Moment Matching Algorithm Research Articles

Forced Measurement of Astronomical Sources at Low Signal-to-noise

We propose a modified moment matching algorithm to avoid catastrophic failures for sources with a low signal to noise ratio. The proposed modifications include a method to eliminate nonphysical negative pixel values and a forced single iteration with an initial guess derived from coadd measurements when iterative methods are unstable. We correct for all biases in measurements introduced by the method. We find that the proposed modifications allow the algorithm to avoid catastrophic failures in nearly 100% of the cases, especially at low SNR. Additionally, with a reasonable guess from coadd measurements, the algorithm measures the flux, centroid, size, shape, and ellipticity with a bias statistically consistent with zero. We show that the proposed method allows us to measure sources 7 times fainter than traditional methods when applied to images obtained from WIYN-ODI. We also present a scheme to find uncertainties in measurements when using the new method to measure astronomical sources.

Multi-source domain adaptive network based on local kernelized higher-order moment matching for rotating machinery fault diagnosis

Unsupervised domain adaptation has been extensively researched in rotating-machinery cross-domain fault diagnosis. A multi-source domain adaptive network based on local kernelized higher-order moment matching is constructed in this research for rotating-machinery fault diagnosis. Firstly, a multi-branch network is designed to map each source-target pair to a domain-specific shared space and to extract domain-invariant features using domain adversarial thought. Then, a local kernelized higher-order moment matching algorithm is proposed to perform fine-grained matching in shared category subspace. Finally, a feature fusion strategy based on the local domain distribution deviation is applied to synthesize the output features of multiple classifiers to obtain diagnostic results. The experimental validation of two-branch and three-branch networks on two public datasets is carried out and average diagnostic accuracies both exceed 99%. The results demonstrate the effectiveness and superiority of the approach.

Angles-Only Initial Orbit Determination via Multivariate Gaussian Process Regression

Vital for Space Situational Awareness, Initial Orbit Determination (IOD) may be used to initialize object tracking and associate observations with a tracked satellite. Classical IOD algorithms provide only a point solution and are sensitive to noisy measurements and to certain target-observer geometry. This work examines the ability of a Multivariate GPR (MV-GPR) to accurately perform IOD and quantify the associated uncertainty. Given perfect test inputs, MV-GPR performs comparably to a simpler multitask learning GPR algorithm and the classical Gauss–Gibbs IOD in terms of prediction accuracy. It significantly outperforms the multitask learning GPR algorithm in uncertainty quantification due to the direct handling of output dimension correlations. A moment-matching algorithm provides an analytic solution to the input noise problem under certain assumptions. The algorithm is adapted to the MV-GPR formulation and shown to be an effective tool to accurately quantify the added input uncertainty. This work shows that the MV-GPR can provide a viable solution with quantified uncertainty which is robust to observation noise and traditionally challenging orbit-observer geometries.

A Deterministic Approximation to Neural SDEs.

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been remained unexplored so far. We report the empirical finding that obtaining well-calibrated uncertainty estimations from NSDEs is computationally prohibitive. As a remedy, we develop a computationally affordable deterministic scheme which accurately approximates the transition kernel, when dynamics is governed by a NSDE. Our method introduces a bidimensional moment matching algorithm: vertical along the neural net layers and horizontal along the time direction, which benefits from an original combination of effective approximations. Our deterministic approximation of the transition kernel is applicable to both training and prediction. We observe in multiple experiments that the uncertainty calibration quality of our method can be matched by Monte Carlo sampling only after introducing high computational cost. Thanks to the numerical stability of deterministic training, our method also improves prediction accuracy.

Online Mental Fatigue Monitoring via Indirect Brain Dynamics Evaluation

Driver mental fatigue leads to thousands of traffic accidents. The increasing quality and availability of low-cost electroencephalogram (EEG) systems offer possibilities for practical fatigue monitoring. However, non-data-driven methods, designed for practical, complex situations, usually rely on handcrafted data statistics of EEG signals. To reduce human involvement, we introduce a data-driven methodology for online mental fatigue detection: self-weight ordinal regression (SWORE). Reaction time (RT), referring to the length of time people take to react to an emergency, is widely considered an objective behavioral measure for mental fatigue state. Since regression methods are sensitive to extreme RTs, we propose an indirect RT estimation based on preferences to explore the relationship between EEG and RT, which generalizes to any scenario when an objective fatigue indicator is available. In particular, SWORE evaluates the noisy EEG signals from multiple channels in terms of two states: shaking state and steady state. Modeling the shaking state can discriminate the reliable channels from the uninformative ones, while modeling the steady state can suppress the task-nonrelevant fluctuation within each channel. In addition, an online generalized Bayesian moment matching (online GBMM) algorithm is proposed to online-calibrate SWORE efficiently per participant. Experimental results with 40 participants show that SWORE can maximally achieve consistent with RT, demonstrating the feasibility and adaptability of our proposed framework in practical mental fatigue estimation.

Unsupervised Ensemble Classification With Sequential and Networked Data

Ensemble learning, the machine learning paradigm where multiple models are combined, has exhibited promising perfomance in a variety of tasks. The present work focuses on unsupervised ensemble classification. The term unsupervised refers to the ensemble combiner who has no knowledge of the ground-truth labels that each classifier has been trained on. While most prior works on unsupervised ensemble classification are designed for independent and identically distributed (i.i.d.) data, the present work introduces an unsupervised scheme for learning from ensembles of classifiers in the presence of data dependencies. Two types of data dependencies are considered: sequential data and networked data whose dependencies are captured by a graph. For both, novel moment matching and Expectation-Maximization algorithms are developed. Performance of these algorithms is evaluated on synthetic and real datasets, which indicate that knowledge of data dependencies in the meta-learner is beneficial for the unsupervised ensemble classification task.

A Priori Error Bound for Moment Matching Approximants of Thermal Models

This article focuses on the moment matching methodology for deriving dynamic compact thermal models (DCTMs) of electronic components. For the first time, an a priori error bound is theoretically established both in the time and frequency domains, which is suited to accurately estimate the approximation error introduced by DCTMs in practical electronics applications. By exploiting this result, it is also shown that the near-optimal choice of matching points previously proposed by one of the authors minimizes the error bound here derived, among all the possible choices of matching points. The introduced error bound is verified by applying the moment matching algorithm to a state-of-the-art packaged InGaP/GaAs heterojunction bipolar transistor (HBT) used in output stages of power amplifiers for handset applications.

Scenario generation in stochastic programming using principal component analysis based on moment-matching approach

In optimization models based on stochastic programming, we often face the problem of representing expectations in proper form known as scenario generation. With advances in computational power, a number of methods starting from simple Monte-Carlo to dedicated approaches such as method of moment-matching and scenario reduction are being used for multistage scenario generation. Recently, various variations of moment-matching approach have been proposed with the aim to reduce computational time for better outputs. In this paper, we describe a methodology to speed up moment-matching based multistage scenario generation by using principal component analysis. Our proposal is to pre-process the data using dimensionality reduction approaches instead of using returns as variables for moment-matching problem directly. We also propose a hybrid multistage extension of heuristic based moment-matching algorithm and compare it with other variants of moment-matching algorithm. Computational results using non-normal and correlated returns show that the proposed approach provides better approximation of returns distribution in lesser time.

A new model order reduction method for the design of compensator by using moment matching algorithm

The aim of this paper is the construction of a new model reduction technique for large scale stable linear dynamic systems. It is principally focused on the dominant modes and time moments retention. This reduction implicates the translation of the overall important features confined in the large scale complete order model into the lower order system, allowing the computation of approximant denominator by using generalized pole clustering method. The approximant numerator is obtained by means of the factor division algorithm. As a result, a lower order system is obtained. To demonstrate its effectiveness, to highlight some fundamental of its features, and to accomplish its accuracy, a comparative study is done. Two standard numerical examples are taken, where approximant model computed by the proposed method is compared with the reduced order models computed from the recently proposed methods as well as well-known model reduction schemes. The paper is also emphasized on the design of compensator by using moment matching algorithm with the help of the reduced model. The design of compensator is validated and illustrated with the help of a standard numerical example taken from the literature.

Parameterized Model Order Reduction of Delayed PEEC Circuits

In this paper, we propose a novel parameterized model order reduction technique for circuits described by the delayed partial element equivalent circuit method. The moment vectors associated with frequency are excluded while forming the moments’ subspace. This leads to obtaining very compact parameterized reduced order models. An implicit multiparameter moment matching algorithm is used for the moments related to the design parameters. Numerical results validate the accuracy and efficiency of the proposed technique in both frequency- and time-domain. The time-domain response of the reduced order models is obtained using the numerical inversion of Laplace transform, which avoids stability issues as well as the computationally expensive repeated interpolation steps associated with conventional time-stepping integration method for delayed differential equations.

Destriping Remote Sensing Imagery by Wavelet Moment Matching Algorithm

Destriping Remote Sensing Imagery by Wavelet Moment Matching Algorithm

Stagewise learning for noisy k-ary preferences

The aggregation of k-ary preferences is a novel ranking problem that plays an important role in several aspects of daily life, such as ordinal peer grading, online image-rating, meta-search and online product recommendation. Meanwhile, crowdsourcing is increasingly emerging as a way to provide a plethora of k-ary preferences for these types of ranking problems, due to the convenience of the platforms and the lower costs. However, preferences from crowd workers are often noisy, which inevitably degenerates the reliability of conventional aggregation models. In addition, traditional inferences usually lead to massive computational costs, which limits the scalability of aggregation models. To address both of these challenges, we propose a reliable CrowdsOUrced Plackett–LucE (COUPLE) model combined with an efficient Bayesian learning technique. To ensure reliability, we introduce an uncertainty vector for each crowd worker in COUPLE, which recovers the ground truth of the noisy preferences with a certain probability. Furthermore, we propose an Online Generalized Bayesian Moment Matching (OnlineGBMM) algorithm, which ensures that COUPLE is scalable to large-scale datasets. Comprehensive experiments on four large-scale synthetic datasets and three real-world datasets show that, COUPLE with OnlineGBMM achieves substantial improvements in reliability and noisy worker detection over other well-known approaches.

Methods of removal wide-stripe noise in short-wave infrared hyperspectral remote sensing image

PurposeThis paper aims to study the removal of wide-stripe noise in hyperspectral remote sensing images. There is a great deal of stripe noises in short-wave infrared hyperspectral remote sensing image, especially wide-stripe noise, which brings great challenge to the interpretation and application of hyperspectral images.Design/methodology/approachTo remove the noise and to reduce the impact based on in-depth study of the mechanism of the stripe noise generation and its distribution characteristics, this paper proposed two statistical local processing and moment matching algorithms for the elimination of wide-stripe noise, namely, the gradient mean moment matching (GMMM) algorithm and the gradient interpolation moment matching (GIMM) algorithm.FindingsThe experiments were carried out with the practical short-wave infrared hyperspectral image data and good experiment results were obtained. Experiments show that both can reduce the impact of wide-stripe noise, and the filtering effect and the application range of the GIMM algorithm is better than that of the GMMM algorithm.Originality/valueUsing new methods to deal with the hyperspectral remote sensing images, it can effectively improve the quality of hyperspectral images and improve their utilization efficiency and value.

Improving Predictive State Representations via Gradient Descent

Predictive state representations (PSRs) model dynamical systems using appropriately chosen predictions about future observations as a representation of the current state. In contrast to the hidden states posited by HMMs or RNNs, PSR states are directly observable in the training data; this gives rise to a moment-matching spectral algorithm for learning PSRs that is computationally efficient and statistically consistent when the model complexity matches that of the true system generating the data. In practice, however, model mismatch is inevitable and while spectral learning remains appealingly fast and simple it may fail to find optimal models. To address this problem, we investigate the use of gradient methods for improving spectrally-learned PSRs. We show that only a small amount of additional gradient optimization can lead to significant performance gains, and moreover that initializing gradient methods with the spectral learning solution yields better models in significantly less time than starting from scratch.

A robust mosaicking procedure for high spatial resolution remote sensing images

With the rapid development of sensor manufacturing technology, high spatial resolution (HR) images are becoming more easily acquired and more widely used. However, it is common that a region of interest (ROI) cannot be completely acquired from a single image. Image mosaicking can resolve the problem by creating a new large-area image from multiple images with overlapping areas. A typical mosaicking procedure for HR remote sensing images includes three successive steps: tonal adjustment, seamline detection, and image blending. In this paper, we propose a robust mosaicking procedure featuring novel ideas in all three steps, which is aimed at processing HR remote sensing images of urban areas. Firstly, the tonal adjustment is realized by a local moment matching (LMM) algorithm, which solves the nonlinear photometric correlation problem between adjacent images. Secondly, an automatic piecewise dynamic program (APDP) algorithm for seamline detection is proposed to detect the optimal seamline on the overlapped area. Last but not least, we propose a cosine distance weighted blending (CDWB) method to ensure that the seamline is as invisible as possible. Compared to the state-of-the-art methods, the proposed method was proved to be effective in experiments with high resolution aerial and satellite images.

A Non-Uniformity Correction Algorithm Based on Single Infrared Image

To overcome the shortcoming that most of the recent Non-uniformity Correction (NUC) algorithms which need a large number of underlying images, a non-uniformity correction method based on single infrared image is proposed. In the proposed method, the moment matching algorithm is used to correct the non-uniformity image to get the pilot image. Then, the banding occurring in the pilot image is removed by the local weighted-histogram specification algorithm to get the final result. Experiment results show the effectiveness of the proposed non-uniformity correction algorithm.

Multi-stage scenario generation by the combined moment matching and scenario reduction method

We describe an opportunity to speed up multi-stage scenario generation and reduction using a combination of two well-known methods: the moment matching method (Høyland and Wallace, 2001) and the method for scenario reduction to approximately minimize a metric (Heitsch and Römish, 2009). Our suggestion is to combine them rather than using them in serial by making use of a stage-wise approximation to the moment matching algorithm. Computational results show that combining the methods can bring significant benefits.

LibMoM : a library for stochastic simulations in engineering using statistical moments

Stochastic simulations are becoming increasingly important in numerous engineering applications. The solution to the governing equations are complicated due to the high-dimensional spaces and the presence of randomness. In this paper we present libMoM(http://libmom.sourceforge.net), a software library to solve various types of Stochastic Differential Equations (SDE) as well as estimate statistical distributions from the moments. The library provides a suite of tools to solve various SDEs using the method of moments (MoM) as well as estimate statistical distributions from the moments using moment matching algorithms. For a large class of problems, MoM provide efficient solutions compared with other stochastic simulation techniques such as Monte Carlo (MC). In the physical sciences, the moments of the distribution are usually the primary quantities of interest. The library enables the solution of moment equations derived from a variety of SDEs, with closure using non-standard Gaussian quadrature. In engineering risk assessment and decision making, statistical distributions are required. The library implements tools for fitting the Generalized Lambda Distribution (GLD) with the given moments. The objectives of this paper are (1) to briefly outline the theory behind moment methods for solving SDEs/estimation of statistical distributions; (2) describe the organization of the software and user interfaces; (3) discuss use of standard software engineering tools for regression testing, aid collaboration, distribution and further development. A number of representative examples of the use of libMoMin various engineering applications are presented and future areas of research are discussed.

A Framework for Reduced Order Modeling with Mixed Moment Matching and Peak Error Objectives

We examine a new method of producing reduced order models for LTI systems which attempts to minimize a bound on the peak error between the original and reduced order models subject to a bound on the peak value of the input. The method, which can be implemented by solving a set of linear programming problems that are parameterized via a single scalar quantity, is able to minimize an error bound subject to a number of moment matching constraints. Moreover, because all optimization is performed in the time domain, the method can also be used to perform model reduction for infinite dimensional systems, rather than being restricted to finite order state space descriptions. We begin by contrasting the method we present here with two classes of standard model reduction algorithms, namely, moment matching algorithms and singular value-based methods. After motivating the class of reduction tools we propose, we describe the algorithm (which minimizes the $L_1$ norm of the difference between the original and reduced order impulse responses) and formulate the corresponding linear programming problem that is solved during each iteration of the algorithm. We then prove that, for a certain class of LTI systems, the method we propose can be used to produce reduced order models of arbitrary accuracy even when the original system is infinite dimensional. We then show how to incorporate moment matching constraints into the basic error bound minimization algorithm, and present three examples which utilize the techniques described herein. We conclude with some comments on extensions to multi-input, multi-output systems, as well as some general comments for future work.

A partially linearized sigma point filter for latent state estimation in nonlinear time series models

A new technique for the latent state estimation of a wide class of nonlinear time series models is proposed. In particular, we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment-matching algorithm and then a linear programming based procedure is used in the update step of the state estimation. The effectiveness of the new filtering procedure is assessed via a simulation example that deals with a highly nonlinear, multivariate time series representing an interest rate process.