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Photo by Yogesh Phuyal on Unsplash

Have you ever wondered how your computer interprets human written (C-) code, compiles it to machine code and executes the operation you just programmed? For me those internal mechanics were a “miracle” for a long time — you hit compile, wait several seconds and voilà, your application runs!

Code in interpreted languages like Python or JavaScript, can be executed immediately, without any intermediate compilation, almost on any arbitrary operating system of your choice.

But what happens underneath? This article thrives to give you some deeper insight in compilers, computer architectures, assembly language and the mysterious machine code. …

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Machine Learning is everywhere. You hear about groundbreaking advances in language processing, computer vision or reinforcement learning everyday. Surprisingly, there are only few prominent examples for applying machine learning as core element in safety critical systems inside the engineering domain. Sure, Autonomous Driving (AD) stack heavily depends on Deep Learning algorithms for perception using radar, LIDAR and video as input, though the control part is still managed by methods developed over centuries in system theory and control engineering.

Reinforcement learning tries to solve the problem of controlling complex systems, but training agents requires thousands of epochs of trial-and-error (exploration/exploitation) in the target environment (i.e. in the AD example: real traffic with real vehicles)—which can be expensive or even dangerous. Alternatively, you could have a sufficiently accurate physical simulation of your environment, which you could use to train the baseline of your agent and later, after you reached a certain threshold with its performance, deploy the agent into real environment to transfer and adjust its knowledge. Physical models often simplify our non-linear real world in order to allow (numerical) calculations. RL agents will adjust their internal non-linear state-value or state-action function to those specific situations and achieve a superior performance as compared to traditional control methods. …

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Photo by Marcin Kempa on Unsplash

During your statistics lectures you surely heard of the famous and fundamental Central Limit Theorem. Especially for political surveys, drug effectiveness evaluations and A/B testing for digital goods this theorem allows us to draw conclusions from relatively small sample size in our tests. The “relatively small” refers to the whole population of objects/people/customers which are usually the goal of our investigation.

In this article I will introduce the most important concepts for applying Central Limit Theorem for inductive statistics and show with a simple visual example, how we get a normal distribution from the sum of any distributed random variable with a simple visual example. …

During my master studies working through homework in probability theory I spend a bunch of hours of drinking coffee and struggling with an assignment, which seemed to be quite trivial at the first glance. Here it is:

Given two independent uniformly distributed random variables X and Y, determine the probability density function p(Z=z) of Z=X+Y . Mathematically speaking:

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We can say, that the resulting function will have the range [0, 2] since there should be a probability for sampling both x=1 and y=1. But — just adding two uniform distributions won’t give us the right solution to the problem.

After a quick web search I found the theoretical tool, which is required to solve the task: Convolution of probability distributions. It…


Marat Kopytjuk

Engineer and student (again) — I love to read and write about statistics, ML, control theory and Python.

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