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 $(1/L)$-cocoercive fixed-point sequence with $L\in(0,1)$ 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