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We propose skewed stable random projections for approximating the pthfrequency moments of dynamic data streams (0<p<=2), which has been frequentlystudied in theoretical computer science and database communities. Our methodsignificantly (or even infinitely when p->1) improves previous methods based on(symmetric) stable random projections.  Our proposed method is applicable to data streams that are (a) insertion only(the cash-register model); or (b) always non-negative (the strict Turnstilemodel), or (c) eventually non-negative at check points. This is only a minorrestriction for practical applications.  Our method works particularly well when p = 1+/- \Delta and \Delta is small,which is a practically important scenario. For example, \Delta may be the decayrate or interest rate, which are usually small. Of course, when \Delta = 0, onecan compute the 1th frequent moment (i.e., the sum) essentially error-freeusing a simple couter. Our method may be viewed as a ``genearlized counter'' inthat it can count the total value in the future, taking in account of theeffect of decaying or interest accruement.  In a summary, our contributions are two-fold. (A) This is the first propsalof skewed stable random projections. (B) Based on first principle, we developvarious statistical estimators for skewed stable distributions, including theirvariances and error (tail) probability bounds, and consequently the samplecomplexity bounds.

On Approximating Frequency Moments of Data Streams with Skewed Projections