(.))/sum(.)}## [1] 0.9993.5 What is the training AUC of the GLM model?
colAUC(predglm, tr$spam)## [,1]
## 0 vs. 1 1#prediction = prediction(predglm, tr$spam)
#as.numeric(performance(prediction, "auc")@y.values)3.6 Building Machine Learning Models
What is the training set accuracy of spamCART, using a threshold of 0.5 for predictions? (Remember that if you used the type=“class” argument when making predictions, you automatically used a threshold of 0.5. If you did not add in the type argument to the predict function, the probabilities are in the second column of the predict output.)
predcart = predict(cart)[,2]
table(tr$spam, predcart>0.5) %>% {sum(diag(.))/sum(.)}## [1] 0.942393.7 What is the training ACC of the CART model?
What is the training set AUC of spamCART? (Remember that you have to pass the prediction function predicted probabilities, so don’t include the type argument when making predictions for your CART model.)
colAUC(predcart, tr$spam)## [,1]
## 0 vs. 1 0.96963.8 What is the training accuracy of the RF model?
predrf = predict(rf,type="prob")[,2]
table(tr$spam, predrf>0.5) %>% {sum(diag(.))/sum(.)}## [1] 0.98083.9 What is the training AUC of the RF model?
What is the training set AUC of spamRF? (Remember to pass the argument type=“prob” to the predict function to get predicted probabilities for a random forest model. The probabilities will be the second column of the output.)
colAUC(predrf, tr$spam)## [,1]
## 0 vs. 1 0.99793.10 Which model had the best training set performance, in terms of accuracy & AUC?
- Logistic regression
Problem 4 - Evaluating on the Test Set
Obtain predicted probabilities for the testing set for each of the models, again ensuring that probabilities instead of classes are obtained.
#將ts的predict結果合併在一起，令為data frame
pred2 = data.frame(
predglm2 = predict(glm, ts, type='response'),
predcart2 = predict(cart, ts)[,2],
predrf2 = predict(rf, ts, type='prob')[,2] )
rbind(
ACC = apply(pred2, 2, function(x) {
table(ts$spam, x > 0.5) %>% {sum(diag(.)) / sum(.)} } ),
AUC = colAUC(pred2, ts$spam) ) %>% t## ACC 0 vs. 1
## predglm2 0.95052 0.96275
## predcart2 0.93946 0.96318
## predrf2 0.97555 0.997774.1
What is the testing set accuracy of spamLog, using a threshold of 0.5 for predictions?
- 0.95052
4.2
What is the testing set AUC of spamLog?
- 0.96275
4.3
What is the testing set accuracy of spamCART, using a threshold of 0.5 for predictions?
- 0.93946
4.4
What is the testing set AUC of spamCART?
- 0.96318
4.5
What is the testing set accuracy of spamRF, using a threshold of 0.5 for predictions?
- 0.97555
4.6
What is the testing set AUC of spamRF?
- 0.99777
4.7
Which model had the best testing set performance, in terms of accuracy and AUC?
- Random forest
4.8
Which model demonstrated the greatest degree of overfitting?
- Logistic regression