23,530 research outputs found
Online change detection in exponential families with unknown parameters
International audienceThis paper studies online change detection in exponential families when both the parameters before and after change are unknown. We follow a standard statistical approach to sequential change detection with generalized likelihood ratio test statistics. We interpret these statistics within the framework of information geometry, hence providing a unified view of change detection for many common statistical models and corresponding distance functions. Using results from convex duality, we also derive an efficient scheme to compute the exact statistics sequentially, which allows their use in online settings where they are usually approximated for the sake of tractability. This is applied to real-world datasets of various natures, including onset detection in audio signals
Sequential anomaly detection in the presence of noise and limited feedback
This paper describes a methodology for detecting anomalies from sequentially
observed and potentially noisy data. The proposed approach consists of two main
elements: (1) {\em filtering}, or assigning a belief or likelihood to each
successive measurement based upon our ability to predict it from previous noisy
observations, and (2) {\em hedging}, or flagging potential anomalies by
comparing the current belief against a time-varying and data-adaptive
threshold. The threshold is adjusted based on the available feedback from an
end user. Our algorithms, which combine universal prediction with recent work
on online convex programming, do not require computing posterior distributions
given all current observations and involve simple primal-dual parameter
updates. At the heart of the proposed approach lie exponential-family models
which can be used in a wide variety of contexts and applications, and which
yield methods that achieve sublinear per-round regret against both static and
slowly varying product distributions with marginals drawn from the same
exponential family. Moreover, the regret against static distributions coincides
with the minimax value of the corresponding online strongly convex game. We
also prove bounds on the number of mistakes made during the hedging step
relative to the best offline choice of the threshold with access to all
estimated beliefs and feedback signals. We validate the theory on synthetic
data drawn from a time-varying distribution over binary vectors of high
dimensionality, as well as on the Enron email dataset.Comment: 19 pages, 12 pdf figures; final version to be published in IEEE
Transactions on Information Theor
Sparse Signal Recovery under Poisson Statistics
We are motivated by problems that arise in a number of applications such as
Online Marketing and explosives detection, where the observations are usually
modeled using Poisson statistics. We model each observation as a Poisson random
variable whose mean is a sparse linear superposition of known patterns. Unlike
many conventional problems observations here are not identically distributed
since they are associated with different sensing modalities. We analyze the
performance of a Maximum Likelihood (ML) decoder, which for our Poisson setting
involves a non-linear optimization but yet is computationally tractable. We
derive fundamental sample complexity bounds for sparse recovery when the
measurements are contaminated with Poisson noise. In contrast to the
least-squares linear regression setting with Gaussian noise, we observe that in
addition to sparsity, the scale of the parameters also fundamentally impacts
sample complexity. We introduce a novel notion of Restricted Likelihood
Perturbation (RLP), to jointly account for scale and sparsity. We derive sample
complexity bounds for regularized ML estimators in terms of RLP and
further specialize these results for deterministic and random sensing matrix
designs.Comment: 13 pages, 11 figures, 2 tables, submitted to IEEE Transactions on
Signal Processin
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