559,285 research outputs found
Classification methods for Hilbert data based on surrogate density
An unsupervised and a supervised classification approaches for Hilbert random
curves are studied. Both rest on the use of a surrogate of the probability
density which is defined, in a distribution-free mixture context, from an
asymptotic factorization of the small-ball probability. That surrogate density
is estimated by a kernel approach from the principal components of the data.
The focus is on the illustration of the classification algorithms and the
computational implications, with particular attention to the tuning of the
parameters involved. Some asymptotic results are sketched. Applications on
simulated and real datasets show how the proposed methods work.Comment: 33 pages, 11 figures, 6 table
Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing
Branching processes are a class of continuous-time Markov chains (CTMCs) with
ubiquitous applications. A general difficulty in statistical inference under
partially observed CTMC models arises in computing transition probabilities
when the discrete state space is large or uncountable. Classical methods such
as matrix exponentiation are infeasible for large or countably infinite state
spaces, and sampling-based alternatives are computationally intensive,
requiring a large integration step to impute over all possible hidden events.
Recent work has successfully applied generating function techniques to
computing transition probabilities for linear multitype branching processes.
While these techniques often require significantly fewer computations than
matrix exponentiation, they also become prohibitive in applications with large
populations. We propose a compressed sensing framework that significantly
accelerates the generating function method, decreasing computational cost up to
a logarithmic factor by only assuming the probability mass of transitions is
sparse. We demonstrate accurate and efficient transition probability
computations in branching process models for hematopoiesis and transposable
element evolution.Comment: 18 pages, 4 figures, 2 table
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