High-dimensional Search Problem Research Articles

Direct Position Determination of Noncircular Sources with Multiple Nested Arrays: Reduced Dimension Subspace Data Fusion

Direct position determination (DPD) of noncircular (NC) sources with multiple nested arrays (NA) is investigated in this paper. Noncircular sources are used to expand the dimension of the received signal matrix, so the number of identifiable information sources and the accuracy of direct position determination are improved. Furthermore, nested array increases spatial degree of freedom. In this paper, the high‐dimensional search problem of noncircular sources is investigated. Therefore, we propose algorithm dimension reduction subspace data fusion (RD‐SDF) to reduce complexity and increase positioning accuracy. Simulation results show that the proposed RD‐SDF algorithm for multiple nested arrays with noncircular sources has improved positioning accuracy with higher spatial degree of freedom than SDF, Capon, and two‐step algorithms with uniform linear array and circular sources (CS).

Maximum Likelihood Angle-Range Estimation for Monostatic FDA-MIMO Radar with Extended Range Ambiguity Using Subarrays

In this paper, we consider the joint angle-range estimation in monostatic FDA-MIMO radar. The transmit subarrays are first utilized to expand the range ambiguity, and the maximum likelihood estimation (MLE) algorithm is first proposed to improve the estimation performance. The range ambiguity is a serious problem in monostatic FDA-MIMO radar, which can reduce the detection range of targets. To extend the unambiguous range, we propose to divide the transmitting array into subarrays. Then, within the unambiguous range, the maximum likelihood (ML) algorithm is proposed to estimate the angle and range with high accuracy and high resolution. In the ML algorithm, the joint angle-range estimation problem becomes a high-dimensional search problem; thus, it is computationally expensive. To reduce the computation load, the alternating projection ML (AP-ML) algorithm is proposed by transforming the high-dimensional search into a series of one-dimensional search iteratively. With the proposed AP-ML algorithm, the angle and range are automatically paired. Simulation results show that transmitting subarray can extend the range ambiguity of monostatic FDA-MIMO radar and obtain a lower cramer-rao low bound (CRLB) for range estimation. Moreover, the proposed AP-ML algorithm is superior over the traditional estimation algorithms in terms of the estimation accuracy and resolution.

Variable Selection in Panel Models with Breaks

We develop a Bayesian approach that performs variable selection in panel regression models that are subject to breaks. Our variable selection approach enables deactivation of pervasive regressors and activation of weak regressors for short periods. Allowing the coefficients on individual variables to change at each break point introduces a high-dimensional search problem even in settings with modest numbers of cross-sectional units and time-series observations. Our methodology is demonstrated on simulated data and in an empirical application to firms' choice of capital structure. We find that ignoring breaks to the data generating process typically results in overestimating the number of relevant regressors, but also leads to a failure to activate regressors that are only informative for short periods.

Reply to comment by Chu et al. on “High‐dimensional posterior exploration of hydrologic models using multiple‐try DREAM (ZS) and high‐performance computing”

PUBLICATIONS Water Resources Research COMMENTARY 10.1002/2013WR014425 This article is a reply to Chu et al. [2014] doi:10.1002/2012WR013341. Reply to comment by Chu et al. on ‘‘High-dimensional posterior exploration of hydrologic models using multiple-try DREAM (ZS) and high-performance computing’’ Jasper A. Vrugt 1,2,3 and Eric Laloy 4 Correspondence to: J. A. Vrugt, jasper@uci.edu Citation: Vrugt, J. A., and E. Laloy (2014), Reply to comment Chu et al. on ‘‘High- dimensional posterior exploration of hydrologic models using multiple-try DREAM (ZS) and high-performance computing,’’ Water Resour. Res., 50, 2781–2786, doi:10.1002/ 2013WR014425. Received 15 JULY 2013 Accepted 8 FEB 2014 Accepted article online 15 FEB 2014 Published online 21 MAR 2014 Department of Civil and Environmental Engineering, University of California, Irvine, California, USA, 2 Department of Earth System Science, University of California, Irvine, California, USA, 3 Institute for Biodiversity and Ecosystems Dynamics, University of Amsterdam, Amsterdam, Netherlands, 4 Institute for Environment, Health and Safety, Belgian Nuclear Research Centre, Mol, Belgium 1. Introduction The comment of Chu et al. [2014], hereafter referred to as CYG, raises questions about some of the results presented in our paper (Laloy and Vrugt [2012], hereinafter LV, which is not to be confused with Las Vegas, although appropriate concerning the subject of this work on Monte Carlo simulation). As a preamble, we would like to remark that the work presented in Chu et al. [2010] and LV (2012) concern two different fields of study. CYG view the model calibration as an optimization problem, and use common concepts to efficiently find a single realization of the parameter values that minimizes (or maximizes, if appropriate) some user-defined objective function. Our work, on the contrary, uses Bayesian principles coupled with MCMC simulation to derive a distribution of parameter values that honor the observed data. This distribution summarizes parameter and model predictive (simulation) uncertainty, a requirement for probabilistic analysis, operational forecasting, disentangling error sources, and decision making. The maxi- mum a posteriori density (MAP) parameter values derived with MCMC simulation should reside in close vicinity of the ‘‘best’’ solution found with an optimization algorithm, if the exact same data set, prior distribu- tion, and likelihood (objective) function are used. In this reply, we assume that CYG used a correct imple- mentation of the MT-DREAM (ZS) algorithm and similar data set, prior and likelihood function as LV. Otherwise, the comparative analysis is meaningless. We emphasize this for three reasons. First, the results presented herein contradict CYG and are similar to those reported in LV but now with more trials plotted. Second, contributions in physics [Horowitz et al., 2012; Toyli et al., 2012; Yale et al., 2013] and geophysics [Linde and Vrugt, 2013; Laloy et al., 2012, Rosas-Carbajal et al., 2014; T. Lochbuehler et al., Summary statistics from training images as model constraints in probabilistic inversion, Geophysical Journal International, in review, 2014] demonstrate proper convergence behavior of MT-DREAM (ZS) on complex and high- dimensional targets involving hundreds of parameters. Third, to justify their SP-UCI algorithm the original paper of Chu et al. [2010] portrays misleading results of the predecessor of DREAM, called SCEM-UA. Section 4 of this reply will address this latter issue in more detail. We now respond to the comments of CYG. We use different sections with numbering corresponding to CYG. 2. Computational Time Unit CYG find the Computational Time Unit (CTU) diagnostic to be a poor indicator of the performance of MT- DREAM (ZS) . They suggest using the number of function evaluations or clock time instead. The CPU-time (s) scales linearly with CTU, or CPU 5 aCTU, where a (s) denotes the average time it takes to complete a sin- gle function (model) evaluation. As a is dependent on the processor speed (hardware), LV purposely reported the CTU values. Note that we neglect the actual run time of MT-DREAM (ZS) , in the determination of a, which is appropriate given the intended application of this algorithm to CPU-intensive forward models. We purposely do not use the number of function evaluations as performance diagnostic. This metric does not properly convey the CPU-time (CTU) of parallel algorithms such as DREAM (ZS) or MT-DREAM (ZS) . These VRUGT AND LALOY C 2014. American Geophysical Union. All Rights Reserved. V

Encoding subcomponents in cooperative co-evolutionary recurrent neural networks

Cooperative coevolution employs evolutionary algorithms to solve a high-dimensional search problem by decomposing it into low-dimensional subcomponents. Efficient problem decomposition methods or encoding schemes group interacting variables into separate subcomponents in order to solve them separately where possible. It is important to find out which encoding schemes efficiently group subcomponents and the nature of the neural network training problem in terms of the degree of non-separability. This paper introduces a novel encoding scheme in cooperative coevolution for training recurrent neural networks. The method is tested on grammatical inference problems. The results show that the proposed encoding scheme achieves better performance when compared to a previous encoding scheme.

Cancer: A Computational Disease That AI Can Cure

Cancer kills millions of people each year. From an AI perspective, finding effective treatments for cancer is a high-dimensional search problem characterized by many molecularly distinct cancer subtypes, many potential targets and drug combinations, and a dearth of high quality data to connect molecular subtypes and treatments to responses. The broadening availability of molecular diagnostics and electronic medical records, presents both opportunities and challenges to apply AI techniques to personalize and improve cancer treatment. We discuss these in the context of Cancer Commons, a “rapid learning” community where patients, physicians, and researchers collect and analyze the molecular and clinical data from every cancer patient, and use these results to individualize therapies. Research opportunities include: adaptively-planning and executing individual treatment experiments across the whole patient population, inferring the causal mechanisms of tumors, predicting drug response in individuals, and generalizing these findings to new cases. The goal is to treat each patient in accord with the best available knowledge, and to continually update that knowledge to benefit subsequent patients. Achieving this goal is a worthy grand challenge for AI.

"Turbo DPSK" using soft multiple-symbol differential sphere decoding

Coded interleaved differential M-ary phase-shift keying (M-DPSK) with iterative decoding, the so-called "Turbo DPSK," is known as a power-efficient transmission format. Due to the rotational invariance of DPSK, it particularly enables detection without channel state information (CSI). However, the soft-input soft-output (SISO) component decoder for DPSK is the computational bottleneck if performance close to the ideal case of perfect CSI is desired. In this paper, we take a fresh look at SISO decoding without CSI and apply sphere decoding (SD) to reduce complexity. In particular, we devise a maximum a posteriori probability (MAP) multiple-symbol differential sphere decoder (MSDSD) which efficiently solves the high-dimensional search problem inherent to detection without CSI. Together with a soft-output generation device the MAP-MSDSD algorithm forms a new SISO-MSDSD module for iterative decoding. We analyze the extrinsic information transfer (EXIT) characteristic of the novel module, by means of which we are able to design powerful encoder and decoder structures. For, respectively, the additive white Gaussian noise (AWGN) and the continuously time-varying Rayleigh-fading channel without CSI these designs operate within 1.7-1.9 and 2.3-2.5 dB of channel capacity assuming perfect CSI. These figures compare favorably with results available in the literature, especially for reasonably high data rates of 1-2 bit/channel use. Simulation studies of the average and the maximum complexity required by SISO-MSDSD demonstrate the advantageous performance versus complexity tradeoff of our approach.

A new algorithm for optimal 2-constraint satisfaction and its implications

We present a novel method for exactly solving (in fact, counting solutions to) general constraint satisfaction optimization with at most two variables per constraint (e.g. MAX-2-CSP and MIN-2-CSP), which gives the first exponential improvement over the trivial algorithm. More precisely, the runtime bound is a constant factor improvement in the base of the exponent: the algorithm can count the number of optima in MAX-2-SAT and MAX-CUT instances in O ( m 3 2 ω n / 3 ) time, where ω < 2.376 is the matrix product exponent over a ring. When the constraints have arbitrary weights, there is a ( 1 + ε ) -approximation with roughly the same runtime, modulo polynomial factors. Our construction shows that improvement in the runtime exponent of either k - clique solution (even when k = 3 ) or matrix multiplication over GF ( 2 ) would improve the runtime exponent for solving 2-CSP optimization. Our approach also yields connections between the complexity of some (polynomial time) high-dimensional search problems and some NP-hard problems. For example, if there are sufficiently faster algorithms for computing the diameter of n points in ℓ 1 , then there is an ( 2 - ε ) n algorithm for MAX-LIN. These results may be construed as either lower bounds on the high-dimensional problems, or hope that better algorithms exist for the corresponding hard problems.