In probability theory, a sub-Gaussian distribution is a probability distribution with strong tail decay. Informally, the tails of a sub-Gaussian distribution are dominated by (i.e. decay at least as fast as) the tails of a Gaussian. This property gives sub-Gaussian distributions their name. Formally, the probability distribution of a random variable is called sub-Gaussian if there are positive constant C such that for every , WebWe use the standard euclidean norm k · k and inner product h·,··i over Rd. The unit sphere this space is denoted by Sd−1:= {u ∈ Rd: kuk = 1}. Letting Rd×d denote the space of d ×d matrices, we also use k · k to denote the operator norm over this space, and tr(·) denotes the trace. Rd×d sym is the subspace consisting of symmetric ...
Sub-Gaussian distribution - Wikipedia
Webdecomposable norms, atomic norms, or general norms all rely on concentration properties of sub-Gaussian distributions [16, 7, 2]. Certain estimators, such as the Dantzig selector and variants, consider a constrained problem rather than a regularized problem as in (2) but the analysis again relies on entries of Xbeing sub-Gaussian [6, 8]. WebThis proves the desired bound. The above bound implies the following bound: If X EX b, for some b>0, then P[X EX+ ] exp[ n 2=(2Var(X) + 2 b=3)]: This is similar to the Gaussian … breathing brain break for kids
On the Parallelization Upper Bound for Asynchronous Stochastic ...
Web28 Mar 2024 · This paper considers an SA involving a contraction mapping with respect to an arbitrary norm, and shows its finite-sample error bounds while using different stepsizes, and uses it to establish the first-known convergence rate of the V-trace algorithm for off-policy TD-learning. 23 Highly Influential PDF Webr k r r 1.2. Sub-Gaussian random variables and Chernoff bounds 19 The second statement follows from Γ(k/2) ≤ (k/2) k/2 Web6 Jul 2024 · In your first equation, you assumed the sub-Gaussianity of the squared norm of $y$, which is not our hypothesis. For a vector to be sub-Gaussian with norm $C$, the … cotswold wednesbury