GLM And QDA Identical Results With Different Random Seeds Anomaly In Binary Classification

Hey guys! Ever scratched your head over a seemingly impossible result in machine learning? I recently stumbled upon a puzzling scenario in a binary classification analysis that I just had to share. I'm talking about getting the exact same accuracy, recall, and specificity for both a Generalized Linear Model (GLM) and Quadratic Discriminant Analysis (QDA) model, even when using different random seeds. Sounds weird, right? Let's dive deep into what might be causing this and how we can make sense of it.

The Curious Case of Identical Classification Results

In machine learning, especially in classification tasks, we expect some degree of variability when using different algorithms or even the same algorithm with different random seeds. This is because most algorithms have some element of randomness, whether it's in the initial parameter settings, the way data is shuffled, or the subset of data used for training in each iteration. So, when you see identical results across different models, it's a big red flag that something interesting—or perhaps problematic—is going on.

When dealing with binary classification, it’s crucial to understand that the models' performance metrics—accuracy, recall, and specificity—tell us different things about how well the model is performing. Accuracy gives us an overall sense of how often the model is correct, but it can be misleading if the classes are imbalanced. Recall, also known as sensitivity, tells us how well the model identifies the positive class, while specificity tells us how well it identifies the negative class. Identical metrics across different models suggest that both models are making the same predictions, which is highly unusual when they are trained independently.

To really grasp this, let's break down why GLM and QDA are typically different. GLM is a flexible framework that includes logistic regression, a common method for binary classification. It models the probability of the outcome using a linear combination of the predictors. QDA, on the other hand, is a more complex method that assumes the data for each class follows a Gaussian distribution and uses a quadratic decision boundary. Because QDA makes fewer assumptions about the linearity of the data, it can often capture more complex relationships than GLM. However, this also means it's more prone to overfitting, especially with limited data. So, when these two very different approaches yield identical results, we need to investigate further.

Potential Culprits Behind Identical Outcomes

So, what could be causing this? There are several potential explanations, and each one points us in a different direction for troubleshooting:

• Data Issues: The most common culprit is the dataset itself. If the dataset is very simple, or if the classes are perfectly separable by a linear boundary, both GLM and QDA might converge to the same solution. This is especially true if the dataset is small, where both models might overfit to the same patterns. Think of it like trying to fit a complex curve through just a few points – sometimes a straight line will do just as well.
• Overfitting: As mentioned earlier, overfitting occurs when a model learns the training data too well, capturing noise rather than the underlying patterns. In this case, both GLM and QDA could be overfitting to the same noise in the training data, leading to identical predictions on the test set. This is more likely when the model is too complex for the amount of data available.
• Implementation Bugs: It's always a good idea to double-check your code for errors. A subtle bug in your data preprocessing, model training, or evaluation code could lead to identical results. For instance, if you're accidentally using the same subset of data for training both models, or if there's an error in how you're calculating the metrics, you might see identical outcomes even if the models are behaving differently internally.
• Random Seed Shenanigans: While using different random seeds should lead to different results, there might be cases where the random number generator is not behaving as expected. This is rare, but it's worth considering, especially if you're using a custom implementation of a random number generator.
• Feature Engineering and Selection: The features you choose to include in your model can have a significant impact on the results. If the features are highly correlated or if there are only a few strong predictors, both GLM and QDA might end up focusing on the same features, leading to similar predictions. Moreover, if you've applied feature engineering steps, such as polynomial transformations or interactions, that effectively linearize the data, GLM might perform just as well as QDA.

Digging Deeper: Steps to Investigate

Okay, so we know the potential causes. Now, how do we go about figuring out what's happening in our specific case? Here’s a systematic approach:

1. Inspect the Data: The first step is always to take a close look at your data. Are the classes balanced? Are there any obvious patterns or relationships between the features and the target variable? Visualizing the data can be incredibly helpful here. Scatter plots, histograms, and box plots can reveal whether the classes are easily separable or if there are any outliers or anomalies that might be influencing the models.
2. Check for Class Imbalance: If one class significantly outnumbers the other, accuracy can be a misleading metric. In such cases, you might need to use other metrics like precision, recall, F1-score, or area under the ROC curve (AUC) to get a better sense of the model's performance. You can also try techniques like oversampling the minority class or undersampling the majority class to balance the dataset.
3. Examine Feature Correlations: High correlation between features can cause issues with model stability and interpretability. If features are highly correlated, it might be difficult for the models to tease out their individual effects, leading to similar predictions. You can use correlation matrices or variance inflation factor (VIF) to identify highly correlated features. Consider removing redundant features or using dimensionality reduction techniques like principal component analysis (PCA).
4. Evaluate Model Complexity: Are you using the right level of model complexity for your data? If the data is simple, a complex model like QDA might be overkill and could overfit. On the other hand, if the data has complex non-linear relationships, a simple model like GLM might not be able to capture them. Try varying the model complexity (e.g., using different polynomial degrees in QDA or adding regularization to GLM) and see how the results change.
5. Review Code for Errors: This might seem obvious, but it's crucial to double-check your code for any bugs. Are you preprocessing the data correctly? Are you using the correct evaluation metrics? Are you splitting the data into training and testing sets properly? Sometimes a fresh pair of eyes can help spot errors that you might have missed.
6. Experiment with Different Seeds and Data Splits: Try running your models with several different random seeds and different splits of the data into training and testing sets. If the results are consistently identical across different seeds and splits, it's a strong indication that something fundamental is going on with your data or model setup.
7. Visualize Decision Boundaries: Plotting the decision boundaries of your models can give you a visual sense of how they are separating the classes. If GLM and QDA have the same decision boundaries, it’s a clear sign that they are making the same predictions.

Real-World Examples and Scenarios

To make this more concrete, let's consider a few real-world scenarios where you might encounter this issue:

• Medical Diagnosis: Imagine you're building a model to predict whether a patient has a certain disease based on a few key symptoms. If the symptoms are highly indicative of the disease (or lack thereof), both GLM and QDA might perform similarly, especially if the dataset is small.
• Credit Risk Assessment: In credit risk, you might be trying to predict whether a loan applicant will default based on factors like credit score, income, and debt-to-income ratio. If the relationship between these factors and default is relatively linear, GLM might perform just as well as QDA.
• Spam Detection: In spam detection, you might use features like the presence of certain keywords or the sender's email address to classify emails as spam or not spam. If there are clear-cut patterns in the data (e.g., emails with certain keywords are almost always spam), both GLM and QDA might achieve similar results.

In each of these cases, understanding the underlying data and the assumptions of your models is key to interpreting the results. Identical outcomes don't necessarily mean that something is wrong, but they should prompt you to investigate further.

Conclusion: Embracing the Mystery in Machine Learning

So, there you have it! The mystery of identical results in GLM and QDA classification, unraveled. While it can be frustrating to encounter such puzzles, they're also an opportunity to deepen our understanding of machine learning and data analysis. Remember, machine learning is as much an art as it is a science. There's always a chance to learn something new when faced with unexpected results. By systematically investigating the potential causes, we can not only solve the immediate problem but also gain valuable insights that will help us in future projects.

Keep exploring, keep questioning, and most importantly, keep learning, guys! Happy classifying!

Why do I get the exact same results for GLM and QDA in a binary classification when using different random seeds?

GLM and QDA Identical Results with Different Random Seeds Anomaly in Binary Classification