Subgaussian random vector
Web11 Feb 2024 · In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm … Web19 Jun 2024 · An approximation problem w.r.t marginal distribution of coordinates of uniform random vector on high-dimensional unit-sphere 3 Does the space of Lipschitz functions have the Radon-Nikodym property?
Subgaussian random vector
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WebI Sub-Gaussian and sub-exponential random variables I Symmetrization I Applications to uniform laws I Azuma-Hoe ding inequalities I Doob martingales and bounded di erences inequality Reading: (this is more than su cient) I Wainwright, High Dimensional Statistics, Chapters 2.1{2.2 I Vershynin, High Dimensional Probability, Chapters 1{2. Web23 Apr 2024 · a is expressed through a normally distributed random vector whose variance is distributed by an a 2-stable distribution [13–16] X = m+ p s1 s2, (1) where s1 is a subordinator with the stability parameter a 2 < 1; s2 is a random vector, dis-tributed by the d-variate normal law N(0,W); and m is a random vector of the means. The random a-stable ...
Web1 Aug 2004 · A traditional method for simulating a sub-Gaussian random vector is by using (1), which we call it method 1 (M1). We can rewrite (1) as follows: (3) X = (X 1 ,…,X n )′ = d … Web1 Aug 2004 · The class of sub-Gaussian random vectors is a parametric subclass of symmetric stable random vectors that includes multivariate normal distributions (when α =2). This subclass of multivariate distributions is …
Web20 Nov 2024 · In this paper, we will prove that even when a subgaussian vector \xi ^ {\left ( i\right) } \in {\mathbb {C}}^m does not fulfill a small-ball probability assumption, the PhaseLift method is still able to reconstruct a large class of signals x_0 \in {\mathbb {R}}^n from the measurements. This extends recent work by Krahmer and Liu from the real ... WebSubgaussian random variables, Hoeffding’s inequality, and Cram´er’s large deviation theorem Jordan Bell June 4, 2014 1 Subgaussian random variables For a random variable X, let Λ X(t) = logE(etX), the cumulant generating function of X. A b-subgaussian random variable, b>0, is a random variable Xsuch that Λ X(t) ≤ b 2t 2, t∈R. We ...
WebAbstract. We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices of coordinates in which the mean changes. We propose an online algorithm that produces …
Webbe a linear operator. Let xbe a random vector in Rn whose coordinates are independent, mean zero, unit variance, subgaussian random variables. Then, for every t 0, we have P 2 kAxk H k Ak HS t 2exp ct kAk2 op : (1.3) Here c>0 depends only on the bound on the subgaussian norms. In this result, kAk HS and kAk op denote the Hilbert-Schmidt and ... office depot griffin gaIn 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 , my cholesterol is 206 is that highWebif its distribution is dominated by that of a normal random variable. This can be expressed by requiring that Eexp(˘2=K2) 2 for some K >0; the in mum of such K is traditionally called the sub-gaussian or 2 norm of ˘. This turns the set of subgaussian random variables into the Orlicz space with the Orlicz function 2(t) = exp(t2) 1. A number of ... office depot green bay wiWebiin that convex combination as probabilities that a random vector Ztakes the values z i;i= 1;:::;m, respectively. That is, we define P(Z= z i) = i; i= 1;:::;m: This is possible by the fact that the weights i2[0;1] and sum to 1. Consider now a sequence (Z j) j2Nof copies of Z. office depot großostheimWeb12 Jan 2024 · prove that X is a sub-gaussian random vector no matter if coordinates are independent or dependent. It is easy to prove the result in the case of independent … office depot grey office chairWeb20 Mar 2024 · Expectation of the norm of a random vector. Suppose X is a random vector denoted as ( X 1, ⋯, X n), where X 1, ⋯, X n are iid random variables with sub-Gaussian distributions. For all i, suppose E [ X i 2] = 1 for simplicity and ‖ X i ‖ ψ 2 = K where ‖ ⋅ ‖ ψ 2 is the sub-Gaussian norm. Let Y = ‖ X ‖ be the 2-norm of X. office depot grevgatanWebwith some vector a. We de ne Y to be P n i=1 a iX i. We will prove concentration inequalities for Y by imposing conditions on X i: one such condition is requiring X ito be subgaussian. 2.1.1 Subgaussian random variables De nition 2.1 (Subgaussian decay). A random variable X is said to be ˙-subgaussian if my cholesterol is 222