Complexity of Newton’s Method
Newton’s method has a favorable convergence rate, but its complexity can be higher compared to methods like gradient descent. The reason for this could be:
- Computational Cost per Iteration: Each iteration of Newton’s method requires the computation of both the gradient and the Hessian of the function. For functions with a large number of variables, computing the Hessian can be computationally expensive, especially if it’s dense.
- Storage Requirements: Storing and manipulating the Hessian matrix can be memory-intensive, especially for functions with a large number of variables. This can become a bottleneck for high-dimensional optimization problems.
- Numerical Stability: The numerical computation of the Hessian can introduce errors, especially if the function has regions of high curvature or ill-conditioned Hessian matrices. Ensuring numerical stability adds computational overhead.
Newton’s method in Machine Learning
Optimization algorithms are essential tools across various fields, ranging from engineering and computer science to economics and physics. Among these algorithms, Newton’s method holds a significant place due to its efficiency and effectiveness in finding the roots of equations and optimizing functions, here in this article we will study more about Newton’s method and it’s use in machine learning.
Table of Content
- Newton’s Method for Optimization
- Second-Order Approximation
- Newton’s Method for Finding Local Minima or Maxima in Python
- Convergence Properties of Newton’s Method
- Complexity of Newton’s Method
- Time Complexity of Newton’s Method
- Parameter Estimation in Logistic Regression using Newton’s Method
- Data Fitting with Newton’s Method
- Newton’s Method vs Other Optimization Algorithms
- Applications of Newton’s Method
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