Kwstakhcc's Blog https://github.com/kwstakhcc/cool_math_blog/ Posts regarding some relatively unknown and cool theorems in Stochastic Analysis quarto-1.9.37 Tue, 19 May 2026 21:00:00 GMT First Post https://github.com/kwstakhcc/cool_math_blog/posts/welcome/ This is a post to test what stuff can i actually write on a qmd file.

def f(x: int):
    return x+1
Warning

Be careful of not writing functions like these in python, and using lambda expressions instead.

For example, we can initialize a function object that matches the aforementioned procedure, as follows,

    # Initializing function object.
    f = lambda x : x + 1

    # Evaluating the function at a specific point.
    x0 = 5 ; eval_f_x0 = f(x0);

    # Printing the result.
    print(eval_f_x0)

A dumby dumbo image
]]> news code https://github.com/kwstakhcc/cool_math_blog/posts/welcome/ Tue, 19 May 2026 21:00:00 GMT The Gradient Descent Algorithm https://github.com/kwstakhcc/cool_math_blog/posts/optimization-gd/

Introduction

Let’s try and understand the gradient descent algorithm and it’s use cases in optimization.

The Problem Setup

Firstly, we want to formulate some kind of optimization problem, which typically involves a sufficiently “regular” function that we want to maximize/minimize on a “good” subset of . The exact notion of “regular” and “good” will be highlighted later on.

How do we Approach such a Problem?

Can we Devise a Systematic Way that Yields a Nice Result?

Formulating the Iterative Scheme

But when is it Guaranteed to “Work”?

Example

Conclusion/Comments

]]> Optimization https://github.com/kwstakhcc/cool_math_blog/posts/optimization-gd/ Tue, 19 May 2026 21:00:00 GMT