AI/ML Model API Design and Numerical Stability (follow-up)

AI/ML Model API Design and Numerical Stability (Follow-Up)

Hello folks, StylePoint here! Today, I want to delve into two significant topics in computer science — API design and numerical stability. These concepts are integral to our work in the Implement series, where we've already implemented three different machine learning (ML) models from scratch. To explore these topics, we'll also look at insights from our community member, Rado Grosso.

Community Insights

Rado left two comments under our video "Implement Gaussian Naive Bayes." The first comment pointed out that the API design for input data (training data saved on the instance) could be improved. Instead, the features and labels should be passed directly to the fit method rather than the init (constructor) method. The rationale is to avoid unnecessary data copying and potential redundancy.

Another more crucial insight by Rado was about numerical stability, emphasizing the importance of using log-likelihoods and sums instead of direct product multiplications to avoid numerical instability issues.

Exploring the Codebase

API Design Adjustments

Initially, our Gaussian Naive Bayes model had features and labels directly in the initializer. The suggestion is to pass these directly to the fit method. This avoids storing potentially large data arrays within the class, making it more memory-efficient. Here’s the revised API for Gaussian Naive Bayes:

class GaussianNaiveBayes:
    def __init__(self):
        self.labels = None

    def fit(self, features, labels):
        self.labels = labels
        # fit model using features directly

    def predict(self, features):
        # prediction logic using self.labels

Update the training code:

model = GaussianNaiveBayes()
model.fit(features, labels)

This pattern reduces memory usage as we're not storing the features unnecessarily.

Numerical Stability

For numerical stability, the main issue revolves around multiplying probabilities in the Gaussian Naive Bayes model. When we multiply many numbers between 0 and 1, the result rapidly approaches zero, potentially causing numerical precision issues.

Instead, we should use logarithms:

import math

## Introduction
prob_product = math.prod(likelihoods)

## Introduction
log_likelihood_sum = sum(map(math.log, likelihoods))
prob_product = math.exp(log_likelihood_sum)

This log-based approach avoids the diminishing product issue and maintains numerical precision over much larger scales. Here’s the revised predict function using log-likelihoods:

def predict(self, features):
    log_prior = math.log(self.prior)
    log_likelihoods = [math.log(self.compute_likelihood(feature)) for feature in features]
    log_posterior = log_prior + sum(log_likelihoods)

    # Convert back from log-scale if necessary
    posterior = math.exp(log_posterior)
    return posterior

By switching to log-based calculations, we significantly improve the numerical stability of our model.

Final Thoughts

We’ve covered essential improvements in API design and tackled numerical stability using logarithms to prevent underflow issues. These insights will also be crucial in our next video on implementing Logistic Regression from scratch, where numerical stability will again play a critical role.

Thank you for your questions and suggestions! Feel free to comment below, and I’ll be sure to address them.

Stay tuned for our next video on Logistic Regression!

Keywords

• API design
• Numerical stability
• Log-likelihoods
• Gaussian Naive Bayes
• Machine learning
• Numerical precision
• Logarithms
• Logistic regression
• Hyperparameters
• Fit method

FAQ

Q1: Why should we pass features and labels directly to the fit method instead of storing them in the initializer?

Storing features and labels directly in the initializer unnecessarily retains large arrays within the class instance, consuming more memory. By passing them directly to the fit method, we avoid redundancies and make the model more memory-efficient.

Q2: What is numerical stability, and why is it important?

Numerical stability refers to the robustness of algorithms against numerical precision errors, such as underflows and overflows, that arise from operations on very large or very small numbers. It is crucial for obtaining accurate and reliable results in ML models.

Q3: How does using logarithms solve numerical stability issues?

Using logarithms converts multiplication of probabilities to summation of log-likelihoods, preventing the product from rapidly approaching zero. This maintains numerical precision over larger scales and avoids underflow.

Q4: How can we ensure API designs are more efficient in machine learning models?

Efficient API designs in ML models can be achieved by minimizing data storage within class instances, passing data directly to methods, and only storing necessary hyperparameters and small data types like floats, ints, and booleans.

Q5: Can these principles be applied to other machine learning models?

Absolutely! The principles of efficient API design and numerical stability are broadly applicable across various ML models, including unsupervised learning models and more complex deep learning architectures.