1,246,203 research outputs found
Stream Sampling for Frequency Cap Statistics
Unaggregated data, in streamed or distributed form, is prevalent and come
from diverse application domains which include interactions of users with web
services and IP traffic. Data elements have {\em keys} (cookies, users,
queries) and elements with different keys interleave. Analytics on such data
typically utilizes statistics stated in terms of the frequencies of keys. The
two most common statistics are {\em distinct}, which is the number of active
keys in a specified segment, and {\em sum}, which is the sum of the frequencies
of keys in the segment. Both are special cases of {\em cap} statistics, defined
as the sum of frequencies {\em capped} by a parameter , which are popular in
online advertising platforms. Aggregation by key, however, is costly, requiring
state proportional to the number of distinct keys, and therefore we are
interested in estimating these statistics or more generally, sampling the data,
without aggregation. We present a sampling framework for unaggregated data that
uses a single pass (for streams) or two passes (for distributed data) and state
proportional to the desired sample size. Our design provides the first
effective solution for general frequency cap statistics. Our -capped
samples provide estimates with tight statistical guarantees for cap statistics
with and nonnegative unbiased estimates of {\em any} monotone
non-decreasing frequency statistics. An added benefit of our unified design is
facilitating {\em multi-objective samples}, which provide estimates with
statistical guarantees for a specified set of different statistics, using a
single, smaller sample.Comment: 21 pages, 4 figures, preliminary version will appear in KDD 201
A Bayesian approach to adaptive frequency sampling
This paper introduces an adaptive frequency sampling scheme, based on a Bayesian approach to the well-known vector fitting algorithm. This Bayesian treatment results in a data-driven measure of intrinsic model uncertainty. This uncertainty measure can in turn be leveraged to sample sequentially in an efficient and robust way. A realistic example is used to visualize the proposed scheme, and to confirm its proficiency
High frequency sampling of a continuous-time ARMA process
Continuous-time autoregressive moving average (CARMA) processes have recently
been used widely in the modeling of non-uniformly spaced data and as a tool for
dealing with high-frequency data of the form , where
is small and positive. Such data occur in many fields of application,
particularly in finance and the study of turbulence. This paper is concerned
with the characteristics of the process (Y_{n\Delta})_{n\in\bbz}, when
is small and the underlying continuous-time process (Y_t)_{t\in\bbr}
is a specified CARMA process.Comment: 13 pages, submitte
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