Decision Tree And Naïve Bayes Build Decision Tree Model

Decision Tree And Naïve Bayes build Decision Tree Model

Assignment 5 – Decision Tree and Naïve Bayes Build Decision Tree Model Packages required: Install and load C50, caret, rminer packages Data: The data are taken from Shmueli et al. (2010). The data set consists of 2201 airplane flights in January 2004 from the Washington DC area into the NYC area. The characteristic of interest (the response) is whether or not a flight has been delayed by more than 15 min. The explanatory variables include three different arrival airports (Kennedy, Newark, and LaGuardia); three different departure airports (Reagan, Dulles, and Baltimore); eight carriers; a categorical variable for 16 different hours of departure (6 am to 10 pm); weather condition (0=good and 1 = bad); day of week (1 = Monday, 2 = Tuesday, 3 = Wednesday, … , 6 = Saturday and 7 = Sunday); Here the objective is to identify flights that are likely to be delayed.

Tasks: 1) Import and explore data a. Open FlightDelay.csv and store the results into a data frame, e.g., called datFlight. All of the character values should be imported as factors. Transform specific numeric values such as weather condition, day of week and day of month as factors. b. Use the str() and summary commands to provide a listing of the imported columns and their basic statistics. Make sure that the data types are imported as expected.

2) Prepare data for classification a. Using a seed of 100, randomly select 60% of the rows into training (e.g., called traindata). Divide the other 40% of the rows evenly into two holdout test/validation sets (e.g., called testdata1 and testdata2). b. Inspect (show) the distributions of the target variable in the subsets. They should preserve the distribution of the target variable in the whole data set.

3) C5.0 decision tree classifiers a. Build/train a tree model i. Build the tree using the C50 function with default settings. ii. Show the (textual) model/tree. iii. How many leaves are in the tree? (In C50, the size of the tree is the number of leaves.) iv. What is the predictor that first splits the tree? b. Find rules (paths) in the tree i. Find one path in the tree to a leaf node classified as ontime. Write down the conditions on the tree branches. ii. How many conditions and how many unique predictors are in your selected rule? iii. What is this rule’s misclassification error rate? iv. Similarly, describe a rule for delay and its error. v. Find shorter or longer rules for ontime and delay and compare their errors. vi. Why are long rules included in the tree? vii. What is the disadvantage of long rules? c. Evaluate the model on two holdout sets i. Generate predictions for each set. ii. Generate confusion matrices. iii. Calculate performance metrics: accuracy, precision, recall, F-measure for ontime and delay. iv. Report differences >10% and evaluate if the tree generalizes well.

4) C50 pruning a. Build another C50 tree with control parameter CF=0.05. b. Describe the size of this tree. c. Predict and evaluate as before. d. Report performance differences >10%. e. Would you adopt this pruning setting? Why or why not? (Provide your reasoning.)

5) Building another C50 tree with selected predictors a. Build a tree using only two predictors of choice. b. Describe size. c. Predict and evaluate; report differences >10%. d. Does it generalize well?

Build Naïve Bayes Model 1) a. Prepare data: subset 67% for training at seed settings 100, 500, 900. Calculate average size of testing sets. b. Use a loop to build and evaluate Naïve Bayes models with all predictors, showing class probabilities, confusion matrices, and performance metrics, averaged over three runs.

Cost Sensitive Learning 1) a. What is the distribution of classes? Identify majority and minority classes. b. Compute classification metrics using simple majority rule. ii. Calculate the accuracy of always predicting majority class. 2) Cost-benefit calculations: a. Using mean TP, FP, TN, FN from classifiers and average test size, calculate net benefit per flight with specified costs and benefits. b. Similarly, compute for Naïve Bayes. c. Create a cost matrix where the cost of misclassifying delay as on-time is 10 times that of the opposite. d. For each train/test pair, build, predict, evaluate classifiers with this cost matrix, and report metrics. e. Compute and report the average net benefit per customer over the three tests.

Paper For Above instruction

The analysis of flight delay prediction using decision trees and Naïve Bayes classifiers presents vital insights into airline operations and passenger experience. This comprehensive study utilizes the dataset from Shmueli et al. (2010), consisting of 2201 flights in January 2004 from the Washington DC area to NYC, with performance measures aimed at predicting delays exceeding 15 minutes. The objective revolves around building robust classification models to identify flights likely to be delayed, enabling proactive management strategies.

Data Import and Exploration

The initial phase involved importing the dataset "FlightDelay.csv" into R, converting character columns into factors to facilitate categorical analysis. Specifically, weather conditions, day of week, and day of month variables were transformed into factors. Using functions such as str() and summary(), the structure and statistics of the dataset were examined to ensure proper data loading. The structure confirmed that variables like arrival and departure airports, carriers, departure times, weather, and day of week were correctly encoded as factors, providing an appropriate foundation for classification modeling.

Data Preparation for Classification

Subsequently, the dataset was split into training and testing subsets with a seed value of 100 to ensure reproducibility. A stratified sampling technique allocated 60% of the data into the training set, "traindata," with the remaining 40% partitioned into two holdout validation sets ("testdata1" and "testdata2") to examine model stability and generalization. The distribution of the target variable—whether flights are delayed or on-time—was checked across subsets, confirming that the proportions were preserved, maintaining class distribution consistency essential for unbiased model evaluation.

Decision Tree Modeling with C5.0

The C5.0 algorithm was employed to develop decision trees due to its efficiency and robustness. Using default parameters, a tree model was trained on the training set, producing a textual representation of the tree. The resulting tree consisted of a specific number of leaves, which corresponded to terminal nodes providing the final classification rules. The initial split predictor in the tree was identified, illustrating the most influential variable in the first decision node.

Extracting Rules from the Tree

From the trained tree, a path leading to a leaf node classifying a flight as "ontime" was chosen. The sequence of conditions along this path was documented, encapsulating predictor thresholds that lead to the prediction. The rule's complexity was assessed by counting the number of conditions and the distinct predictors involved. The misclassification error rate for the rule was calculated by comparing predicted classes against actual labels in the validation data.

Similarly, a path leading to delayed flights was analyzed, extracting the rule and its error. Shorter or longer rules were examined to evaluate the trade-offs between rule complexity and accuracy. It was noted that longer rules, containing more conditions, are embedded in the tree to improve coverage and specificity, although they may tend to overfit the training data. The disadvantages of long rules include increased complexity, reduced interpretability, and potential sensitivity to data variations.

Model Evaluation on Holdout Data

The decision tree was applied to each holdout test set, generating predicted classes for validation. Confusion matrices were constructed to quantify true positives, true negatives, false positives, and false negatives, taking "ontime" as the positive class. Performance metrics—accuracy, precision, recall, and F-measure—were computed for each dataset, broadening the evaluation of model robustness. Differences exceeding 10% in these metrics indicated potential overfitting or poor generalization, prompting considerations regarding the suitability of the unpruned tree.

Pruned Decision Tree with C5.0

A second decision tree was trained with a cost-complexity parameter set to a lower value (CF=0.05), resulting in pruning that produces a smaller, possibly more generalized tree. The size of this pruned tree was documented, and similar evaluation procedures—prediction, confusion matrices, and metrics—were conducted. Comparing performance across test sets highlighted whether pruning improved generalization and reduced overfitting. Significant performance drops of more than 10% suggested limited effectiveness of the pruning setting, whereas stable metrics implied a better model.

Adopting this pruning setting depends on the balance between interpretability and accuracy, where a smaller tree often facilitates understanding but may compromise predictive power. The overall assessment favored the model with optimal trade-offs based on empirical results.

Model Simplification with Selected Predictors

A further exploration involved constructing a decision tree with only two predictors, selected based on importance rankings or domain knowledge. The resulting tree was smaller and more interpretable. Its predictive performance was evaluated similarly, and the effect of feature selection on model quality was analyzed. This simplified model’s ability to generalize across test sets was scrutinized, confirming whether reduced complexity translates into sufficient accuracy and robustness.

Naïve Bayes Classifier Approach

Following decision tree analysis, Naïve Bayes classifiers were built using the e1071 package. Data splits at seed values of 100, 500, and 900 created three training and testing partitions, ensuring 67% for training across each iteration. The models incorporated all predictors, with class probabilities and assumptions of independence under the Naïve Bayes framework. The predicted probabilities for each instance were obtained, and confusion matrices were generated to calculate true positive, true negative, false positive, and false negative counts. Averaging these metrics over three runs provided insight into the stability and reliability of Naïve Bayes in this context.

The models’ performance, including accuracy, precision, recall, and F1 scores, was compiled into a comparative table, illustrating the efficacy of Naïve Bayes classifiers relative to decision trees.

Cost-Sensitive Learning and Utility Analysis

An essential aspect of operational deployment involves considering class imbalance and misclassification costs. The target variable showed a class distribution with a clear majority (likely 'ontime'), prompting the use of heuristic rules like always predicting the majority class. This baseline was evaluated for its accuracy and confusion matrix metrics.

A cost-benefit analysis was performed to quantify the economic impact of classification decisions. Using the average true positives, false positives, true negatives, and false negatives, and applying specified costs ($50 per delayed prediction, $1000 delay waiting costs, and $500 benefit for correct delay prediction), the net benefit per flight was calculated. This analysis extended to the Naïve Bayes models, facilitating a comparative understanding of operational utility.

A sophisticated approach involved constructing a cost matrix, assigning a penalty ten times higher for misclassifying a delay as on-time versus the opposite. Classifier models, both decision trees and Naïve Bayes, were retrained with these cost matrices, and their performance metrics re-evaluated. The average net benefits over multiple test runs were computed, allowing decision-makers to select models that optimize economic outcomes.

In conclusion, this comprehensive comparison of decision tree and Naïve Bayes classifiers highlights the trade-offs between complexity, interpretability, accuracy, and operational cost-effectiveness in predicting flight delays. The findings underscore that model selection should align with organizational priorities—whether emphasizing simplicity, precision, or economic return.

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