Machine Learning || Checking Gradient Descent for Conversions || Choosing the learning rate

How to Ensure Gradient Descent is Working Correctly?

Understanding Gradient Descent and Learning Rate

• The video discusses how to verify if the gradient descent algorithm is functioning correctly, focusing on convergence and reaching the global minimum cost.

• It emphasizes that selecting a small learning rate can slow down the model significantly, while a large learning rate may lead to divergence, preventing the model from reaching the global minimum.

Key Topics of Discussion

• The presenter outlines two main topics: confirming whether gradient descent operates correctly and how to choose an appropriate learning rate for studies.

• Previous equations are referenced that detail adjustments made by gradient descent in order to achieve optimal weights (w) and biases (b).

Analyzing Cost Function Behavior

• The goal of gradient descent is to find parameter values that minimize the global cost function (J).

• A plot illustrating the relationship between cost (J) and iterations shows how many times weights and biases have been adjusted from the starting point until convergence.

Interpreting Iteration Results

• The curve representing cost versus iterations indicates whether gradient descent is working properly; a decreasing trend in cost suggests effective operation.

• If after several iterations, costs continue decreasing, it confirms that gradient descent is functioning as intended.

Convergence Analysis

• After 300 iterations, if costs stabilize between 300 and 400 iterations, this indicates convergence has been achieved.

• Different applications may require varying numbers of iterations for convergence; some might converge after 30 iterations while others could take up to 100,000.

Alternative Verification Methods

• Another method for verifying training effectiveness involves checking if changes in cost fall below a certain threshold (epsilon), indicating proper convergence behavior.

• If plotting results shows fluctuating costs with increasing iterations, it suggests issues with either code or an excessively high learning rate leading to divergence.

Troubleshooting Divergence Issues

• If costs increase consistently with more iterations, it often points towards problems in coding or an inappropriate learning rate selection.

• Adjusting the learning rate downwards can help rectify issues where costs are not decreasing as expected during training.

Common Coding Errors

• A frequent coding error occurs when incorrectly writing update equations for weights. Using addition instead of subtraction can lead to increased costs over time.

• Correct formulation should involve subtracting a fraction of the derivative from current weight values rather than adding it.

Selecting Appropriate Learning Rates

• Choosing an optimal learning rate requires experimentation; too low will ensure convergence but at a slow pace while too high risks divergence.

Exploring Alpha Values in Iterations

Understanding Alpha Values and Their Impact

• The discussion begins with the exploration of different alpha values commonly used in studies, specifically mentioning "clearing great alpha."

• The process involves testing various alpha values, starting from 1/10 to 1/100, and observing how these affect the cost curve over iterations.

• It is suggested to adjust the alpha value by multiplying it by three instead of ten for more nuanced results during iterations.

• The goal is to identify which curve represents a consistent decrease in cost over iterations, indicating an effective learning rate for the study.

Selecting the Optimal Curve

• Observing the relationship between cost and number of iterations helps in selecting the best curve; ideally, this should show a rapid and continuous decline.

• After experimenting with different alpha values and plotting curves, one must choose the optimal curve that aligns with their learning rate objectives.

Conclusion