# probabilistic method

Published articles for probabilistic method.

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## 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.

## 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.

## Ramsey Number Lower Bound

DevFeed: [Ramsey Number Lower Bound](<https://devfeed.tech/articles/ramsey-number-lower-bound-40293.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/12/02/ramsey-number-lower-bound/>)

Published: 2012-12-02T15:17:26Z

Content type: article

Language: en

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

Topics: [graph theory](<https://devfeed.tech/topics/graph-theory.md>), [Graphs](<https://devfeed.tech/topics/graphs.md>), [Mathematics](<https://devfeed.tech/topics/mathematics.md>)

Tags: [combinatorics](<https://devfeed.tech/tags/combinatorics.md>), [computational-complexity](<https://devfeed.tech/tags/computational-complexity.md>), [graph](<https://devfeed.tech/tags/graph.md>), [graph-coloring](<https://devfeed.tech/tags/graph-coloring.md>), [graph-theory](<https://devfeed.tech/tags/graph-theory.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [number-theory](<https://devfeed.tech/tags/number-theory.md>), [probabilistic-method](<https://devfeed.tech/tags/probabilistic-method.md>), [ramsey-numbers](<https://devfeed.tech/tags/ramsey-numbers.md>), [random-graph](<https://devfeed.tech/tags/random-graph.md>)

### AI overview

The article proves a lower bound for the diagonal Ramsey number R(m,m). By randomly coloring the edges of a complete graph, it shows that if binom(n,m)2^(1−binom(m,2)) is less than 1, there exists a coloring with no monochromatic m-vertex subgraph, so R(m,m) > n.

### Source excerpt

Define the Ramsey number $ R(k,m)$ to be the minimum number $ n$ of vertices required of the complete graph $ K_n$ so that for any two-coloring (red, blue) of the edges of $ K_n$ one of two things will happen: There is a red $ k$-clique; that is, a complete subgraph of $ k$ vertices for which all edges are red. There is a blue $ m$-clique. It is known that these numbers are always finite, but it is very difficult to compute them exactly.