In probability theory, the term i.i.d. condition is loosely stated to describe random variables that are independent of each other and are identically distributed. This is equivalent to saying that there is a joint distribution whose marginals are identical and independent of each other. In an infinite dimensional setting, Daniel-Kolmogorov theorem is invoked to explore the conditions under which such a joint distribution can be established.

1

Ironically, in many cases, especially in linear regression, calculations become simpler when approached through multi-dimensional matrix algebra rather than one-dimensional methods. Let's explore the foundational concepts of linear regression to understand this phenomenon.

2

The Pintos project is a mini-implementation of an operating system. If you're finding it challenging to install a source file and simulate it on macOS, here is a guideline to help you with the process. Additionally, I'll offer some tips to ease the initiation into the project.

3

We discuss here some system-level implementations of functions in C.

4

We present a greedy-based approximation algorithm designed to reconstruct the vector $x$. It is applicable to matrices $A$ that satisfy the condition $\delta_{3s}\leq\frac 1{12}$. Additionally, the article includes a proof demonstrating the convergence of this algorithm.

5

We explain the motivation of the Kernel method in machine learning theory and how one might go about overcoming the computational challenges.

6

I analyzed the trend of Mathematical Preprint for the last 15 years.

7

I built upon a final project from an advanced linear modeling course, diving deeper into the statistical nuances of obsidian sample data.

8