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In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure.For a real-valued continuous function f, defined on an interval [a, b] ⊂ R, its total variation on the interval of definition is a measure of the one-dimensional arclength of the curve with parametric equation x ↦ f(x ...
Total variation distance is half the absolute area between the two curves: Half the shaded area above. In probability theory, the total variation distance is a statistical distance between probability distributions, and is sometimes called the statistical distance, statistical difference or variational distance.
From the two definitions above, it is clear that the total variation distance between probability measures is always between 0 and 2. To illustrate the meaning of the total variation distance, consider the following thought experiment. Assume that we are given two probability measures μ and ν, as well as a random variable X.
The total variation distance of two distributions and over a finite domain , (often referred to as statistical difference [2] or statistical distance [3] in ...
This definition does not depend on , i.e. the Hellinger distance between P and Q does not change if is replaced with a different probability measure with respect to which both P and Q are absolutely continuous. For compactness, the above formula is often written as
(The Center Square) – Street racers could soon face a rude awakening under legislation considered by state lawmakers on Thursday to require speed-limiters for certain offenses. Rep. Mari Leavitt ...
The regularization parameter plays a critical role in the denoising process. When =, there is no smoothing and the result is the same as minimizing the sum of squares.As , however, the total variation term plays an increasingly strong role, which forces the result to have smaller total variation, at the expense of being less like the input (noisy) signal.
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