Robert J. Adler
Multiple testing of local maxima for detection of peaks in 1D.
Thu, 03/15/2012 - 15:01 — SomNambulAuthors: Robert J. Adler, Armin Schwartzman, Yulia Gavrilov
Subjects: Statistics
AbstractA topological multiple testing scheme for one-dimensional domains is proposed
where, rather than testing every spatial or temporal location for the presence
of a signal, tests are performed only at the local maxima of the smoothed
observed sequence.Peak Detection as Multiple Testing.
Thu, 08/12/2010 - 15:01 — SomNambulAuthors: Robert J. Adler, Armin Schwartzman, Yulia Gavrilov
Subjects: Methodology
AbstractThis paper considers the problem of detecting equal-shaped non-overlapping
unimodal peaks in the presence of Gaussian ergodic stationary noise, where the
number, location and heights of the peaks are unknown. A multiple testing
approach is proposed in which, after kernel smoothing, the presence of a peak
is tested at each observed local maximum.Persistent Homology for Random Fields and Complexes.
Fri, 03/05/2010 - 16:01 — SomNambulAuthors: Robert J. Adler, Shmuel Weinberger, Omer Bobrowski, Matthew S. Borman, Eliran Subag
Subjects: Probability
AbstractWe discuss and review recent developments in the area of applied algebraic
topology, such as persistent homology and barcodes. In particular, we discuss
how these are related to understanding more about manifold learning from random
point cloud data, the algebraic structure of simplicial complexes determined by
random vertices, and, in most detail, the algebraic topology of the excursion
sets of random fields.Gaussian processes, kinematic formulae and Poincar\'{e}'s limit.
Mon, 08/31/2009 - 17:16 — SomNambulAuthors: Jonathan E. Taylor, Robert J. Adler
Subjects: Differential Geometry
AbstractWe consider vector valued, unit variance Gaussian processes defined over
stratified manifolds and the geometry of their excursion sets. In particular,
we develop an explicit formula for the expectation of all the
Lipschitz--Killing curvatures of these sets. Whereas our motivation is
primarily probabilistic, with statistical applications in the background, this
formula has also an interpretation as a version of the classic kinematic
fundamental formula of integral geometry. All of these aspects are developed in
the paper.
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