… vector norms studied in the data stream and sketching models, … α)-sketching family if from
L(A), one can approximate A q→p … bounds on the sketching dimension k for every p, q ∈ [1, ∞], …

… -p norms for p > 2, for which we prove an Ω(n2−4/p) lower bound, and give a matching O(n2−4/p)
upper bound for even integers p. … σ to be an ordered pair of a sequence of length q: σ = …

… allows efficient sketches if and only if it … norms that are closed under sum-product, efficient
sketching is equivalent to embedding into l1 with constant distortion. Examples of such norms …

… p-norm up to a constant factor (except for the p = ∞ case) with constant probability in both
the bilinear sketching and general sketching … an r × s submatrix Q of UV T from an r × s …

… ± ε)approximating the Lp norm, for real p with 1 ≤ p ≤ 2, of a … Our result also holds for 0 <p<
1; although Lp is not a norm in … a prime q and treating all updates (i, v) as (i mod q, v), our Lp …

… x 2 Rn and p ≥ 1, we use kxkp to denote its `p norm, and kxk0 to denote its `0 norm, ie, the
… Throughout the discussion, we use ⇠(q) 2 Rn to denote a vector with q non-zero entries and …

… consider the ℓp-norm for p > 2, where the task is to approximate the k-residual x − xk p up to
a constant factor, where xk is the optimal k-sparse approximation to x. Such vector norms are …

… Then the variance is roughly equal to dp as it is in the form of Schatten p norms with p ≥ 2.
In this … In the following we consider the case where q > 0 where, without loss of generality, we …

… A collection of vectors {C1,..., Cn}∈[q]t is called a code with alphabet size q and block
length t, and we define (Ci, Cj) = |{k : (Ci)k = (Cj)k}|. The relative distance of the code is maxi=j …

… output a vector x for which x − x p ⩽ Cxtail(k) q, where xtail(k) denotes x with its top k
coefficients (in magnitude) replaced with zero, p and q are norms, and C > 1 is an approximation …