Gradient Descent and Regression Models

Overview of Regression Models

• Definition: Regression models are simple models in machine learning used for predicting continuous numerical values (e.g., stock prices, temperatures).
• Example Use Case: Predicting salaries based on years of experience.

Understanding the Relationship in Data

• Regression Problem: Involves predicting unknown continuous values (e.g., salaries).
• Explanatory Data Analysis: Understand the relationship between years of experience and salaries by plotting data.
  • Observation: Typically, as experience increases, salaries increase (positive relationship).

Training the Regression Model

• Model Representation: Regression model is a straight line represented by the equation:
  Y = WX + B
  Where:
  • Y: Predicted value
  • W: Model weight
  • X: Input value
  • B: Bias term
• Model Parameters: W and B are the parameters the model learns during training.

Error Measurement

• Definition of Error: The difference between the model's predicted value and the actual value.
• Error Calculation:
  • Subtract actual Y value from predicted Y value.
  • Focus on the magnitude of the error, either by taking the absolute value or squaring it.
• Loss Functions: Commonly used loss functions for regression tasks include:
  • Mean Squared Error (MSE):
    Calculation:
    • Sum of squared errors divided by the number of data points.
  • Mean Absolute Error (MAE):
    Calculation:
    • Sum of absolute errors divided by the number of data points.

Model Training Process

• Objective: Find the best combination of model parameters (W and B) that minimize the loss function.
• Gradient Descent: Algorithm that iteratively adjusts model parameters based on the gradient of the loss function.
  • Learning Rate: Controls how fast the model learns (often a small value).

Standardizing the Dataset

• Importance: Standardizing ensures features are on the same scale with mean 0 and standard deviation 1, aiding model learning efficiency.

Training Steps Overview

1. Initialize model with random parameters.
2. Set a learning rate (e.g., 0.06).
3. Calculate loss for parameter values.
4. Update parameters based on loss gradient.
5. Repeat the process (an Epoch) until minimum loss is achieved.

Observing Changes in Loss

• Epochs: The process of training (adjusting parameters) continues until the loss function reaches a minimum value.
• Learning Rate Impact:
  • Small learning rate = gradual convergence.
  • Large learning rate (e.g., 0.9) = unstable learning, causing the model to oscillate.

Incorporating Bias

• Additional Parameter: Adding bias into the model necessitates calculating gradients for both weight and bias concurrently.
• 3D Representation: The loss plot becomes three-dimensional with respect to both weight and bias.

Applications of Gradient Descent

• Gradient descent allows for the modeling of various relationships in different datasets.
• Advanced Optimization Algorithms: Concepts of gradient descent lead to more sophisticated methods like Adam, adaptive momentum, mini-batch, and stochastic gradient descent.

Conclusion

• Understanding gradient descent is fundamental for building and optimizing regression models in machine learning.