Variance Reduction Research Articles

Middle-throughput LC-MS-based platelet proteomics with minute sample amounts using semi-automated positive pressure FASP in 384-well format (PF384)

Comprehensive characterization of platelets requires various functional assays and analysis techniques, including omics-disciplines, each requiring an individual aliquot of a given sample. Consequently, the sample material per assay is often highly limited rendering downscaling a prerequisite for effective sample exploitation. Here we present a transfer of our recently introduced 96-well-based proteomics workflow (PF96) into the 384-well format (PF384) allowing for a significant increase in sensitivity when processing minute platelet protein amounts. In addition, the 4-fold higher throughput (1500 samples per lab worker per week) allows to easily meet the throughput capacities of modern LC-MS instruments. We determined optimal sample loads followed by highlighting the strengths in comparison to our previous sample preparation approach by processing only 3 µg of purified platelet protein from 22 healthy donors. Major advantages are: (I) improved identification and analyte recovery, especially of low copy number proteins, with signal intensity gains of +130 % and +107 % (peptide and protein level, respectively) (II) substantial intensity gains for key-players in platelet activation including the membrane receptors PAR4, P2X1, GPVI, GPV, GPIX and the downstream mediators AKT, PKA, Rap1, Lyn (III) improved reproducibility with a reduction of technical variance from 22 / 25 % down to 16 / 19 % for detection of lower / higher abundant disease markers and (IV) a 4-fold increase in sample preparation throughput. Taken together, these advantages render PF384 a promising future in clinical proteomics and might pave the way of platelet proteomics with minute sample amounts into molecular diagnostics.

Prediction and influence factors analysis of IP backbone network traffic based on Prophet model and variance reduction

Prediction and influence factors analysis of IP backbone network traffic based on Prophet model and variance reduction

Federated Learning Based on Model Discrepancy and Variance Reduction

Federated Learning Based on Model Discrepancy and Variance Reduction

Leveraging simplex gradient variance and bias reduction for black-box optimization of noisy and costly functions

Leveraging simplex gradient variance and bias reduction for black-box optimization of noisy and costly functions

Hand gestures classification of sEMG signals based on BiLSTM-metaheuristic optimization and hybrid U-Net-MobileNetV2 encoder architecture

Surface electromyography (sEMG) data has been extensively utilized in deep learning algorithms for hand movement classification. This paper aims to introduce a novel method for hand gesture classification using sEMG data, addressing accuracy challenges seen in previous studies. We propose a U-Net architecture incorporating a MobileNetV2 encoder, enhanced by a novel Bidirectional Long Short-Term Memory (BiLSTM) and metaheuristic optimization for spatial feature extraction in hand gesture and motion recognition. Bayesian optimization is employed as the metaheuristic approach to optimize the BiLSTM model’s architecture. To address the non-stationarity of sEMG signals, we employ a windowing strategy for signal augmentation within deep learning architectures. The MobileNetV2 encoder and U-Net architecture extract relevant features from sEMG spectrogram images. Edge computing integration is leveraged to further enhance innovation by enabling real-time processing and decision-making closer to the data source. Six standard databases were utilized, achieving an average accuracy of 90.23% with our proposed model, showcasing a 3–4% average accuracy improvement and a 10% variance reduction. Notably, Mendeley Data, BioPatRec DB3, and BioPatRec DB1 surpassed advanced models in their respective domains with classification accuracies of 88.71%, 90.2%, and 88.6%, respectively. Experimental results underscore the significant enhancement in generalizability and gesture recognition robustness. This approach offers a fresh perspective on prosthetic management and human-machine interaction, emphasizing its efficacy in improving accuracy and reducing variance for enhanced prosthetic control and interaction with machines through edge computing integration.

Variance-reduced random batch Langevin dynamics.

The random batch method is advantageous in accelerating force calculations in particle simulations, but it poses a challenge of removing the artificial heating effect in application to the Langevin dynamics. We develop an approach to solve this issue by estimating the force variance, resulting in a variance-reduced random batch Langevin dynamics. Theoretical analysis shows the high-order local truncation error of the time step in the numerical discretization scheme, consistent with the fluctuation-dissipation theorem. The numerical results indicate that the method can achieve a significant variance reduction since a smaller batch size provides accurate approximation, demonstrating the attractive feature of the variance-reduced random batch method for Langevin dynamics.

BagStacking: An Integrated Ensemble Learning Approach for Freezing of Gait Detection in Parkinson’s Disease

This study introduces BagStacking, an innovative ensemble learning framework designed to enhance the detection of freezing of gait (FOG) in Parkinson’s disease (PD) using accelerometer data. By synergistically combining bagging’s variance reduction with stacking’s sophisticated blending mechanisms, BagStacking achieves superior predictive performance. Evaluated on a comprehensive PD dataset provided by the Michael J. Fox Foundation, BagStacking attained a mean average precision (MAP) of 0.306, surpassing standalone LightGBM and traditional stacking methods. Furthermore, BagStacking demonstrated superior area under the curve (AUC) metrics across key FOG event classes. Specifically, it achieved AUCs of 0.88 for start hesitation, 0.90 for turning, and 0.84 for walking events, outperforming multistrategy ensemble, regular stacking, and LightGBM baselines. Additionally, BagStacking exhibited reduced runtime compared to other ensemble approaches, making it suitable for real-time clinical monitoring. These results underscore BagStacking’s effectiveness in addressing the variability inherent in FOG detection, thereby contributing to improved patient care in PD.

Sensitivity Analysis on Policy‐Augmented Graphical Hybrid Models With Shapley Value Estimation

ABSTRACTDriven by the critical challenges in biomanufacturing, including high complexity and high uncertainty, we propose a comprehensive and computationally efficient sensitivity analysis framework for general nonlinear policy‐augmented knowledge graphical (pKG) hybrid models that characterize the risk‐ and science‐based understandings of underlying stochastic decision process mechanisms. The criticality of each input (i.e., random factors, policy parameters, and model parameters) is measured by applying Shapley value (SV) sensitivity analysis to pKG (called SV‐pKG), accounting for process causal interdependences. To quickly assess the SV for heavily instrumented bioprocesses, we approximate their dynamics with linear Gaussian pKG models and improve the SV estimation efficiency by utilizing the linear Gaussian properties. In addition, we propose an effective permutation sampling method with TFWW transformation and variance reduction techniques, namely the quasi‐Monte Carlo and antithetic sampling methods, to further improve the sampling efficiency and estimation accuracy of SV for both general nonlinear and linear Gaussian pKG models. Our proposed framework can benefit efficient interpretation and support stable optimal process control in biomanufacturing.

A stochastic primal-dual splitting algorithm with variance reduction for composite optimization problems

This paper revisits the generic structured primal-dual problem involving the infimal convolution in real Hilbert spaces. For this purpose, we develop a stochastic primal-dual splitting with variance reduced for solving this generic problem. Weak almost sure convergence of the iterates is proved. The linear convergence rate of the primal-dual gap is obtained under an additional condition like the strong convexity.

Physics‐Informed Active Learning With Simultaneous Weak‐Form Latent Space Dynamics Identification

ABSTRACTThe parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high‐dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. To enhance robustness against noise, we incorporate the weak‐form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak‐form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent‐space dynamics of high‐dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced‐order modeling. Furthermore, the greedy physics‐informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time‐dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10 Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7 relative errors. Compared with the high‐fidelity models, WgLaSDI achieves 121 to 1779 speed‐up.

Contributon-Informed Approach to RPV Irradiation Study Using Hybrid Shielding Methodology

An important aspect of pressurized water reactor (PWR) lifetime monitoring is supporting radiation shielding analyses which can quantify various in-core and out-core effects induced in reactor materials by varying neutron–gamma fields. A good understanding of such a radiation environment during normal and accidental operating conditions is required by plant regulators to ensure proper shielding of equipment and working personnel. The complex design of a typical PWR is posing a deep penetration shielding problem for which an elaborate simulation model is needed, not only in geometrical aspects but also in efficient computational algorithms for solving particle transport. This paper presents such a hybrid shielding approach of FW-CADIS for characterization of the reactor pressure vessel (RPV) irradiation using SCALE6.2.4 code package. A fairly detailed Monte Carlo model (MC) of typical reactor internals was developed to capture all important streaming paths of fast neutrons which will backscatter the biological shield and thus enhance RPV irradiation through the cavity region. Several spatial differencing and angular segmentation options of the discrete ordinates SN flux solution were compared in connection to a SN mesh size and were inspected by VisIt code. To optimize MC neutron transport toward the upper RPV head, which is a particularly problematic region for particle transport, a deterministic solution of discrete ordinates in forward/adjoint mode was convoluted in a so-called contributon flux, which proved to be useful for subsequent SN mesh refinement and variance reduction (VR) parameters preparation. The pseudo-particle flux of contributons comes from spatial channel theory which can locate spatial regions important for contributing to a shielding response.

Internal Tides From SWOT: A 75‐Day Instantaneous Mode‐1 M2 ${\mathrm{M}}_{2}$ Internal Tide Model

AbstractSeventy‐five days of sea surface height measurements made by the Surface Water and Ocean Topography (SWOT) mission from 7 September to 21 November 2023 are used to explore SWOT's capability of observing internal tides. Mode‐1 internal tides are mapped by our updated mapping technique. SWOT‐75d represents a 75‐day instantaneous model. Nadir‐30y is constructed using 30 years of nadir altimetry data from 1993 to 2022 and represents a climate normal. The nadir altimetry data in 2023 are used for model evaluation. Despite its large errors, SWOT‐75d reveals the basic features of the global mode‐1 internal tide field, and causes positive variance reduction in regions of strong internal tides. Nadir‐30y performs better overall, but SWOT‐75d performs better in the tropical South Atlantic Ocean, the central North Pacific Ocean, and the Melanesian region. Evaluation using seasonally subsetted altimetry data reveals that internal tides have significant temporal variations. SWOT‐75d performs the best in fall, because the model is constructed using data largely in fall. SWOT‐75d has large phase anomalies, which are spatially smoothed and used to adjust the phases in Nadir‐30y. The phase‐adjusted model can better make internal tide correction for SWOT and its performance is improved by 20%. Our results demonstrate that (a) mode‐1 internal tides can be extracted from 75 days of SWOT data by our mapping technique, and (b) the instantaneous internal tide model can be used to improve internal tide correction for SWOT.

Strata Design for Variance Reduction in Stochastic Simulation

Stratified sampling is one of the powerful variance reduction methods for analyzing system performance, such as reliability, with stochastic simulation. It divides the input space into disjoint subsets, called strata, to draw samples from each stratum. Partitioning the input space properly and allocating greater computational effort to crucial strata can help accurately estimate system performance with a limited computational budget. How to create strata, however, has yet to be thoroughly examined. Strata design faces the curse of dimensionality and data scarcity as the input dimension increases. We analytically derive the optimal stratification structure that minimizes the estimation variance for univariate problems. Further, reconciling the optimal stratification into decision trees, we devise a robust algorithm for multi-dimensional problems. Numerical experiments and a wind turbine case study demonstrate the superiority of the proposed method in terms of variance reduction, leading to computational efficiency and scalability.

Solving Inverse PDE Problems using Grid-Free Monte Carlo Estimators

Partial differential equations can model diverse physical phenomena including heat diffusion, incompressible flows, and electrostatic potentials. Given a description of an object's boundary and interior, traditional methods solve such PDEs by densely meshing the interior and then solving a large and sparse linear system derived from this mesh. Recent grid-free solvers take an alternative approach and avoid this complexity in exchange for randomness: they compute stochastic solution estimates and generally bear a striking resemblance to physically-based rendering algorithms. In this article, we develop algorithms targeting the inverse form of this problem: given an already existing solution of a PDE, we infer parameters characterizing the boundary and interior. In the grid-free setting, there are again significant connections to rendering, and we show how insights from both fields can be combined to compute unbiased derivative estimates that enable gradient-based optimization. In this process, we encounter new challenges that must be addressed to obtain practical solutions. We introduce acceleration and variance reduction strategies and show how to differentiate branching random walks in reverse mode. We finally demonstrate our approach on both simulated data and a real-world electrical impedance tomography experiment, where we reconstruct the position of a conducting object from voltage measurements taken in a saline-filled tank.

Imaginary latent variables: Empirical testing for detecting deficiency in reflective measures

Imaginary latent variables are variables with negative variances and have been used to implement constraints in measurement models. This article aimed to advance this practice and rationalize the imaginary latent variables as a method to detect possible latent deficiencies in measurement models. This rationale is based on the theory of complex numbers used in the measurement process of common factor model–based structural equation modeling. Modeling an imaginary latent variable produces a potential deficiency within its relative reflective measures through a considerable reduction in common variance indicating the most affected indicator(s).

Mean-Field-Type Transformers

In this article, we present the mathematical foundations of generative machine intelligence and link them with mean-field-type game theory. The key interaction mechanism is self-attention, which exhibits aggregative properties similar to those found in mean-field-type game theory. It is not necessary to have an infinite number of neural units to handle mean-field-type terms. For instance, the variance reduction in error within generative machine intelligence is a mean-field-type problem and does not involve an infinite number of decision-makers. Based on this insight, we construct mean-field-type transformers that operate on data that are not necessarily identically distributed and evolve over several layers using mean-field-type transition kernels. We demonstrate that the outcomes of these mean-field-type transformers correspond exactly to the mean-field-type equilibria of a hierarchical mean-field-type game. Due to the non-convexity of the operators’ composition, gradient-based methods alone are insufficient. To distinguish a global minimum from other extrema—such as local minima, local maxima, global maxima, and saddle points—alternative methods that exploit hidden convexities of anti-derivatives of activation functions are required. We also discuss the integration of blockchain technologies into machine intelligence, facilitating an incentive design loop for all contributors and enabling blockchain token economics for each system participant. This feature is especially relevant to ensuring the integrity of factual data, legislative information, medical records, and scientifically published references that should remain immutable after the application of generative machine intelligence.

Retraction: The value of Monte Carlo model-based variance reduction technology in the pricing of financial derivatives.

Retraction: The value of Monte Carlo model-based variance reduction technology in the pricing of financial derivatives.

Modal volatility function

We in this article propose a novel non‐parametric estimator for the volatility function within a broad context that encompasses nonlinear time series models as a special case. The new estimator, built on the mode value, is designed to complement existing mean volatility measures to reveal distinct data features. We demonstrate that the suggested modal volatility estimator can be obtained asymptotically as well as if the conditional mean regression function were known, assuming observations are from a strictly stationary and absolutely regular process. Under mild regularity conditions, we establish that the asymptotic distributions of the resulting estimator align with those derived from independent observations, albeit with a slower convergence rate compared to non‐parametric mean regression. The theory and practice of bandwidth selection are discussed. Moreover, we put forward a variance reduction technique for the modal volatility estimator to attain asymptotic relative efficiency while maintaining the asymptotic bias unchanged. We numerically solve the modal regression model with the use of a modified modal‐expectation‐maximization algorithm. Monte Carlo simulations are conducted to assess the finite sample performance of the developed estimation procedure. Two real data analyses are presented to further illustrate the newly proposed model in practical applications. To potentially enhance the accuracy of the bias term, we in the end discuss the extension of the method to local exponential modal estimation. We showcase that the suggested exponential modal volatility estimator shares the same asymptotic variance as the non‐parametric modal volatility estimator but may exhibit a smaller bias.

Variance reduction in Monte Carlo for Integrals

Abstract. Nowadays, the extensive use of Monte Carlo methods in various fields has promoted the scientific decision-making, improved the efficiency of social operation, and enabled better management of many uncertain factors in daily life. However, in some cases, traditional Monte Carlo methods doesn't work so well because of the excessive variance. This paper aims to explore a new numerical integration method called splitting method to minimize intrinsic variance in Monte Carlo simulations. Through this innovative method, we found that the variance was reduced significantly. Despite some oscillating functions which are still difficult to estimate because they have too many turning points, this study provides new insights into variance reduction in Monte Carlo for integrals to optimize calculations in various fields when the modelling functions are not monotonic.

Control of simulated ocean ecosystem indicators by biogeochemical observations

To protect marine ecosystems threatened by climate change and anthropic stressors, it is essential to operationally monitor ocean health indicators. These are metrics synthetizing multiple marine processes relevant to the users of operational services. Here we assess if selected ocean indicators simulated by operational models can be controlled (here meaning constrained effectively) by biogeochemical observations, by using a newly proposed methodological framework. The method consists in firstly screening the sensitivities of the indicators with respect to the initial conditions of the observable variables. These initial conditions are perturbed stochastically in Monte Carlo simulations of one-dimensional configurations of a multi-model ensemble. Then, the models are applied in three-dimensional ensemble assimilation experiments, where the reduction of the ensemble variance corroborates the controllability of the indicators by the observations. The method is applied for ten relevant ecosystem indicators (ranging from inorganic chemicals to plankton production), seven observation types (representing data from satellite and underwater platforms), and an ensemble of five biogeochemical models of different complexity, employed operationally by the European Copernicus Marine Service. We demonstrate that all the indicators are controlled by one or more types of observations. In particular, the indicators of phytoplankton phenology are controlled and improved by the merged observations from the surface ocean colour and chlorophyll profiles. Similar observations also control and reduce the uncertainty of the plankton community structure and production. However, the uncertainty of the trophic efficiency and POC increases when assimilating chlorophyll-a data, though observations were not available to assess whether that was due to a worsen model skill. We recommend that the assessment of controllability proposed here becomes a standard practice in designing operational monitoring, reanalysis and forecast systems, to ultimately provide the users of operational services with more precise estimates of ocean ecosystem indicators.