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[6] [7] It is also known as Fréchet-Cramér–Rao or Fréchet-Darmois-Cramér-Rao lower bound. It states that the precision of any unbiased estimator is at most the Fisher information; or (equivalently) the reciprocal of the Fisher information is a lower bound on its variance.
Moreover, the encoding and decoding energy complexity of generalized polar codes can reach the fundamental lower bounds for energy consumption of two dimensional circuitry to within an O(n ε polylog n) factor for any ε > 0. [2]
Proving lower bounds on size of Boolean circuits computing explicit Boolean functions is a popular approach to separating complexity classes. For example, a prominent circuit class P/poly consists of Boolean functions computable by circuits of polynomial size.
When the cost denotes the running time of an algorithm, Yao's principle states that the best possible running time of a deterministic algorithm, on a hard input distribution, gives a lower bound for the expected time of any Las Vegas algorithm on its worst-case input. Here, a Las Vegas algorithm is a randomized algorithm whose runtime may vary ...
Binary search Visualization of the binary search algorithm where 7 is the target value Class Search algorithm Data structure Array Worst-case performance O (log n) Best-case performance O (1) Average performance O (log n) Worst-case space complexity O (1) Optimal Yes In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search ...
The lower bound on worst-case running time of output-sensitive convex hull algorithms was established to be Ω(n log h) in the planar case. [1] There are several algorithms which attain this optimal time complexity. The earliest one was introduced by Kirkpatrick and Seidel in 1986 (who called it "the ultimate convex hull algorithm").
In general, the VC dimension of a finite classification model, which can return at most different classifiers, is at most (this is an upper bound on the VC dimension; the Sauer–Shelah lemma gives a lower bound on the dimension).
Upper bound inequality: For every , there is a sequence converging to such that F ( x ) ≥ lim sup n → ∞ F n ( x n ) {\displaystyle F(x)\geq \limsup _{n\to \infty }F_{n}(x_{n})} The first condition means that F {\displaystyle F} provides an asymptotic common lower bound for the F n {\displaystyle F_{n}} .