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:
“Consciousness is cerebral celebrity—nothing more and nothing less. Those contents are conscious that persevere, that monopolize resources long enough to achieve certain typical and “symptomatic” effects—on memory, on the control of behavior and so forth.”
—Daniel Clement Dennett (b. 1942)
“He could walk, or rather turn about in his little garden, and feel more solid happiness from the flourishing of a cabbage or the growing of a turnip than was ever received from the most ostentatious show the vanity of man could possibly invent. He could delight himself with thinking, “Here will I set such a root, because my Camilla likes it; here, such another, because it is my little David’s favorite.””
—Sarah Fielding (1710–1768)