Quadratic Estimation Research Articles

Simultaneous Coefficient Clustering and Sparsity for Multivariate Mixed Models

In many applications of multivariate longitudinal mixed models, it is reasonable to assume that each response is informed by only a subset of covariates. Moreover, one or more responses may exhibit the same relationship to a particular covariate for example, if they are capturing the same underlying aspect of an individual physical, mental, and emotional health. To address the above challenges, we propose a method for simultaneous clustering and variable selection of fixed effect coefficients in multivariate mixed models. We achieve this in a computationally scalable manner via a composite likelihood approach: separate mixed models are first fitted to each response, after which the model estimates are combined into a single quadratic form resembling a multivariate Wald statistic. We then augment this with fusion- and sparsity-inducing penalties based on broken adaptive ridge regression. Simulation studies demonstrate that the proposed composite quadratic estimator is similar to or better than several existing techniques for fixed effects selection in (univariate) mixed models while being computationally much more efficient. We apply the proposed method to longitudinal panel data from Australia to quantify how an individual’s overall health, assessed via a set of eight composite scores, evolves as a function of various demographic and lifestyle variables.

Comparison of Arima Model with The Addition of Linear Quadratic Estimation Algorithm for Prediction The Spread of Covid-19 in Kotabaru District

Comparison of Arima Model with The Addition of Linear Quadratic Estimation Algorithm for Prediction The Spread of Covid-19 in Kotabaru District

Statistical inference for Ornstein–Uhlenbeck processes based on low-frequency observations

Low-frequency observations are a common occurrence in real-world applications, making statistical inference for stochastic processes driven by stochastic differential equations (SDEs) based on such observations an important issue. In this paper, we investigate the statistical inference for the Ornstein–Uhlenbeck (OU) process using low-frequency observations. We propose modified least squares estimators (MLSEs) for the drift parameters and a modified quadratic variation estimator for the diffusion parameter based on the solution of the OU process. The MLSEs are derived heuristically using the nonlinear least squares method, despite the OU process satisfying a linear SDE. Unlike previous approaches, these modified estimators are asymptotically unbiased. Leveraging the ergodic properties of the OU process, we also propose ergodic estimators for the three parameters. The asymptotic behavior of these estimators is established using the ergodic properties and central limit theorem for the OU process, achieved through linear model techniques and multivariate Markov chain central limit theorem. Monte Carlo simulation results are presented to illustrate and support our theoretical findings.

Sensitivity of Bayesian 21 cm power spectrum estimation to foreground model errors

ABSTRACT Power spectrum estimators are an important tool in efforts to detect the 21 cm brightness temperature fluctuations from neutral hydrogen at early times. An initial detection will likely be statistical in nature, meaning that it will not be possible to make a coherent map of the brightness temperature fluctuations; instead, only their variance will be measured against a background of noise and residual systematic effects. Optimal quadratic estimator-based methods often apply an inverse covariance weighting to the data. However, inaccurate covariance modelling can lead to reduced sensitivity and, in some cases, severe signal loss. We recently proposed a Bayesian method to jointly estimate the 21 cm fluctuations, their power spectrum, and foreground emission. Instead of requiring a fixed a priori estimate of the covariance, we estimate the covariance as part of the inference. Choices of parametrization, particularly of the foregrounds, are subject to model errors and could lead to biases and other ill effects if not properly controlled. In this paper, we investigate the effects of inaccurate foreground models on 21 cm power spectrum recovery. Using simulated visibilities, we find that, even in the most extreme scenarios tested, our approach is capable of recovering 21 cm delay power spectrum estimates consistent with a known input signal for delays $\gtrsim 300$ ns ($\sim$88 per cent of the available Fourier modes). This is true even when using foreground models derived from modified foreground catalogues containing spatial and spectral perturbations at the quoted level of uncertainty on our foreground catalogues.

Kalman-based estimation of loading conditions from ultrasonic guided wave measurements

Abstract Ultrasonic guided wave-based structural health monitoring (SHM) of structures can be perturbed by environmental and operations conditions (EOCs) that alter wave propagation. In this work, we present an estimation procedure to reconstruct an EOC-free baseline of the structure from the only available Ultrasonic guided wave measurements. This procedure could typically be used as a prior step to increase the robustness of a more general ultrasonic imaging algorithm or SHM process dedicated to flaw detection. Our approach is model-based, i.e. we use a precise modeling of the wave propagation altered by structure loading conditions. This model is coupled with the acquired data through a data assimilation procedure to estimate the deformation caused by the unknown loading conditions. From a methodological point of view, our approach is original since we have proposed an iterated reduced-order unscented Kalman strategy, which we justify as an alternative to a Levenberg–Marquardt strategy for minimizing the non quadratic least-squares estimation criteria. Therefore, from a data assimilation perspective, we provide a quasi-sequential strategy that can valuably replace more classical variational approaches. Indeed, our resulting algorithm proves to be computationally very effective, allowing us to successfully apply our strategy to realistic 3D industrial SHM configurations.

Local quadratic spectral and covariance matrix estimation

The problem of estimating the spectral density matrix of a multi‐variate time series is revisited with special focus on the frequencies and . Recognizing that the entries of the spectral density matrix at these two boundary points are real‐valued, we propose a new estimator constructed from a local polynomial regression of the real portion of the multi‐variate periodogram. The case is of particular importance, since is associated with the large‐sample covariance matrix of the sample mean; hence, estimating is crucial to conduct any sort of statistical inference on the mean. We explore the properties of the local polynomial estimator through theory and simulations, and discuss an application to inflation and unemployment.

AIGen: an artificial intelligence software for complex genetic data analysis.

The recent development of artificial intelligence (AI) technology, especially the advance of deep neural network (DNN) technology, has revolutionized many fields. While DNN plays a central role in modern AI technology, it has rarely been used in genetic data analysis due to analytical and computational challenges brought by high-dimensional genetic data and an increasing number of samples. To facilitate the use of AI in genetic data analysis, we developed a C++ package, AIGen, based on two newly developed neural networks (i.e. kernel neural networks and functional neural networks) that are capable of modeling complex genotype-phenotype relationships (e.g. interactions) while providing robust performance against high-dimensional genetic data. Moreover, computationally efficient algorithms (e.g. a minimum norm quadratic unbiased estimation approach and batch training) are implemented in the package to accelerate the computation, making them computationally efficient for analyzing large-scale datasets with thousands or even millions of samples. By applying AIGen to the UK Biobank dataset, we demonstrate that it can efficiently analyze large-scale genetic data, attain improved accuracy, and maintain robust performance. Availability: AIGen is developed in C++ and its source code, along with reference libraries, is publicly accessible on GitHub at https://github.com/TingtHou/AIGen.

An-QNA: An Adaptive Nesterov Quasi-Newton Acceleration-Optimized CMOS LNA for 65 nm Automotive Radar Applications.

An adaptive Nesterov quasi-Newton acceleration (an-QNA)-optimized low-noise amplifier (LNA) is proposed in this paper. An optimized single-ended-to-differential two-stage LNA circuit is presented. It includes an improved post-linearization (IPL) technique to enhance the linearity. Traditional methods like conventional quasi-Newton (c-QN) often suffer from slow convergence and the tendency to get trapped in local minima. However, the proposed an-QNA method significantly accelerates the convergence speed. Furthermore, in this paper, modifications have been made to the an-QNA algorithm using a quadratic estimation to guarantee global convergence. The optimized an-QNA-based LNA, using standard 65 nm CMOS technology, achieves a simulated gain of 17.5 dB, a noise figure (NF) of 3.7 dB, and a 1 dB input compression point (IP1dB) of -13.1 dBm. It is also noted that the optimized LNA achieves a measured gain of 12.9 dB and an NF of 4.98 dB, and the IP1dB is -17.8 dB. The optimized LNA has a chip area of 0.67 mm2.

First Constraints on the Epoch of Reionization Using the Non-Gaussianity of the Kinematic Sunyaev-Zel'dovich Effect from the South Pole Telescope and Herschel-SPIRE Observations.

We report results from an analysis aimed at detecting the trispectrum of the kinematic Sunyaev-Zel'dovich (kSZ) effect by combining data from the South Pole Telescope (SPT) and Herschel-SPIRE experiments over a 100 deg^{2} field. The SPT observations combine data from the previous and current surveys, namely SPTpol and SPT-3G, to achieve depths of 4.5, 3, and 16 μK-arcmin in bands centered at 95, 150, and 220GHz. For SPIRE, we include data from the 600 and 857GHz bands. We reconstruct the velocity-induced large-scale correlation of the small-scale kSZ signal with a quadratic estimator that uses two cosmic microwave background (CMB) temperature maps, constructed by optimally combining data from all the frequency bands. We reject the null hypothesis of a zero trispectrum at 10.3σ level. However, the measured trispectrum contains contributions from both the kSZ and other undesired components, such as CMB lensing and astrophysical foregrounds, with kSZ being sub-dominant. We use the agora simulations to estimate the expected signal from CMB lensing and astrophysical foregrounds. After accounting for the contributions from CMB lensing and foreground signals, we do not detect an excess kSZ-only trispectrum and use this nondetection to set constraints on reionization. By applying a prior based on observations of the Gunn-Peterson trough, we obtain an upper limit on the duration of reionization of Δz_{re,50}<4.5 (95% confidence level). We find these constraints are fairly robust to foregrounds assumptions. This trispectrum measurement is independent of, but consistent with, Planck's optical depth measurement. This result is the first constraint on the epoch of reionization using the non-Gaussian nature of the kSZ signal.

Uncertainty and information in physiological signals: Explicit physical trade-off with log-normal wavelets

Physiological recordings contain a great deal of information about the underlying dynamics of Life. The practical statistical treatment of these single-trial measurements is often hampered by the inadequacy of overly strong assumptions. Heisenberg’s uncertainty principle allows for more parsimony, trading off statistical significance for localization. By decomposing signals into time–frequency atoms and recomposing them into local quadratic estimates, we propose a concise and expressive implementation of these fundamental concepts based on the choice of a geometric paradigm and two physical parameters. Starting from the spectrogram based on two fixed timescales and Gabor’s normal window, we then build its scale-invariant analogue, the scalogram based on two quality factors and Grossmann’s log-normal wavelet. These canonical estimators provide a minimal and flexible framework for single trial time–frequency statistics, which we apply to polysomnographic signals: EEG representations, HRV extraction from ECG, coherence and mutual information between heart rate and respiration.

Maximizing the valorization potential of lignin through optimization of the Soda pulping conditions

The valorization potential of lignin is strongly dependent on the yield that can be obtained during the pulping process as well as its chemical structure. Both of these are determined by factors such as the biomass type, the selected extraction strategy and the employed conditions. Within this study, Miscanthus x giganteus biomass was subjected to systematically varying Soda pulping conditions, i.e., temperature (100 °C – 180 °C), OH– concentration (0.158 mol/L – 1.000 mol/L) and time (60 min – 360 min). These pulping conditions can be combined into a single factor, reflecting the processing severity, which in this work varied from approximately 1 to 5. The resulting black liquor, precipitated lignin, lignin stock solution (i.e., lignin dissolved in the solvent used in the subsequent depolymerization step) and product pool after mild reductive catalytic depolymerization (200 °C, 10 bar H2 initial, 4 h) were thoroughly characterized using a plethora of analysis techniques. Increasing the severity factor of the pulping was found to result in an enhancement of the delignification degree from 25.3 ± 2.6 % to 95.4 ± 9.9 %. However, beyond a severity factor of 3, fragmentation of native ether linkages and condensation reactions start to cause unfavourable changes in the chemical structure of the lignin and depolymerization product pool. Furthermore, these reactions significantly reduce the total mass yield from biomass to depolymerization product pool. An Adaboost model with quadratic base estimator was trained against the experimental data, and subsequently used to optimize the pulping conditions, aiming at a maximum total mass yield with minimal fragmentation and, hence, condensation, of the lignin. The optimum was experimentally validated, which resulted in a lignin with high β-O-4 content (42.7 ± 2.8 linkages per 100 aromatic units) and a total mass yield of 30.9 ± 3.4 wt% and a pulp with a residual lignin content of 8.25 ± 0.94 wt%.

Linear Quadratic Gaussian Controller for Single-Ended Primary Inductor Converter via Integral Linear Quadratic Regulator Merged with an Offline Kalman Filter

This paper introduces a Linear Quadratic Gaussian (LQG) controller for a Single-Ended Primary Inductor Converter (SEPIC). The LQG design is based on merging an integral Linear Quadratic Regulator (LQR) with an offline Kalman Filter (commonly referred to as a Linear Quadratic Estimator (LQE)). The robustness of the LQG controller is guaranteed based on the separation principle. This manuscript addresses the need to use observer-based systems for the fourth-order SEPIC, which needs a sensor reduction as an essential requirement. This paper provides a comprehensive, yet systematic, approach to designing the LQG system. The work validates the convergences of the states in an LQG system to an actual value. Furthermore, it compares the performance of an LQG system with a benchmark Type-II industrial controller by means of a simulation of the switched converter model in the Simulink/MATLAB 2023a environment.

Spherical bispectrum expansion and quadratic estimators

We describe a general expansion of spherical (full-sky) bispectra into a set of orthogonal modes. For squeezed shapes, the basis separates physically-distinct signals and is dominated by the lowest moments. In terms of reduced bispectra, we identify a set of discrete polynomials that are pairwise orthogonal with respect to the relevant Wigner 3j symbol, and reduce to Chebyshev polynomials in the flat-sky (high-momentum) limit for both parity-even and parity-odd cases. For squeezed shapes, the flat-sky limit is equivalent to previous moment expansions used for CMB bispectra and quadratic estimators, but in general reduces to a distinct expansion in the angular dependence of triangles at fixed total side length (momentum).We use the full-sky expansion to construct a tower of orthogonal CMB lensing quadratic estimators and construct estimators that are immune to foregrounds like point sources or noise inhomogeneities. In parity-even combinations (such as the lensing gradient mode from TT, or the lensing curl mode from EB) the leading two modes can be identified with information from the magnification and shear respectively, whereas the parity-odd combinations are shear-only. Although not directly separable, we show that these estimators can nonetheless be evaluated numerically sufficiently easily.

Kidney Measurement and Glomerular Filtration Rate Evolution in Children with Polycystic Kidney Disease.

Autosomal dominant polycystic kidney disease (ADPKD) is an inherited disorder characterized by renal tubular cystic dilatations. The cysts can develop anywhere along the nephron, and over time the cystic dilatation leads to kidney enlargement. On the other hand, the cysts begin to reduce the number of functional nephrons as a consequence of cystic expansion that further contributes to the decline in renal function over the years. The pressure exerted by the dilated cysts leads to compensatory mechanisms that further contribute to the decline in renal function. These structural changes are responsible of glomerular hyperfiltration states, albuminuria, proteinuria, and hematuria. However, the presentation of ADPKD varies in children, from a completely asymptomatic child with incidental ultrasound detection of cysts to a rapidly progressive disease. There have been reports of early onset ADPKD in children younger than 2 years that showed a more rapid decline in renal function. ADPKD is caused by a mutation in PKD1 and PKD2 genes. Today, the PKD1 gene mutation seems to account for up to 85% of the cases worldwide, and it is associated with worse renal outcomes. Individuals with PKD2 gene mutation seem to present a milder form of the disease, with a more delayed onset of end-stage kidney disease. The cardinal sign of ADPKD is the presence of renal cysts during renal ultrasound. The current guidelines provide clinicians the recommendations for genetic testing in children with a positive family history. Given that the vast majority of children with ADPKD present with normal or supra-normal kidney function, we explored the glomerular filtration rates dynamics and the renal ultrasound-adjusted percentiles. In total, 14 out of 16 patients had kidney percentiles over 90%. The gene mutations were equally distributed among our cohort. In addition, we compared the modified Schwartz formula to the quadratic equation after adjusting the serum creatinine measurements. It seems that even though children with ADPKD have enlarged kidneys, the renal function is more likely normal or near normal when the quadratic estimation of glomerular filtration rate is used (qGFR tended to be lower, 111.95 ± 12.43 mL/min/1.73 m2 when compared to Schwartz eGFR 126.28 ± 33.07 mL/min/1.73 m2, p = 0.14). Also, when the quadratic equation was employed, not even a single patient reached the glomerular hyperfiltration threshold. The quadratic formula showed that glomerular filtration rates are linear or slightly decreasing after 1 year of follow-up (quadratic ΔeGFR = -0.32 ± 5.78 mL/min/1.73 m2), as opposed to the Schwartz formula that can falsely classify children in a hyperfiltration state (ΔeGFR = 7.51 ± 19.46 mL/min/1.73 m2), p = 0.019.

Effects of Chronic Pain Diagnoses on the Antidepressant Efficacy of Transcranial Magnetic Stimulation.

Major depressive disorder (MDD) and chronic pain are highly comorbid and bidirectionally related. Repetitive transcranial magnetic stimulation (rTMS) over the dorsolateral prefrontal cortex is effective in treating MDD, but additional research is needed to determine if chronic pain interferes with rTMS for MDD. Participants were 124 veterans ( Mage = 49.14, SD = 13.83) scheduled for 30 sessions of rTMS across 6 weeks. Depression severity was monitored weekly using the Patient Health Questionnaire-9 (PHQ-9). Having any pain diagnosis, low back pain, or headache/migraine were assessed by chart review. We fit latent basis models to estimate total change by pain diagnosis in depression scores and quadratic latent growth models to examine differences in growth rates. Then, we computed χ2 tests of group differences in response (PHQ-9 reduction ≥50%) and remission rates (final PHQ-9 < 5). A total of 92 participants (74%) had a documented pain diagnosis, 58 (47%) had low back pain, and 32 (26%) had headache/migraine. In growth models, depression scores initially decreased (linear slope estimate = -2.04, SE = 0.26, p < .0001), but the rate of decrease slowed over time (quadratic slope estimate = 0.18, SE = 0.04, p < .001). Overall change was not different as a function of any pain diagnosis ( p = .42), low back pain (p = .11 ), or headache/migraine ( p = .28). However, we found that low back pain was a negative predictor of response ( p = .032). These data support rTMS as a viable treatment option for comorbid populations. Although patients with comorbid chronic pain conditions are likely to receive benefit from rTMS for depression, adjunctive pain treatment may be indicated.

Enhancing CMB map reconstruction and power spectrum estimation with convolutional neural networks

The accurate reconstruction of Cosmic Microwave Background (CMB) maps and the measurement of its power spectrum are crucial for studying the early universe. In this paper, we implement a convolutional neural network to apply the Wiener Filter to CMB temperature maps, and use it intensively to compute an optimal quadratic estimation of the power spectrum. Our neural network has a UNet architecture as that implemented in WienerNet, but with novel aspects such as being written in python 3 and TensorFlow 2. It also includes an extra channel for the noise variance map, to account for inhomogeneous noise, and a channel for the mask. The network is very efficient, overcoming the bottleneck that is typically found in standard methods to compute the Wiener Filter, such as those that apply the conjugate gradient. It scales efficiently with the size of the map, making it a useful tool to include in CMB data analysis. The accuracy of the Wiener Filter reconstruction is satisfactory, as compared with the standard method. We heavily use this approach to efficiently estimate the power spectrum, by performing a simulation-based analysis of the optimal quadratic estimator. We further evaluate the quality of the reconstructed maps in terms of the power spectrum and find that we can properly recover the statistical properties of the signal. We find that the proposed architecture can account for inhomogeneous noise efficiently. Furthermore, increasing the complexity of the variance map presents a more significant challenge for the convergence of the network than the noise level does.

LTI/LQE: A Physics-Based Approach for Online Estimation of Dynamic Loads in the Rotating Frame

Accurate and online load monitoring of vital components located in the rotor system is important for not only inferring usage and estimating fatigue in those components but also for developing load alleviation/limiting control schemes. In the literature, on-board models for online (i.e., real-time) estimation of rotor component loads using available in-flight aircraft fixed-frame measurements are developed using neural networks, a statistical-based approach, or a combination of both. These models are aircraft-specific, do not capture the higher harmonic dynamics of the rotor system vibratory loads, and their synthesis requires obtaining a lot of data. To remedy these issues, this paper introduces a purely physics-based approach to online estimation of rotor system loads. The proposed approach can be applied to any rotary-wing vehicle, does not rely on a large amount of data, and captures the higher harmonic dynamics of the rotor system vibratory loads. The developed model entitled LTI/LQE is synthesized using a linear time invariant (LTI) model of helicopter-coupled body-rotor-inflow dynamics and a linear quadratic estimator (LQE), that is designed to correct the LTI model state response using fixed system measurements. The estimation fidelity of the LTI/LQE model is evaluated in simulation using a high-fidelity nonlinear model of a generic helicopter for online prediction of rotor blade pitch link loads arising from vehicle maneuvers. Results obtained using the LTI/LQE model revealed an interesting finding. It was found that the N/rev (where N is the number of blades) fixed system load measurements have information that can be leveraged to make an inference about the N/rev dynamic loads in the rotating system.

Sawtooth-characteristic-based free matrix integral inequality and its application to sampled-data systems

The focus of this article is to present a sawtooth-characteristic-based free-matrix integral inequality and to discuss its application to sampled-data systems (SDSs). Firstly, the free matrix, which is associated with the sawtooth characteristic of the input delay, is presented and incorporated into the integral inequality. In the development of inequality techniques, this is the first time that a free matrix has been associated with the sawtooth characteristic. On this basis, a corresponding sawtooth-characteristic-based free-matrix integral inequality is established, enabling estimation of the integral quadratic terms of the Lyapunov–Krasovskii functional (LKF) derivative. To overcome the challenges posed by second-order terms resulting from the proposed integral inequality, augmented system variables associated with the sawtooth characteristic are also introduced. Thus, the complicated calculation arising from second-order terms and the conservatism caused by the quadratic estimation of the LKF can be avoided. Finally, through the utilization of the sawtooth-characteristic-based free-matrix integral inequality, stability criteria with less conservatism are derived for the SDSs in the form of linear matrix inequalities. The superiority of the proposed approach is illustrated through two numerical examples and a simplified sampled-data based power market.

Minimization of integral quadratic estimate of controlled variable in systems with distributed parameters

A constructive method for solving the linear-quadratic problem of optimal control of a parabolic-type system with distributed parameters is proposed under the condition of uniform estimation of target sets. The optimality criterion takes the form of an integral quadratic estimate of the controlled state function in the spatio-temporal domain of its definition. A parameterized representation of control inputs is given with the required accuracy within special intervals of the optimal process, where control inputs cannot be determined using first-order analytical optimality conditions. The suggested approach is based on a previously developed alternance method for constructing parameterized algorithms of programmed control, which heavily relies on fundamental regularities of the subject area. It is demonstrated that the equations of the optimal regulators within the special intervals are reduced to the linear feedback algorithms based on the measured states of the objects. These algorithms are supplemented with switches at boundary points to apply admissible control inputs corresponding to the calculated values of the controlled variable.

Minimization of an Integral Quadratic Estimate of the Controlled Variable in Systems with Distributed Parameters

Minimization of an Integral Quadratic Estimate of the Controlled Variable in Systems with Distributed Parameters