Better naming of solutions manuals

Mission374Solutions.Rmd

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-title: "Mission 374 Solutions"
+title: "Answering Business Questions using SQL (Intermediate SQL in R): Guided Project Solutions"
 output: html_document
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Mission376Solutions.Rmd

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-title: "Mission 376 Solutions"
+title: "Designing and Creating a Database (Intermediate SQL in R): Guided Project Solutions"
 output: html_document
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Mission409Solutions.Rmd

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-title: "Mission 409 Solutions"
+title: "Probability Fundamentals in R: Guided Project Solutions"
 output: html_document
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Mission443Solutions.Rmd

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-title: "Mission 443 Solutions"
+title: "Hypothesis Testing in R: Guided Project Solutions"
 output: html_document
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Mission475Solutions.Rmd

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+---
+title: "Conditional Probability in R: Guided Project Solutions"
+output: html_document
+---
+
+```{r, warning = FALSE, message = FALSE }
+library(tidyverse)
+set.seed(1)
+```
+
+# Introduction
+
+This analysis is an application of what we've learned in Dataquest's Conditional Probability course. Using a dataset of pre-labeled SMS messages, we'll create a spam filter using the Naive Bayes algorithm.
+
+# Data 
+
+```{r}
+spam = read.csv("./data/SMSSpamCollection", sep = "\t", header = F)
+colnames(spam) = c("label", "sms")
+```
+
+The `spam` dataset has `r nrow(spam)` rows and `r ncol(spam)` columns. Of these messages, `r mean(spam$label == "ham") * 100`% of them are not classified as spam, the rest are spam.
+
+# Dividing Up Into Training and Test Sets
+
+```{r}
+n = nrow(spam)
+n.training = 2547
+n.cv = 318
+n.test = 319
+
+# Create the random indices for training set
+train.indices = sample(1:n, size = n.training, replace = FALSE)
+
+# Get indices not used by the training set
+remaining.indices = setdiff(1:n, train.indices)
+
+# Remaining indices are already randomized, just allocate correctly
+cv.indices = remaining.indices[1:318]
+test.indices = remaining.indices[319:length(remaining.indices)]
+
+# Use the indices to create each of the datasets
+spam.train = spam[train.indices,]
+spam.cv = spam[cv.indices,]
+spam.test = spam[test.indices,]
+
+# Sanity check: are the ratios of ham to spam relatively constant?
+print(mean(spam.train$label == "ham"))
+print(mean(spam.cv$label == "ham"))
+print(mean(spam.test$label == "ham"))
+```
+
+The number of ham messages in each dataset is relatively close to the original 87%. These datasets look good for future analysis.
+
+# Data Cleaning
+
+```{r}
+# To lowercase, removal of punctuation
+tidy.train = spam.train %>% 
+  mutate(
+    sms = tolower(sms),
+    sms = str_replace_all(sms, "[[:punct:]]", ""),
+    sms = str_replace_all(sms, "[[:digit:]]", " "),
+    sms = str_replace_all(sms, "[\u0094\u0092\n\t]", " ")
+  )
+
+# Creating the vocabulary
+vocabulary = NULL
+messages = pull(tidy.train, sms)
+
+# Iterate through the messages and add to the vocabulary
+for (m in messages) {
+  words = str_split(m, " ")[[1]]
+  words = words[!words %in% ""]
+  vocabulary = c(vocabulary, words)
+}
+vocabulary = unique(vocabulary)
+```
+
+# Calculating Constants and Parameters
+
+```{r}
+# Calculating Constants
+# Mean of a vector of logicals is a percentage
+p.spam = mean(tidy.train$label == "spam")
+p.ham = mean(tidy.train$label == "ham")
+
+# Isolate the spam and ham messages
+spam.messages = tidy.train %>% 
+  filter(label == "spam") %>% 
+  pull("sms")
+
+ham.messages = tidy.train %>% 
+  filter(label == "ham") %>% 
+  pull("sms")
+
+spam.words = NULL
+for (sm in spam.messages) {
+  words = str_split(sm, " ")[[1]]
+  spam.words = c(spam.words, words)
+}
+
+ham.words = NULL
+for (hm in ham.messages) {
+  words = str_split(hm, " ")[[1]]
+  ham.words = c(ham.words, words)
+}
+
+n.spam = length(unique(spam.words))
+n.ham = length(unique(ham.words))
+n.vocabulary = length(vocabulary)
+alpha = 1
+```
+
+```{r}
+# Calculating Parameters
+spam.counts = list()
+ham.counts = list()
+spam.probs = list()
+ham.probs = list()
+
+# This might take a while to run with so many words
+for (vocab in vocabulary) {
+  
+  # Initialize the counts for the word
+  spam.counts[[vocab]] = 0
+  ham.counts[[vocab]] = 0
+  
+  # Break up the message and count how many times word appears
+  for (sm in spam.messages) {
+    words = str_split(sm, " ")[[1]]
+    spam.counts[[vocab]] = spam.counts[[vocab]] + sum(words == vocab)
+  }
+  
+  for (hm in ham.messages) {
+    words = str_split(hm, " ")[[1]]
+    ham.counts[[vocab]] = ham.counts[[vocab]] + sum(words == vocab)
+  }
+  
+  # Use the counts to calculate the probability
+  spam.probs[[vocab]] = (spam.counts[[vocab]] + alpha) / (n.spam + alpha * n.vocabulary)
+  ham.probs[[vocab]] = (ham.counts[[vocab]] + alpha) / (n.ham + alpha * n.vocabulary)
+}
+
+```
+
+# Classifying New Messages
+
+```{r}
+classify = function(message) {
+  
+  # Initializing the probability product
+  p.spam.given.message = p.spam
+  p.ham.given.message = p.ham
+  
+  # Splitting and cleaning the new message
+  clean.message = tolower(message)
+  clean.message = str_replace_all(clean.message, "[[:punct:]]", "")
+  clean.message = str_replace_all(clean.message, "[[:digit:]]", " ")
+  clean.message = str_replace_all(clean.message, "[\u0094\u0092\n\t]", " ")
+  words = str_split(clean.message, " ")[[1]]
+  
+  for (word in words) {
+    
+    # Extra check if word is not in vocabulary
+    wi.spam.prob = ifelse(word %in% vocabulary, 
+                          spam.probs[[word]],
+                          1)
+    wi.ham.prob = ifelse(word %in% vocabulary, 
+                         ham.probs[[word]],
+                        1)
+    
+    p.spam.given.message = p.spam.given.message * wi.spam.prob
+    p.ham.given.message = p.ham.given.message * wi.ham.prob
+  }
+  
+  result = case_when(
+    p.spam.given.message >= p.ham.given.message ~ "spam",
+    p.spam.given.message < p.ham.given.message ~ "ham")
+  
+  return(result)
+}
+
+final.train = tidy.train %>% 
+  mutate(
+    prediction = unlist(map(sms, classify))
+  ) %>% 
+  select(label, prediction, sms)
+
+
+# Results of classification on training
+confusion = table(final.train$label, final.train$prediction)
+accuracy = (confusion[1,1] + confusion[2,2]) / nrow(final.train)
+```
+
+Roughly, the classifier achieves about 97% accuracy on the training set. We aren't interested in how well the classifier performs with training data though, the classifier has already "seen" all of these messages.
+
+# Hyperparameter Tuning
+
+```{r}
+alpha.grid = seq(0.1, 1, by = 0.1)
+cv.accuracy = NULL
+
+for (a in alpha.grid) {
+  
+  spam.probs = list()
+  ham.probs = list()
+
+  # This might take a while to run with so many words
+  for (vocab in vocabulary) {
+    
+    # Use the counts to calculate the probability
+    spam.probs[[vocab]] = (spam.counts[[vocab]] + a) / (n.spam + a * n.vocabulary)
+    ham.probs[[vocab]] = (ham.counts[[vocab]] + a) / (n.ham + a * n.vocabulary)
+  }
+  
+  cv = spam.cv %>% 
+    mutate(
+      prediction = unlist(map(sms, classify))
+    ) %>% 
+  select(label, prediction, sms)
+  
+  confusion = table(cv$label, cv$prediction)
+  acc = (confusion[1,1] + confusion[2,2]) / nrow(cv)
+  cv.accuracy = c(cv.accuracy, acc)
+}
+
+cv.check = tibble(
+  alpha = alpha.grid,
+  accuracy = cv.accuracy
+)
+cv.check
+```
+
+Judging from the cross-validation set, higher $\alpha$ values cause the accuracy to decrease. We'll go with $\alpha = 0.1$ since it produces the highest cross-validation prediction accuracy.
+
+# Test Set Performance
+
+```{r}
+# Reestablishing the  proper parameters
+optimal.alpha = 0.1
+for (a in alpha.grid) {
+  
+  spam.probs = list()
+  ham.probs = list()
+
+  # This might take a while to run with so many words
+  for (vocab in vocabulary) {
+    
+    # Use the counts to calculate the probability
+    spam.probs[[vocab]] = (spam.counts[[vocab]] + optimal.alpha) / (n.spam + optimal.alpha * n.vocabulary)
+    ham.probs[[vocab]] = (ham.counts[[vocab]] + optimal.alpha) / (n.ham + optimal.alpha * n.vocabulary)
+  }
+}
+
+spam.test = spam.test %>% 
+  mutate(
+    prediction = unlist(map(sms, classify))
+    ) %>% 
+  select(label, prediction, sms)
+  
+confusion = table(spam.test$label, spam.test$prediction)
+test.accuracy = (confusion[1,1] + confusion[2,2]) / nrow(cv)
+test.accuracy
+```
+
+We've achieved an accuracy of 93% in the test set. Not bad!