In information theory, the typical set is a set of sequences whose probability is close to two raised to the negative power of the entropy of their source distribution. That this set has total probability close to one is a consequence of the asymptotic equipartition property (AEP) which is a kind of law of large numbers. The notion of typicality is only concerned with the probability of a sequence and not the actual sequence itself.
This has great use in compression theory as it provides a theoretical means for compressing data, allowing us to represent any sequence Xn using nH(X) bits on average, and, hence, justifying the use of entropy as a measure of information from a source.
The AEP can also be proven for a large class of stationary ergodic processes, allowing typical set to be defined in more general cases.
Read more about Typical Set: (Weakly) Typical Sequences (weak Typicality, Entropy Typicality), Strongly Typical Sequences (strong Typicality, Letter Typicality), Jointly Typical Sequences
Famous quotes containing the words typical and/or set:
“Compare the history of the novel to that of rock ‘n’ roll. Both started out a minority taste, became a mass taste, and then splintered into several subgenres. Both have been the typical cultural expressions of classes and epochs. Both started out aggressively fighting for their share of attention, novels attacking the drama, the tract, and the poem, rock attacking jazz and pop and rolling over classical music.”
—W. T. Lhamon, U.S. educator, critic. “Material Differences,” Deliberate Speed: The Origins of a Cultural Style in the American 1950s, Smithsonian (1990)
“But at the coming of the King of Heaven
All’s set at six and seven:
We wallow in our sin;
Christ cannot finde a chamber in the inn.”
—Unknown. Yet if His Majesty, Our Sovereign Lord (l. 25–28)