2,917 research outputs found
Multiple Testing for Composite Null with FDR Control Guarantee
False discovery rate (FDR) controlling procedures provide important
statistical guarantees for reproducibility in signal identification experiments
with multiple hypotheses testing. In many recent applications, the same set of
candidate features are studied in multiple independent experiments. For
example, experiments repeated at different facilities and with different
cohorts, and association studies with the same candidate features but different
outcomes of interest. These studies provide us opportunities to identify
signals by considering the experiments jointly. We study the question of how to
provide reproducibility guarantees when we test composite null hypotheses on
multiple features. Specifically, we test the unions of the null hypotheses from
multiple experiments. We present a knockoff-based variable selection method to
identify mutual signals from multiple independent experiments, with a finite
sample size FDR control guarantee. We demonstrate the performance of this
method with numerical studies and applications in analyzing crime data and TCGA
data
Unconstrained Proximal Operator: the Optimal Parameter for the Douglas-Rachford Type Primal-Dual Methods
In this work, we propose an alternative parametrized form of the proximal
operator, of which the parameter no longer needs to be positive. That is, the
parameter can be a non-zero scalar, a full-rank square matrix, or, more
generally, a bijective bounded linear operator. We demonstrate that the
positivity requirement is essentially due to a quadratic form. We prove several
key characterizations for the new form in a generic way (with an operator
parameter). We establish the optimal choice of parameter for the
Douglas-Rachford type methods by solving a simple unconstrained optimization
problem. The optimality is in the sense that a non-ergodic worst-case
convergence rate bound is minimized. We provide closed-form optimal choices for
scalar and orthogonal matrix parameters under zero initialization.
Additionally, a simple self-contained proof of a sharp linear convergence rate
for a -cocoercive fixed-point sequence with is provided
(as a preliminary result).
To our knowledge, an operator parameter is new. To show its practical use, we
design a dedicated parameter for the 2-by-2 block-structured semidefinite
program (SDP). Such a structured SDP is strongly related to the quadratically
constrained quadratic program (QCQP), and we therefore expect the proposed
parameter to be of great potential use. At last, two well-known applications
are investigated. Numerical results show that the theoretical optimal
parameters are close to the practical optimums, except they are not a priori
knowledge. We then demonstrate that, by exploiting problem model structures,
the theoretical optimums can be well approximated. Such approximations turn out
to work very well, and in some cases almost reach the underlying limits
Distributed traffic control for reduced fuel consumption and travel time in transportation networks
This paper proposes a distributed framework for optimal control of vehicles in transportation networks. The objective is to reduce the balanced fuel consumption and travel time through hybrid control on speed limit and ramp metering rate. The dual decomposition theory associated with the subgradient method is then applied in order to decompose the optimal control problem into a series of suboptimal problems and then solve them individually via networked road infrastructures (RIs). Coordination among connected RIs is followed in each iteration to update the individual controls. An example is demonstrated to verify the reduction in terms of fuel consumption and travel time using the proposed approach
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