16,088 research outputs found
A Knowledge Gradient Policy for Sequencing Experiments to Identify the Structure of RNA Molecules Using a Sparse Additive Belief Model
We present a sparse knowledge gradient (SpKG) algorithm for adaptively
selecting the targeted regions within a large RNA molecule to identify which
regions are most amenable to interactions with other molecules. Experimentally,
such regions can be inferred from fluorescence measurements obtained by binding
a complementary probe with fluorescence markers to the targeted regions. We use
a biophysical model which shows that the fluorescence ratio under the log scale
has a sparse linear relationship with the coefficients describing the
accessibility of each nucleotide, since not all sites are accessible (due to
the folding of the molecule). The SpKG algorithm uniquely combines the Bayesian
ranking and selection problem with the frequentist regularized
regression approach Lasso. We use this algorithm to identify the sparsity
pattern of the linear model as well as sequentially decide the best regions to
test before experimental budget is exhausted. Besides, we also develop two
other new algorithms: batch SpKG algorithm, which generates more suggestions
sequentially to run parallel experiments; and batch SpKG with a procedure which
we call length mutagenesis. It dynamically adds in new alternatives, in the
form of types of probes, are created by inserting, deleting or mutating
nucleotides within existing probes. In simulation, we demonstrate these
algorithms on the Group I intron (a mid-size RNA molecule), showing that they
efficiently learn the correct sparsity pattern, identify the most accessible
region, and outperform several other policies
Beyond Support in Two-Stage Variable Selection
Numerous variable selection methods rely on a two-stage procedure, where a
sparsity-inducing penalty is used in the first stage to predict the support,
which is then conveyed to the second stage for estimation or inference
purposes. In this framework, the first stage screens variables to find a set of
possibly relevant variables and the second stage operates on this set of
candidate variables, to improve estimation accuracy or to assess the
uncertainty associated to the selection of variables. We advocate that more
information can be conveyed from the first stage to the second one: we use the
magnitude of the coefficients estimated in the first stage to define an
adaptive penalty that is applied at the second stage. We give two examples of
procedures that can benefit from the proposed transfer of information, in
estimation and inference problems respectively. Extensive simulations
demonstrate that this transfer is particularly efficient when each stage
operates on distinct subsamples. This separation plays a crucial role for the
computation of calibrated p-values, allowing to control the False Discovery
Rate. In this setup, the proposed transfer results in sensitivity gains ranging
from 50% to 100% compared to state-of-the-art
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