William's Data Science Blog

Category: Gaussian Naive Bayes

  • Experimenting with Model Stacking on Student Alcohol Consumption Data

    Experimenting with Model Stacking on Student Alcohol Consumption Data

    William's Data Science Blog

    In this blog post, I’m building on my previous work with the Student Alcohol Consumption dataset on Kaggle. My latest experiments can be found in the updated Jupyter notebook. In this updated analysis, I explored several new approaches—including using linear regression, stacking models, applying feature transformations, and leveraging visualization—to compare model performances in both prediction and classification scenarios.

    Recap: From the Previous Notebook

    Before diving into the latest experiments, here’s a quick overview of what I did earlier:

    • I explored using various machine learning algorithms on the student alcohol dataset.
    • I identified promising model combinations and created baseline plots to display their performance.
    • My earlier analysis provided a solid framework for experimentation with stacking and feature transformation techniques.

    This post builds directly on that foundation.

    Experiment 1: Using Linear Regression

    Motivation:

    I decided to try a linear regression model because it excels at predicting continuous numerical values—like house prices or temperature. In this case, I was curious to see how well it could predict student grades or scaled measures of drinking behavior.

    What I Did:
    • I trained a linear regression model on the dataset.
    • I applied a StandardScaler to ensure that numeric features were well-scaled.
    • The predictions were then evaluated by comparing them visually (using plots) and numerically to other approaches.
    Observation:

    Interestingly, the LinearRegression model, when calibrated with the StandardScaler, yielded better results than using Gaussian Naive Bayes (GNB) alone. A plot of the predictions against actual values made it very clear that the linear model provided smoother and more reliable estimates.

    Experiment 2: Stacking Gaussian Naive Bayes with Linear Regression

    Motivation:

    I wanted to experiment with stacking models that are generally not used together. Despite the literature primarily avoiding a combination of Gaussian Naive Bayes with linear regression, I was intrigued by the possibility of capturing complementary characteristics of both:

    • GNB brings in a generative, probabilistic perspective.
    • Linear Regression excels in continuous predictions.
    What I Did:
    • I built a stacking framework where the base learners were GNB and linear regression.
    • Each base model generated predictions, which were then used as input (meta-features) for a final meta-model.
    • The goal was to see if combining these perspectives could offer better performance than using either model alone.
    Observation:

    Stacking GNB with linear regression did not appear to improve results over using GNB alone. The combined predictions did not outperform linear regression’s stand-alone performance, suggesting that in this dataset the hybrid approach might have introduced noise rather than constructive diversity in the predictions.

    Experiment 3: Stacking Gaussian Naive Bayes with Logistic Regression

    Motivation:

    While exploring stacking architectures, I found that combining GNB with logistic regression is more common in the literature. Since logistic regression naturally outputs calibrated probabilities and aligns well with classification tasks, I hoped that:

    • The generative properties of GNB would complement the discriminative features of logistic regression.
    • The meta-model might better capture the trade-offs between these approaches.
    What I Did:
    • I constructed a stacking model where the two base learners were GNB and logistic regression.
    • Their prediction probabilities were aggregated to serve as inputs to the meta-learner.
    • The evaluation was then carried out using test scenarios similar to those in my previous notebook.
    Observation:

    Even though the concept seemed promising, stacking GNB with logistic regression did not lead to superior results. The final performance of the stack was not significantly better than what I’d seen with GNB alone. In some cases, the combined output underperformed compared to linear regression alone.

    Experiment 4: Adding a QuantileTransformer

    Motivation:

    A QuantileTransformer remaps features to follow a uniform or a normal distribution, which can be particularly useful when dealing with skewed data or outliers. I introduced it into the stacking pipeline because:

    • It might help models like GNB and logistic regression (which assume normality) to produce better-calibrated probability outputs.
    • It provides a consistent, normalized feature space that might enhance the meta-model’s performance.
    What I Did:
    • I added the QuantileTransformer as a preprocessing step immediately after splitting the data.
    • The transformed features were used to train both the base models and the meta-learner in the stacking framework.
    Observation:

    Surprisingly, the introduction of the QuantileTransformer did not result in a noticeable improvement over the GNB results without the transformer. It appears that, at least under my current experimental settings, the transformed features did not bring out the expected benefits.

    Experiment 5: Visualizing Model Results with Matplotlib

    Motivation:

    Visual analysis can often reveal trends and biases that plain numerical summaries might miss. Inspired by examples on Kaggle, I decided to incorporate plots to:

    • Visually compare the performance of different model combinations.
    • Diagnose potential issues such as overfitting or miscalibration.
    • Gain a clearer picture of model behavior across various scenarios.
    What I Did:
    • I used Matplotlib to plot prediction distributions and error metrics.
    • I generated side-by-side plots comparing the predictions from linear regression, the stacking models, and GNB alone.
    Observation:

    The plots proved invaluable. For instance, a comparison plot clearly highlighted that linear regression with StandardScaler outperformed the other approaches. Visualization not only helped in understanding the behavior of each model but also served as an effective communication tool for sharing results.

    Experiment 6: Revisiting Previous Scenarios with the Stacked Model

    Motivation:

    To close the loop, I updated my previous analysis function to use the stacking model that combined GNB and logistic regression. I reran several test scenarios and generated plots to directly compare these outcomes with earlier results.

    What I Did:
    • I modified the function that earlier produced performance plots.
    • I then executed those scenarios with the new stacked approach and documented the differences.
    Observation:

    The resulting plots confirmed that—even after tuning—the stacked model variations (both with linear regression and logistic regression) did not surpass the performance of linear regression alone. While some combinations were competitive, none managed to outshine the best linear regression result that I had seen earlier.

    Final Thoughts and Conclusions

    This journey into stacking models, applying feature transformations, and visualizing the outcomes has been both enlightening and humbling. Here are my key takeaways:

    • LinearRegression Wins (for Now): The linear regression model, especially when combined with a StandardScalar, yielded better results compared to using GNB or any of the stacked variants.
    • Stacking Challenges:
      • GNB with Linear Regression: The combination did not improve performance over GNB alone.
      • Stacking GNB with Logistic Regression: Although more common in literature, this approach did not lead to a significant boost in performance in my first attempt.
    • QuantileTransformer’s Role: Despite its promise, the QuantileTransformer did not produce the anticipated improvements. Its impact may be more nuanced or require further tuning.
    • Visualizations Are Game Changers: Adding plots was immensely helpful to better understand model behavior, compare the effectiveness of different approaches, and provide clear evidence of performance disparities.
    • Future Directions: It’s clear that further experimentation is necessary. I plan to explore finer adjustments and perhaps more sophisticated stacking strategies to see if I can bridge the gap between these models.

    In conclusion, while I was hoping that combining GNB with logistic regression would yield better results, my journey shows that sometimes the simplest approach—in this case, linear regression with proper data scaling—can outperform more complex ensemble methods. I look forward to further refinements and welcome any ideas or insights from the community on additional experiments I could try.

    I hope you found this rundown as insightful as I did during the experimentation phase. What do you think—could there be yet another layer of transformation or model combination that might tip the scales? Feel free to share your thoughts, and happy modeling!

    – William

  • Exploring the Impact of Alcohol Consumption on Student Grades with Gaussian Naive Bayes

    Exploring the Impact of Alcohol Consumption on Student Grades with Gaussian Naive Bayes

    William's Data Science Blog

    In today’s data-driven world, even seemingly straightforward questions can reveal surprising insights. In this post, I investigate whether students’ alcohol consumption habits bear any relationship to their final math grades. Using the Student Alcohol Consumption dataset from Kaggle, which contains survey responses on a myriad aspects of students’ lives—ranging from study habits and social factors to gender and alcohol use—I set out to determine if patterns exist that can predict academic performance.

    Dataset Overview

    The dataset originates from a survey of students enrolled in secondary school math and Portuguese courses. It includes rich, social, and academic information, such as:

    • Social and family background
    • Study habits and academic support
    • Alcohol consumption details during weekdays and weekends

    I focused on predicting the final math grade (denoted as G3 in the raw data) while probing how alcohol-related features, especially weekend consumption, might play a role in performance. The binary insight wasn’t just about whether students drank, but which drinking pattern might be more telling of their academic results.

    Data Preprocessing: Laying the Groundwork

    Before diving into modeling, the data needed some cleanup. Here’s how I systematically prepared the dataset for analysis:

    1. Loading the Data: I imported the CSV into a Pandas DataFrame for easy manipulation.
    2. Renaming Columns: Clarity matters. I renamed ambiguous columns for better readability (e.g., renaming walc to weekend_alcohol and dalc to weekday_alcohol).
    3. Label Encoding: Categorical data were converted to numeric representations using scikit-learn’s LabelEncoder, ensuring all features could be numerically processed.
    4. Reusable Code: I encapsulated the training and testing phases within a reusable function, which made it straightforward to test different feature combinations.

    Here’s are some snippets:

    In those cells:

    • I rename columns to make them more readable.
    • I instantiate a LabelEncoder object and encode a list of columns that have string values.
    • I add an absence category to normalize absence count a little due to how variable that data is.

    Experimenting With Gaussian Naive Bayes

    The heart of this exploration was to see how well a Gaussian Naive Bayes classifier could predict the final math grade based on different selections of features. Naive Bayes, while greatly valued for its simplicity and speed, operates under the assumption that features are independent—a condition that might not fully hold in educational data.

    Training and Evaluation Function

    To streamline the experiments, I wrote a function that:

    • Splits the data into training and testing sets.
    • Trains a GaussianNB model.
    • Evaluates accuracy on the test set.

    In that cell:

    • I create a function that:
      • Drops unwanted columns.
      • Runs 100 training cycles with the given data.
      • Captures the accuracy measured from each run and returns the average.

    Single and Two column sampling

    In those cells:

    • I get a list of all columns.
    • I create loop(s) over the column list and create a list of features to test.
    • I call my function to measure the the accuracy of the features at predicting student grades.

    Diving Into Feature Combinations

    I aimed to assess the predictive power by testing different combinations of features:

    1. All Columns: This gave the best accuracy of around 22%, yet it was clear that even the full spectrum of information struggled to make strong predictions.
    2. Handpicked Features: I manually selected features that I hypothesized might be influential. The resulting accuracy dipped below that of the full dataset.
    3. Individual Features: Evaluating each feature solo revealed that the column indicating whether students planned to pursue higher education yielded the highest individual accuracy—though still far lower than all features combined.
    4. Two-Feature Combinations: By testing all pairs, I noticed that combinations including weekend alcohol consumption appeared in the top 20 predictive pairs four times, including in both of the top two.
    5. Three-Feature Combinations: The trend became stronger—combinations featuring weekend alcohol consumption topped the list ten times and were present in each of the top three combinations!
    6. Four-Feature Combinations: Here, weekend alcohol consumption featured in the top 20 combination results even more robustly—15 times in total.

    These experiments showcased one noteworthy pattern: weekend alcohol consumption consistently emerged as a common denominator in the best-performing feature combinations, while weekday consumption rarely made an appearance.

    Analysis of the Findings

    Several key observations emerged from this series of experiments:

    • Predictive Accuracy: Even with the full set of features, the best accuracy reached was only around 22%. This underwhelming performance is indicative of the challenges posed by the dataset and the restrictive assumptions embedded within the Naive Bayes model.
    • Role of Alcohol Consumption: The repeated appearance of weekend alcohol consumption in high-ranking feature combinations suggests a potential association—it may capture lifestyle or social habits that indirectly correlate with academic performance. However, it is not a standalone predictor; rather, it seems to be relevant as part of a multifactorial interaction.
    • Model Limitations: The Gaussian Naive Bayes classifier assumes feature independence. The complexities inherent in student performance—where multiple social, educational, and psychological factors interact—likely violate this assumption, leading to lower predictive performance.

    Conclusion and Future Directions

    While the Gaussian Naive Bayes classifier provided some interesting insights, especially regarding the recurring presence of weekend alcohol consumption in influential feature combinations, its overall accuracy was modest. Predicting the final math grade, a multifaceted outcome influenced by numerous interdependent factors, appears too challenging for this simplistic probabilistic model.

    Next Steps:

    • Alternative Machine Learning Algorithms: Investigating other approaches like decision trees, random forests, support vector machines, or ensemble methods may yield better performance.
    • Enhanced Feature Engineering: Incorporating interaction terms or domain-specific features might help capture the complex relationships between social habits and academic outcomes.
    • Broader Data Explorations: Diving deeper into other factors—such as study habits, parental support, and extracurricular involvement—could provide additional clarity.

    Final Thoughts and Next Steps

    This journey reinforced the idea that while Naive Bayes is a great tool for its speed and interpretability, it might not be the best choice for all datasets. More sophisticated models and careful feature engineering are necessary when dealing with some datasets like student academic performance.

    The new Jupyter notebook can be found here in my GitHub.

    – William

  • Leveraging Scikit-Learn and Polars to Test a Naive Bayes Classifier

    Leveraging Scikit-Learn and Polars to Test a Naive Bayes Classifier

    William's Data Science Blog

    In today’s post, I use scikit-learn with the same sample dataset I used in the previous post. I need to use the LabelEncoder to encode the strings as numeric values and then the GaussianNB to train and testing a Gaussian Naive Bayes classifier model and to predict the class of an example record. While many tutorials use pandas, I use Polars for fast data manipulation alongside scikit-learn for model development.

    Understanding Our Data and Tools

    Remember that the dataset includes ‘features’ for height, weight, foot size. It also has a categorical field for gender. Because classifiers like Gaussian Naive Bayes require numeric inputs, I need to transform the string gender values into a numeric format.

    In my new Jupyter notebook I use two libraries:

    Scikit-Learn for its machine learning utilities. Specifically, LabelEncoder for encoding and GaussianNB for classification.

    Polars for fast, efficient DataFrame manipulations.

    Step 1: Encoding Categorical Variables

    The first step is to convert our categorical column (gender) to a numeric format using scikit-learn’s LabelEncoder. This conversion is vital because machine learning models generally can’t work directly with string labels.

    Below is the code from our first notebook cell:

    In that cell:

    • I instantiate a LabelEncoder object.
    • For every feature in columns_to_encode (in this case, just "gender"), I create a new Polars Series with the suffix "_num", containing the encoded numeric values.
    • Finally, I add these series as new columns to our original DataFrame.

    This ensures that our categorical data is transformed into a machine-friendly format, an also preserves the human-readable string values for future reference.

    Step 2: Mapping Encoded Values to Original Labels

    Once we’ve encoded the data, it’s important to retain the mapping between the original string values and their corresponding numeric codes. This mapping is particularly useful when you want to interpret or display the model’s predictions.

    The following code block demonstrates how to generate and view this mapping:

    In that cell:

    • I save the original "gender" column and its encoded counterpart "gender_num".
    • By grouping on "gender" and aggregating with the first encountered numeric value, I create a mapping from string labels to numerical codes.

    Step 3: Training and Testing the Gaussian Naive Bayes Classifier

    Now it’s time to build, train, and evaluate our model. I separate the features and target, split the data, and then initialize the classifier.

    In that cell:

    • Get the data to use in training: I drop the raw "gender" and its encoded version from the Dataframe (X) and save the encoded classification in (y).
    • Data Splitting: train_test_split is used to randomly partition the data into training and testing sets.
    • Model Training: A GaussianNB classifier is instantiated and trained on the training data using the fit() method.
    • Prediction and Evaluation: The model’s predictions on the test set (y_pred) are generated and compared against the true labels using accuracy_score. This gives us a quantitative measure of the model’s performance.

    Step 4: Classifying a New Record

    Now I can test it on the sample observation. Consider the following code snippet:

    In that cell:

    • Create Example Data: I define a new sample record (with features like height, weight, and foot size) and create a Polars DataFrame to hold this record.
    • Prediction: The classifier is then used to predict the gender (encoded as a number) for this new record.
    • Decoding: Use the gender_mapping to display the human-readable gender label corresponding to the model’s prediction.

    Final Thoughts and Next Steps

    This step-by-step notebook shows how to preprocess data, map categorical values, train a Gaussian Naive Bayes classifier, and test new data with the combination of Polars and scikit-learn.

    The new Jupyter notebook can be found here in my GitHub. If you follow the instructions in my previous post you can run this notebook for yourself.

    – William

  • What I learned about the Gaussian Naive Bayes Classifier

    What I learned about the Gaussian Naive Bayes Classifier

    William's Data Science Blog

    Description of Gaussian Naive Bayes Classifier

    Naive Bayes classifiers are simple supervised machine learning algorithms used for classification tasks. They are called “naive” because they assume that the features are independent of each other, which may not always be true in real-world scenarios. The Gaussian Naive Bayes classifier is a type of Naive Bayes classifier that works with continuous data. Naive Bayes classifiers have been shown to be very effective, even in cases where the the features aren’t independent. They can also be trained even with small datasets and are very fast once trained.

    Main Idea: The main idea behind the Naive Bayes classifier is to use Bayes’ Theorem to classify data based on the probabilities of different classes given the features of the data. Bayes’ Theorem says that we can tell how likely something is to happen, based on what we already know about something else that has already happened.

    Gaussian Naive Bayes: The Gaussian Naive Bayes classifier is used for data that has a continuous distribution and does not have defined maximum and minimum values. It assumes that the data is distributed according to a Gaussian (or normal) distribution. In a Gaussian distribution the data looks like a bell curve if it is plotted. This assumption lets us use the Gaussian probability density function to calculate the likelihood of the data. Below are the steps needed to train a classifier and then use to to classify a sample record.

    Steps to Calculate Probabilities (the hard way):

    1. Calculate the Averages (Means):
      • For each feature in the training data, calculate the mean (average) value.
      • To calculate the mean the sum of the values are divided by the number of values.
    2. Calculate the Square of the Difference:
      • For each feature in the training data, calculate the square of the difference between each feature value and the mean of that feature.
      • To calculate the square of the difference we subtract the mean from a value and square the result.
    3. Sum the Square of the Difference:
      • Sum the squared differences for each feature across all data points.
      • Calculating this is easy, we just add up all the squared differences for each feature.
    4. Calculate the Variance:
      • Calculate the variance for each feature using the sum of the squared differences.
      • We calculate the variance by dividing the sum of the squares of the differences by the number of values minus 1.
    5. Calculate the Probability Distribution:
      • Use the Gaussian probability density function to calculate the probability distribution for each feature.
      • The formula for this is complicated! It goes like this:
        • First take: 1 divided by the square root of 2 times pi times the variance.
        • Multiply that by e to the power of -1 times the square of the value to test minus the mean of the value divided by 2 times the variance.
    6. Calculate the Posterior Numerators:
      • Calculate the posterior numerator for each class by multiplying the prior probability of the class with the probability distributions of each feature given the class.
    7. Classify the sample data:
      • The higher result from #6 is the result.

    I created a Jupyter notebook that performs these calculations based on this example I found on Wikipedia. Here is my notebook on GitHub. If you follow the instructions in my previous post you can run this notebook for yourself.

    – William

    References

    1. Wikipedia contributors. (2025, February 17). Naive Bayes classifier. In Wikipedia, The Free Encyclopedia. Retrieved from https://en.wikipedia.org/wiki/Naive_Bayes_classifier
    2. Wikipedia contributors. (2025, February 17). Variance: Population variance and sample variance. In Wikipedia, The Free Encyclopedia. Retrieved from https://en.wikipedia.org/wiki/Variance#Population_variance_and_sample_variance
    3. Wikipedia contributors. (2025, February 17). Probability distribution. In Wikipedia, The Free Encyclopedia. Retrieved from https://en.wikipedia.org/wiki/Probability_distribution