11,409 research outputs found
Improved Algorithms for Time Decay Streams
In the time-decay model for data streams, elements of an underlying data set arrive sequentially with the recently arrived elements being more important. A common approach for handling large data sets is to maintain a coreset, a succinct summary of the processed data that allows approximate recovery of a predetermined query. We provide a general framework that takes any offline-coreset and gives a time-decay coreset for polynomial time decay functions.
We also consider the exponential time decay model for k-median clustering, where we provide a constant factor approximation algorithm that utilizes the online facility location algorithm. Our algorithm stores O(k log(h Delta)+h) points where h is the half-life of the decay function and Delta is the aspect ratio of the dataset. Our techniques extend to k-means clustering and M-estimators as well
Deterministic Sampling and Range Counting in Geometric Data Streams
We present memory-efficient deterministic algorithms for constructing
epsilon-nets and epsilon-approximations of streams of geometric data. Unlike
probabilistic approaches, these deterministic samples provide guaranteed bounds
on their approximation factors. We show how our deterministic samples can be
used to answer approximate online iceberg geometric queries on data streams. We
use these techniques to approximate several robust statistics of geometric data
streams, including Tukey depth, simplicial depth, regression depth, the
Thiel-Sen estimator, and the least median of squares. Our algorithms use only a
polylogarithmic amount of memory, provided the desired approximation factors
are inverse-polylogarithmic. We also include a lower bound for non-iceberg
geometric queries.Comment: 12 pages, 1 figur
Computing the likelihood of sequence segmentation under Markov modelling
I tackle the problem of partitioning a sequence into homogeneous segments,
where homogeneity is defined by a set of Markov models. The problem is to study
the likelihood that a sequence is divided into a given number of segments.
Here, the moments of this likelihood are computed through an efficient
algorithm. Unlike methods involving Hidden Markov Models, this algorithm does
not require probability transitions between the models. Among many possible
usages of the likelihood, I present a maximum \textit{a posteriori} probability
criterion to predict the number of homogeneous segments into which a sequence
can be divided, and an application of this method to find CpG islands
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