But what is Entropy?

This write-up re-introduces the concept of entropy from different perspectives with a focus on its importance in machine learning, probabilistic programming, and information theory.

Here is how it is defined by the dictionaries as per a quick google search -

Image for post

Source: Screenshot of Google Search

Based on this result, you can notice that there are two core ideas here and at first, the correlation between them does not seem to be quite obvious -

  • Entropy is the missing (or required) energy to do work as per thermodynamics
  • Entropy is a measure of disorder or randomness (uncertainty)

So what is it — missing energy, or a measure, or both? Let me provide some perspectives that hopefully would help you come to peace with these definitions.

Shit Happens!

Rephrasing this obnoxious title into something bit more acceptable

Anything that can go wrong, will go wrong — Murphy’s Law

We have all accepted this law because we observe and experience this all the time and the culprit behind this is none other than the topic of this writeup — yup, you got it, it’s Entropy!

So now I have confused you more — entropy is not only the missing energy and the measure of disorder but it is also responsible for the disorder. Great!

We can not make up our minds here as far as the definition is concerned. However, the truth is all of the above mentioned 3 perspectives are correct given the appropriate context. To understand these contexts let’s first check out disorder and its relation with entropy.

Disorder is the dominating force

I explain this with the help of examples from an article by James Clear (Author of Atomic Habits).

Image for post

Source: Left Image (https://pixabay.com/illustrations/puzzle-puzzle-piece-puzzles-3303412/) Right Image (Photo by James Lee on Unsplash) + annotated by Author

Theoretically, both of these are possible but the odds of them happening are astronomically small. Ok, fine, call it impossible 🤐 !. The main message here is the following:

There are always far more disorderly variations than orderly ones!

and borrowing the wisdom of great Steven Pinker -:

Image for post

#kl-divergence #machine-learning #entropy #intuition #tensorflow-probability #tensorflow

What is GEEK

Buddha Community

But what is Entropy?

But what is Entropy?

This write-up re-introduces the concept of entropy from different perspectives with a focus on its importance in machine learning, probabilistic programming, and information theory.

Here is how it is defined by the dictionaries as per a quick google search -

Image for post

Source: Screenshot of Google Search

Based on this result, you can notice that there are two core ideas here and at first, the correlation between them does not seem to be quite obvious -

  • Entropy is the missing (or required) energy to do work as per thermodynamics
  • Entropy is a measure of disorder or randomness (uncertainty)

So what is it — missing energy, or a measure, or both? Let me provide some perspectives that hopefully would help you come to peace with these definitions.

Shit Happens!

Rephrasing this obnoxious title into something bit more acceptable

Anything that can go wrong, will go wrong — Murphy’s Law

We have all accepted this law because we observe and experience this all the time and the culprit behind this is none other than the topic of this writeup — yup, you got it, it’s Entropy!

So now I have confused you more — entropy is not only the missing energy and the measure of disorder but it is also responsible for the disorder. Great!

We can not make up our minds here as far as the definition is concerned. However, the truth is all of the above mentioned 3 perspectives are correct given the appropriate context. To understand these contexts let’s first check out disorder and its relation with entropy.

Disorder is the dominating force

I explain this with the help of examples from an article by James Clear (Author of Atomic Habits).

Image for post

Source: Left Image (https://pixabay.com/illustrations/puzzle-puzzle-piece-puzzles-3303412/) Right Image (Photo by James Lee on Unsplash) + annotated by Author

Theoretically, both of these are possible but the odds of them happening are astronomically small. Ok, fine, call it impossible 🤐 !. The main message here is the following:

There are always far more disorderly variations than orderly ones!

and borrowing the wisdom of great Steven Pinker -:

Image for post

#kl-divergence #machine-learning #entropy #intuition #tensorflow-probability #tensorflow

Entropy Application in the Stock Market

Note from Towards Data Science’s editors:_ While we allow independent authors to publish articles in accordance with our rules and guidelines, we do not endorse each author’s contribution. You should not rely on an author’s works without seeking professional advice. See our Reader Terms for details._

A lot of definitions and formulations of entropy are available. What in general is true is that entropy is used to measure informationsurprise, or _uncertainty _regarding experiments’ possible outcomes. In particular, Shannon entropy is the one that is used most frequently in statistics and machine learning. For this reason, it’s the focus of our attention here.

Surprise and uncertainty are daily concepts in the financial market. So using the entropy as an instrument to explore the market sounds like a very spicy idea. What we expect is to reveal a remarkable pattern between the new measure and the volatility of the assets’ prices over time.

Considering our aims, I think it’s valuable to introduce the standard approach and considerations provided in this work. The authors introduced the concept of **Structural Entropy **and used it to monitor a correlation-based network over time with application to financial markets.

#entropy #finance #machine-learning #data-science #editors-pick

Learn Entropy for Data Science - Clearly Explained

Entropy is a fundamental concept in Data Science because it shows up all over the place - from Decision Trees, to similarity metrics, to state of the art dimension reduction algorithms. It's also surprisingly simple, but often poorly explained. Traditionally the equation is presented with the expectation that you memorize it without thoroughly understanding what it means and where it came from. This video takes a very different approach by showing you, step-by-step, where this simple equation comes from, making it easy to remember (and derive), understand and explain to your friends at parties.

0:00 Awesome song and introduction
1:28 Introduction to surprise
4:34 Equation for surprise
6:09 Calculating surprise for a series of events
9:35 Entropy defined for a coin
10:45 Entropy is the expected value of surprise
11:41 The entropy equation
13:01 Entropy in action!!!

Subscribe: https://www.youtube.com/c/joshstarmer/featured 

#Entropy #data-science #machine-learning 

Rusty  Shanahan

Rusty Shanahan

1597716000

Enhance Decision Tree accuracy with Tsallis Entropy

We have been using decision trees for regression and classification problems for good amount of time. In the training process, growth of the tree depends on the split criteria after random selection of samples and features from the training data. We have been using Gini Index or Shannon Entropy as the split criteria across techniques developed around decision tree. And its well accepted decision criteria across time and domain.

Its has been suggested that choosing between Gini Index and Shannon Entropy does not make significant different. In practice we choose Gini Index over Shanon Entropy just to avoid logarithmic computations.

The most methodical part of decision tree is spliting the nodes. We can understand the criticality of the meaurement we choose for the split. Gini Index has worked out for most of the solutions but whats the harm in getting additional few points of accuracy.

The very near by alternative to Gini Index and Shannon Entropy is Tsallis Entropy. Actually Tsallis is not alternative but the parent of Gini and Entropy. Lets see how -

#machine-learning #data-science #entropy #decision-tree #information-theory #deep learning

Arno  Bradtke

Arno Bradtke

1601293080

Why and How to use Cross Entropy

Introduction

This post discusses why logistic regression necessarily uses a different loss function than linear regression. First, the simple yet inefficient way to solve logistic regression will be presented, then the slightly less simple but much more efficient way will be explained and compared.

The simple way

Linear regression is the predecessor of logistic regression for most people studying statistics or machine learning. Some reasons for this might include the following: the equation for making predictions looks just like the y=mx+b equation from high school algebra; the mean squared error cost function can be visualized; it comes with a nice closed-form equation for solving; and best of all, you actually don’t need to know linear algebra or calculus to find the solution.

#log-loss #machine-learning #logistic-regression #cross-entropy #statistics