Unitary Approximate Message Passing for Sparse Bayesian Learning and Bilinear Recovery

Over the past several years, the approximate message passing (AMP) algorithm has been applied to a broad range of problems, including compressed sensing (CS), robust regression, Bayesian estimation, etc. AMP was originally developed for compressed sensing based on the loopy belief propagation (BP). Compared to convex optimization based algorithms, AMP has low complexity and its performance can be rigorously characterized by a scalar state evolution (SE) in the case of a large independent and identically distributed (i.i.d.) (sub-) Gaussian matrix. AMP was then extended to solve general estimation problems with a generalized linear observation model. However, AMP performs poorly on a generic matrix such as non-zero mean, rank-deficient, correlated, or ill-conditioned matrix, resulting in divergence and degraded performance. It was discovered later that applying AMP to a unitary transform of the original model can remarkably enhance the robustness to difficult matrices. This variant is named unitary AMP (UAMP), or formally called UTAMP. In this thesis, leveraging UAMP, we propose UAMP-SBL for sparse signal recovery and Bi-UAMP for bilinear recovery, both of which inherit the low complexity and robustness of UAMP. Sparse Bayesian learning (SBL) is a powerful tool for recovering a sparse signal from noisy measurements, which finds numerous applications in various areas. As a traditional implementation of SBL, e.g., Tipping’s method, involves matrix inversion in each iteration, the computational complexity can be prohibitive for large scale problems. To circumvent this, AMP and its variants have been used as low-complexity solutions. Unfortunately, they will diverge for ‘difficult’ measurement matrices as previously mentioned. In this thesis, leveraging UAMP, a novel SBL algorithm called UAMP-SBL is proposed where UAMP is incorporated into the structured variational message passing (SVMP) to handle the most computationally intensive part of message computations. It is shown that, compared to state-of-the-art AMP based SBL algorithms, the proposed UAMP-SBL is more robust and efficient, leading to remarkably better performance. The bilinear recovery problem has many applications such as dictionary learning, selfcalibration, compressed sensing with matrix uncertainty, etc. Compared to existing nonmessage passing alternates, several AMP based algorithms have been developed to solve bilinear problems. By using UAMP, a more robust and faster approximate inference algorithm for bilinear recovery is proposed in this thesis, which is called Bi-UAMP. With the lifting approach, the original bilinear problem is reformulated as a linear one. Then, variational inference (VI), expectation propagation (EP) and BP are combined with UAMP to implement the approximate inference algorithm Bi-UAMP, where UAMP is adopted for the most computationally intensive part. It is shown that, compared to state-of-the-art bilinear recovery algorithms, the proposed Bi-UAMP is much more robust and faster, and delivers significantly better performance. Recently, UAMP has also been employed for many other applications such as inverse synthetic aperture radar (ISAR) imaging, low-complexity direction of arrival (DOA) estimation, iterative detection for orthogonal time frequency space modulation (OTFS), channel estimation for RIS-Aided MIMO communications, etc. Promising performance was achieved in all of the applications, and more applications of UAMP are expected in the future

Time-varying Learning and Content Analytics via Sparse Factor Analysis

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education

Matrix Factorization Based Blind Bayesian Receiver for Grant-Free Random Access in mmWave MIMO mMTC

Grant-free random access is promising for massive connectivity with sporadic transmissions in massive machine type communications (mMTC), where the hand-shaking between the access point (AP) and users is skipped, leading to high access efficiency. In grant-free random access, the AP needs to identify the active users and perform channel estimation and signal detection. Conventionally, pilot signals are required for the AP to achieve user activity detection and channel estimation before active user signal detection, which may still result in substantial overhead and latency. In this paper, to further reduce the overhead and latency, we explore the problem of grant-free random access without the use of pilot signals in a millimeter wave (mmWave) multiple input and multiple output (MIMO) system, where the AP performs blind joint user activity detection, channel estimation and signal detection (UACESD). We show that the blind joint UACESD can be formulated as a constrained composite matrix factorization problem, which can be solved by exploiting the structures of the channel matrix and signal matrix. Leveraging our recently developed unitary approximate message passing based matrix factorization (UAMP-MF) algorithm, we design a message passing based Bayesian algorithm to solve the blind joint UACESD problem. Extensive simulation results demonstrate the effectiveness of the blind grant-free random access scheme

S-AMP for Non-linear Observation Models

Recently we extended Approximate message passing (AMP) algorithm to be able to handle general invariant matrix ensembles. In this contribution we extend our S-AMP approach to non-linear observation models. We obtain generalized AMP (GAMP) algorithm as the special case when the measurement matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation propagation (EP) like algorithms from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory to get low-complexity updates for the second moment quantities.Comment: 6 page

Signal Detection in MIMO Systems with Hardware Imperfections: Message Passing on Neural Networks

In this paper, we investigate signal detection in multiple-input-multiple-output (MIMO) communication systems with hardware impairments, such as power amplifier nonlinearity and in-phase/quadrature imbalance. To deal with the complex combined effects of hardware imperfections, neural network (NN) techniques, in particular deep neural networks (DNNs), have been studied to directly compensate for the impact of hardware impairments. However, it is difficult to train a DNN with limited pilot signals, hindering its practical applications. In this work, we investigate how to achieve efficient Bayesian signal detection in MIMO systems with hardware imperfections. Characterizing combined hardware imperfections often leads to complicated signal models, making Bayesian signal detection challenging. To address this issue, we first train an NN to "model" the MIMO system with hardware imperfections and then perform Bayesian inference based on the trained NN. Modelling the MIMO system with NN enables the design of NN architectures based on the signal flow of the MIMO system, minimizing the number of NN layers and parameters, which is crucial to achieving efficient training with limited pilot signals. We then represent the trained NN with a factor graph, and design an efficient message passing based Bayesian signal detector, leveraging the unitary approximate message passing (UAMP) algorithm. The implementation of a turbo receiver with the proposed Bayesian detector is also investigated. Extensive simulation results demonstrate that the proposed technique delivers remarkably better performance than state-of-the-art methods