# markov

Published articles for markov.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## A Proofless Introduction to Information Theory

DevFeed: [A Proofless Introduction to Information Theory](<https://devfeed.tech/articles/a-proofless-introduction-to-information-theory-40377.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2015/02/16/a-proofless-introduction-to-information-theory/>)

Published: 2015-02-16T09:00:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Encoding](<https://devfeed.tech/topics/encoding.md>), [digital](<https://devfeed.tech/topics/digital.md>)

Tags: [channel](<https://devfeed.tech/tags/channel.md>), [coding-theory](<https://devfeed.tech/tags/coding-theory.md>), [communication](<https://devfeed.tech/tags/communication.md>), [compression](<https://devfeed.tech/tags/compression.md>), [digital](<https://devfeed.tech/tags/digital.md>), [encoding](<https://devfeed.tech/tags/encoding.md>), [entropy](<https://devfeed.tech/tags/entropy.md>), [error](<https://devfeed.tech/tags/error.md>), [error-correction](<https://devfeed.tech/tags/error-correction.md>), [example](<https://devfeed.tech/tags/example.md>), [explain](<https://devfeed.tech/tags/explain.md>), [hamming](<https://devfeed.tech/tags/hamming.md>), [independent](<https://devfeed.tech/tags/independent.md>), [information](<https://devfeed.tech/tags/information.md>), [information-theory](<https://devfeed.tech/tags/information-theory.md>), [kolmogorov-complexity](<https://devfeed.tech/tags/kolmogorov-complexity.md>), [language](<https://devfeed.tech/tags/language.md>), [markov](<https://devfeed.tech/tags/markov.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [messages](<https://devfeed.tech/tags/messages.md>), [models](<https://devfeed.tech/tags/models.md>), [probabilistic-method](<https://devfeed.tech/tags/probabilistic-method.md>), [problems](<https://devfeed.tech/tags/problems.md>), [shannon](<https://devfeed.tech/tags/shannon.md>), [theory](<https://devfeed.tech/tags/theory.md>)

### AI overview

A proofless introduction to information theory explains noiseless and noisy communication problems, encoding schemes, entropy, and how entropy differs from Kolmogorov complexity.

### Source excerpt

There are two basic problems in information theory that are very easy to explain. Two people, Alice and Bob, want to communicate over a digital channel over some long period of time, and they know the probability that certain messages will be sent ahead of time. For example, English language sentences are more likely than gibberish, and "Hi" is much more likely than "asphyxiation." The problems are: Say communication is very expensive.

## The Giant Component and Explosive Percolation

DevFeed: [The Giant Component and Explosive Percolation](<https://devfeed.tech/articles/the-giant-component-and-explosive-percolation-40375.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2015/02/02/the-giant-component-and-explosive-percolation/>)

Published: 2015-02-02T09:00:00Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Graphs](<https://devfeed.tech/topics/graphs.md>), [Data analysis](<https://devfeed.tech/topics/data-analysis.md>)

Tags: [big-o-notation](<https://devfeed.tech/tags/big-o-notation.md>), [erdos-renyi](<https://devfeed.tech/tags/erdos-renyi.md>), [first-moment-method](<https://devfeed.tech/tags/first-moment-method.md>), [giant-component](<https://devfeed.tech/tags/giant-component.md>), [graph](<https://devfeed.tech/tags/graph.md>), [graphs](<https://devfeed.tech/tags/graphs.md>), [inequality](<https://devfeed.tech/tags/inequality.md>), [markov](<https://devfeed.tech/tags/markov.md>), [method-of-moments](<https://devfeed.tech/tags/method-of-moments.md>), [network-science](<https://devfeed.tech/tags/network-science.md>), [percolation](<https://devfeed.tech/tags/percolation.md>), [probability-theory](<https://devfeed.tech/tags/probability-theory.md>), [random-graph](<https://devfeed.tech/tags/random-graph.md>), [random-graphs](<https://devfeed.tech/tags/random-graphs.md>), [random-variables](<https://devfeed.tech/tags/random-variables.md>)

### AI overview

This article develops rigorous results about Erdős-Rényi random graphs, following a conjecture about connectivity at edge probability p = 5/n. It introduces threshold theorems and begins explaining the first moment method, Markov's inequality, and isolated vertices.

### Source excerpt

Last time we left off with a tantalizing conjecture: a random graph with edge probability $ p = 5/n$ is almost surely a connected graph. We arrived at that conjecture from some ad-hoc data analysis, so let's go back and treat it with some more rigorous mathematical techniques. As we do, we'll discover some very interesting "threshold theorems" that essentially say a random graph will either certainly have a property, or it will certainly not have it.

## Probabilistic Bounds -- A Primer

DevFeed: [Probabilistic Bounds -- A Primer](<https://devfeed.tech/articles/probabilistic-bounds-a-primer-40312.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2013/04/15/probabilistic-bounds-a-primer/>)

Published: 2013-04-15T11:14:32Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>), [math](<https://devfeed.tech/topics/math.md>), [Learning](<https://devfeed.tech/topics/learning.md>), [Streaming](<https://devfeed.tech/topics/streaming.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [algorithms](<https://devfeed.tech/tags/algorithms.md>), [chebyshev](<https://devfeed.tech/tags/chebyshev.md>), [chernoff](<https://devfeed.tech/tags/chernoff.md>), [chernoff-bound](<https://devfeed.tech/tags/chernoff-bound.md>), [inequality](<https://devfeed.tech/tags/inequality.md>), [learning-theory](<https://devfeed.tech/tags/learning-theory.md>), [machine-learning](<https://devfeed.tech/tags/machine-learning.md>), [markov](<https://devfeed.tech/tags/markov.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [probabilistic](<https://devfeed.tech/tags/probabilistic.md>), [probabilistic-method](<https://devfeed.tech/tags/probabilistic-method.md>), [probability-theory](<https://devfeed.tech/tags/probability-theory.md>), [random-variables](<https://devfeed.tech/tags/random-variables.md>), [streaming](<https://devfeed.tech/tags/streaming.md>), [streaming-algorithms](<https://devfeed.tech/tags/streaming-algorithms.md>), [variance](<https://devfeed.tech/tags/variance.md>)

### AI overview

This tutorial introduces probabilistic bounds used in algorithm analysis, machine learning theory, randomized algorithms, and streaming algorithms. It focuses on the Chernoff bound and presents simpler bounds from Markov's and Chebyshev's inequalities, including short proofs.

### Source excerpt

Probabilistic arguments are a key tool for the analysis of algorithms in machine learning theory and probability theory. They also assume a prominent role in the analysis of randomized and streaming algorithms, where one imposes a restriction on the amount of storage space an algorithm is allowed to use for its computations (usually sublinear in the size of the input). While a whole host of probabilistic arguments are used, one theorem in particular (or family of theorems) is ubiquitous: the Chernoff bound.