Solution Method

Solution Method#

Ordinary Least Squares (OLS) Regression#

  1. Formulation of the Problem

  2. Objective Function

  3. Expanding the Objective Function

  4. Finding the Minimum

  5. Solving for \( \boldsymbol{\beta} \)

  6. Solution Summary

  7. Additional Considerations

  8. Example

Least Mean Squares (LMS) and Recursive Least Squares (RLS) Algorithms#

  1. Formulation of the Problem

  2. Objective Function

  3. Gradient Descent Approach

  4. Convergence Analysis

  5. Variants of LMS

Kalman Filter#

  1. Formulation of the Problem

  2. State Space Model

  3. Prediction Step

  4. Update Step

  5. Convergence and Stability

Proximal Mapping: A Comprehensive Overview#

  1. Proximal Operator Definition

  2. Proximal Operator for \( g(x) = \lambda |x| \)

  3. Interpretation

  4. Proximal Operator for the Zero Function \( g(x) \equiv 0 \)

  5. Conclusion