120,046 research outputs found
ECA: High Dimensional Elliptical Component Analysis in non-Gaussian Distributions
We present a robust alternative to principal component analysis (PCA) ---
called elliptical component analysis (ECA) --- for analyzing high dimensional,
elliptically distributed data. ECA estimates the eigenspace of the covariance
matrix of the elliptical data. To cope with heavy-tailed elliptical
distributions, a multivariate rank statistic is exploited. At the model-level,
we consider two settings: either that the leading eigenvectors of the
covariance matrix are non-sparse or that they are sparse. Methodologically, we
propose ECA procedures for both non-sparse and sparse settings. Theoretically,
we provide both non-asymptotic and asymptotic analyses quantifying the
theoretical performances of ECA. In the non-sparse setting, we show that ECA's
performance is highly related to the effective rank of the covariance matrix.
In the sparse setting, the results are twofold: (i) We show that the sparse ECA
estimator based on a combinatoric program attains the optimal rate of
convergence; (ii) Based on some recent developments in estimating sparse
leading eigenvectors, we show that a computationally efficient sparse ECA
estimator attains the optimal rate of convergence under a suboptimal scaling.Comment: to appear in JASA (T&M
Event-Clock Nested Automata
In this paper we introduce and study Event-Clock Nested Automata (ECNA), a
formalism that combines Event Clock Automata (ECA) and Visibly Pushdown
Automata (VPA). ECNA allow to express real-time properties over non-regular
patterns of recursive programs. We prove that ECNA retain the same closure and
decidability properties of ECA and VPA being closed under Boolean operations
and having a decidable language-inclusion problem. In particular, we prove that
emptiness, universality, and language-inclusion for ECNA are EXPTIME-complete
problems. As for the expressiveness, we have that ECNA properly extend any
previous attempt in the literature of combining ECA and VPA
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