Mcmc- Based Optimization And Application

In the thesis, we study the theory of Markov Chain Monte Carlo (MCMC) and its application in statistical optimization. The MCMC method is a class of evolutionary algorithms for generating samples from given probability distributions. In the thesis, we first focus on the methods of slice sampling and simulated annealing. While slice sampling has a merit to generate samples based on the underlying distribution with adjustable step size, simulated annealing can facilitate samples to jump out of local optima and converge quickly to the global optimum. With this MCMC method, we then solve two practical optimization problems. The first problem is image transmission over varying channels. Existing work in media transmission generally assumes that channel condition is stationary. However, communication channels are often varying with time in practice. Adaptive design needs frequent feedback for channel updates, which is often impractical due to the complexity and delay. In this application, we design an unequal error protection scheme for image transmission over noisy varying channels based on MCMC. First, the problem cost function is mapped into a multi-variable probability distribution. Then, with the “detailed balance , MCMC is used to generate samples from the mapped stationary distribution so that the optimal solution is the one that gives the lowest data distortion. We also show that the final rate allocation designed with this method works better than a conventional design that considers the mean value of the channel. In the second application, we consider a terminal-location-planning problem for intermodal transportation systems. With a given number of potential locations, it needs to find the most appropriate number of terminals and their locations to provide the economically most efficient operation when multiple service pairs exist simultaneously. The problem also has an inherent issue that for a particular planning, the optimal route paths must be determined for the co-existing service pairs. To solve this NP-hard problem, we design a MCMC-based two-layer method. The lower-layer is an optimal routing design for all service pairs given a particular planning that considers both efficiency and fairness. The upper-layer is finding the optimal planning based on MCMC with the stationary distribution that is mapped from the cost function. The effectiveness of this method is demonstrated through computer simulations and comparison with one state-of-the-art method. The work of this thesis has shown that a MCMC-method, consisting of both slice sampling and simulated annealing, can be successfully applied to solving practical optimization problems. Particularly, the method has advantages in dealing with high-dimensional problems with large searching spaces

Recovery from Linear Measurements with Complexity-Matching Universal Signal Estimation

We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal during recovery, the signal structure that can be leveraged is often not known a priori. In this paper, we consider universal CS recovery, where the statistics of a stationary ergodic signal source are estimated simultaneously with the signal itself. Inspired by Kolmogorov complexity and minimum description length, we focus on a maximum a posteriori (MAP) estimation framework that leverages universal priors to match the complexity of the source. Our framework can also be applied to general linear inverse problems where more measurements than in CS might be needed. We provide theoretical results that support the algorithmic feasibility of universal MAP estimation using a Markov chain Monte Carlo implementation, which is computationally challenging. We incorporate some techniques to accelerate the algorithm while providing comparable and in many cases better reconstruction quality than existing algorithms. Experimental results show the promise of universality in CS, particularly for low-complexity sources that do not exhibit standard sparsity or compressibility.Comment: 29 pages, 8 figure

Infinite Factorial Finite State Machine for Blind Multiuser Channel Estimation

New communication standards need to deal with machine-to-machine communications, in which users may start or stop transmitting at any time in an asynchronous manner. Thus, the number of users is an unknown and time-varying parameter that needs to be accurately estimated in order to properly recover the symbols transmitted by all users in the system. In this paper, we address the problem of joint channel parameter and data estimation in a multiuser communication channel in which the number of transmitters is not known. For that purpose, we develop the infinite factorial finite state machine model, a Bayesian nonparametric model based on the Markov Indian buffet that allows for an unbounded number of transmitters with arbitrary channel length. We propose an inference algorithm that makes use of slice sampling and particle Gibbs with ancestor sampling. Our approach is fully blind as it does not require a prior channel estimation step, prior knowledge of the number of transmitters, or any signaling information. Our experimental results, loosely based on the LTE random access channel, show that the proposed approach can effectively recover the data-generating process for a wide range of scenarios, with varying number of transmitters, number of receivers, constellation order, channel length, and signal-to-noise ratio.Comment: 15 pages, 15 figure

Doctor of Philosophy

dissertationThis dissertation addresses several key challenges in multiple-antenna communications, including information-theoretical analysis of channel capacity, capacity-achieving signaling design, and practical statistical detection algorithms. The first part of the thesis studies the capacity limits of multiple-input multiple-output (MIMO) multiple access channel (MAC) via virtual representation (VR) model. The VR model captures the physical scattering environment via channel gains in the angular domain, and hence is a realistic MIMO channel model that includes many existing channel models as special cases. This study provides analytical characterization of the optimal input distribution that achieves the sum-capacity of MAC-VR. It also investigates the optimality of beamforming, which is a simple scalar coding strategy desirable in practice. For temporally correlated channels, beamforming codebook designs are proposed that can efficiently exploit channel correlation. The second part of the thesis focuses on statistical detection for time-varying frequency-selective channels. The proposed statistical detectors are developed based on Markov Chain Monte Carlo (MCMC) techniques. The complexity of such detectors grows linearly in system dimensions, which renders them applicable to inter-symbol-interference (ISI) channels with long delay spread, for which the traditional trellis-based detectors fail due to prohibitive complexity. The proposed MCMC detectors provide substantial gain over the de facto turbo minimum-mean square-error (MMSE) detector for both synthetic channel and underwater acoustic (UWA) channels. The effectiveness of the proposed MCMC detectors is successfully validated through experimental data collected from naval at-sea experiments

Project 1640 Observations of Brown Dwarf GJ 758 B: Near-infrared Spectrum and Atmospheric Modeling

The nearby Sun-like star GJ 758 hosts a cold substellar companion, GJ 758 B, at a projected separation of ≾30 au, previously detected in high-contrast multi-band photometric observations. In order to better constrain the companion's physical characteristics, we acquired the first low-resolution (R ~ 50) near-infrared spectrum of it using the high-contrast hyperspectral imaging instrument Project 1640 on Palomar Observatory's 5 m Hale telescope. We obtained simultaneous images in 32 wavelength channels covering the Y, J, and H bands (~952–1770 nm), and used data processing techniques based on principal component analysis to efficiently subtract chromatic background speckle-noise. GJ 758 B was detected in four epochs during 2013 and 2014. Basic astrometric measurements confirm its apparent northwest trajectory relative to the primary star, with no clear signs of orbital curvature. Spectra of SpeX/IRTF observed T dwarfs were compared to the combined spectrum of GJ 758 B, with χ 2 minimization suggesting a best fit for spectral type T7.0 ± 1.0, but with a shallow minimum over T5–T8. Fitting of synthetic spectra from the BT-Settl13 model atmospheres gives an effective temperature T_(eff) = 741 ± 25 K and surface gravity log g = 4.3 ± 0.5 dex (cgs). Our derived best-fit spectral type and effective temperature from modeling of the low-resolution spectrum suggest a slightly earlier and hotter companion than previous findings from photometric data, but do not rule out current results, and confirm GJ 758 B as one of the coolest sub-stellar companions to a Sun-like star to date

Towards Space-like Photometric Precision from the Ground with Beam-Shaping Diffusers

We demonstrate a path to hitherto unachievable differential photometric precisions from the ground, both in the optical and near-infrared (NIR), using custom-fabricated beam-shaping diffusers produced using specialized nanofabrication techniques. Such diffusers mold the focal plane image of a star into a broad and stable top-hat shape, minimizing photometric errors due to non-uniform pixel response, atmospheric seeing effects, imperfect guiding, and telescope-induced variable aberrations seen in defocusing. This PSF reshaping significantly increases the achievable dynamic range of our observations, increasing our observing efficiency and thus better averages over scintillation. Diffusers work in both collimated and converging beams. We present diffuser-assisted optical observations demonstrating $62^{+26}_{-16}$ppm precision in 30 minute bins on a nearby bright star 16-Cygni A (V=5.95) using the ARC 3.5m telescope---within a factor of $\sim$2 of Kepler's photometric precision on the same star. We also show a transit of WASP-85-Ab (V=11.2) and TRES-3b (V=12.4), where the residuals bin down to $180^{+66}_{-41}$ppm in 30 minute bins for WASP-85-Ab---a factor of $\sim$4 of the precision achieved by the K2 mission on this target---and to 101ppm for TRES-3b. In the NIR, where diffusers may provide even more significant improvements over the current state of the art, our preliminary tests have demonstrated $137^{+64}_{-36}$ppm precision for a $K_S =10.8$ star on the 200" Hale Telescope. These photometric precisions match or surpass the expected photometric precisions of TESS for the same magnitude range. This technology is inexpensive, scalable, easily adaptable, and can have an important and immediate impact on the observations of transits and secondary eclipses of exoplanets.Comment: Accepted for publication in ApJ. 30 pages, 20 figure

Statistical and Mechanistic Approaches to Study Cell Signaling Dynamics

Cells use complex signaling systems to constantly detect environmental changes, relay extracellular information from the cell membrane to the nucleus, and drive cell responses, such as transcription. The ability of each single cell to dynamically respond to changes in its environment is the basis for healthy, functioning, multicellular beings. Diseases often arise from dysregulated signaling, and our ability to manipulate cell responses, that stems from our growing understanding of signaling processes, is often the basis for disease treatments. Computational approaches can complement experimental studies of cellular systems, allowing us to formalize our growing body of knowledge of cellular biochemistry. Mechanistic modeling provides a natural framework to describe and simulate complex systems with many system components and causal interactions that often lead to non-intuitive emergent behavior, lending itself well to the analysis of signaling systems. Statistical approaches can complement mechanistic modeling by enabling an analysis of complex input-output relationships in the data, providing insight into how cells translate input environmental cues into output responses, even when the underlying mechanisms are only partially understood. In this thesis, we explore both mechanistic and statistical approaches and address several challenges in modeling signaling processes within a cell, and signaling heterogeneity between cells, using the NF-kB pathway as a model system. First, we evaluate methods to efficiently determine numerical values of model parameters, enabling model simulations that are comparable to experimental data. Second, we develop methods to identify reduced submodels that are sufficient for the data, highlighting simple mechanisms that drive emergent behavior. Third, switching gears to study signaling heterogeneity, we use information-theoretic analyses to evaluate the capabilities of the NF-kB pathway to effectively transduce cytokine dosage information in the presence of biochemical noise. Finally, we develop a framework to calibrate mechanistic models to heterogeneous signaling data, enabling simulation-based analyses of single-cell signaling capabilities