Nonparametric Model Research Articles

Neural Operator Variational Inference Based on Regularized Stein Discrepancy for Deep Gaussian Processes.

Deep Gaussian process (DGP) models offer a powerful nonparametric approach for Bayesian inference, but exact inference is typically intractable, motivating the use of various approximations. However, existing approaches, such as mean-field Gaussian assumptions, limit the expressiveness and efficacy of DGP models, while stochastic approximation can be computationally expensive. To tackle these challenges, we introduce neural operator variational inference (NOVI) for DGPs. NOVI uses a neural generator to obtain a sampler and minimizes the regularized Stein discrepancy (RSD) between the generated distribution and true posterior in L2 space. We solve the minimax problem using Monte Carlo estimation and subsampling stochastic optimization techniques and demonstrate that the bias introduced by our method can be controlled by multiplying the Fisher divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm. Our experiments on datasets ranging from hundreds to millions demonstrate the effectiveness and the faster convergence rate of the proposed method. We achieve a classification accuracy of 93.56 on the CIFAR10 dataset, outperforming state-of-the-art (SOTA) Gaussian process (GP) methods. We are optimistic that NOVI possesses the potential to enhance the performance of deep Bayesian nonparametric models and could have significant implications for various practical applications.

A semi-parametric maximum-likelihood analysis of measurement error in population size estimation

Abstract This work addresses the challenge of measurement errors in capture–recapture (CR) studies with covariates. These errors can introduce bias and undermine inference quality. To address this issue, we introduce a nonparametric measurement error model tailored to the ‘repeated counts’ setting, employing EM-type algorithms for parameter estimation. We use the Horvitz–Thompson estimator for population size estimates. Rigorous simulations, covering varying degrees of measurement error reliability, confirm our approach’s effectiveness. Applied to benchmark datasets, it consistently provides more accurate point estimates and robust uncertainty quantification, enhancing the reliability of CR analyses.

On complete convergence for weighted sums of m-widely acceptable random variables under sub-linear expectations and its statistical applications

. In this article, by means of Rosenthal-type inequality, we study the complete convergence and strong law of large numbers for weighted sums of m-widely accpetable random variables under sub-linear expectations, which extend some existing results in classical probability space. As applications, we investigate the complete consistency and strong consistency of weighted estimators in nonparametric regression models under sub-linear expectations. In addition, we provide some simulation studies to verify the finite sample performance of the theoretical results.

History-restricted marginal structural model and latent class growth analysis of treatment trajectories for a time-dependent outcome.

In previous work, we introduced a framework that combines latent class growth analysis (LCGA) with marginal structural models (LCGA-MSM). LCGA-MSM first summarizes the numerous time-varying treatment patterns into a few trajectory groups and then allows for a population-level causal interpretation of the group differences. However, the LCGA-MSM framework is not suitable when the outcome is time-dependent. In this study, we propose combining a nonparametric history-restricted marginal structural model (HRMSM) with LCGA. HRMSMs can be seen as an application of standard MSMs on multiple time intervals. To the best of our knowledge, we also present the first application of HRMSMs with a time-to-event outcome. It was previously noted that HRMSMs could pose interpretation problems in survival analysis when either targeting a hazard ratio or a survival curve. We propose a causal parameter that bypasses these interpretation challenges. We consider three different estimators of the parameters: inverse probability of treatment weighting (IPTW), g-computation, and a pooled longitudinal targeted maximum likelihood estimator (pooled LTMLE). We conduct simulation studies to measure the performance of the proposed LCGA-HRMSM. For all scenarios, we obtain unbiased estimates when using either g-computation or pooled LTMLE. IPTW produced estimates with slightly larger bias in some scenarios. Overall, all approaches have good coverage of the 95 % confidence interval. We applied our approach to a population of older Quebecers composed of 57,211 statin initiators and found that a greater adherence to statins was associated with a lower combined risk of cardiovascular disease or all-cause mortality.

Seasonality in synthetic average wind speed

There is a growing demand for computer-generated realistic high-fidelity wind speed data for various applications in the wind industry. Such data should capture the non-stationary dynamics of real-world wind time series, as well as be consistent with the statistical descriptors – the probability density function and power spectral density – of the observed wind speed. However, complying with the statistical descriptors is not a guarantee that the seasonality will be correctly reproduced in synthetic data. The seasonality, characterized by the average diurnal and seasonal variations, is driven by the periodicities embedded in diurnal and annual harmonic series respectively. Those periodicities are determined by the long-term orbital forcing components, which establish the insolation for a given latitude and longitude. We show that average diurnal and seasonal variations can be visualized as the output of comb filters, whose fundamental frequencies match the diurnal and annual fundamental frequency respectively. The aforementioned theoretical findings are readily reproduced in synthetic wind speed, generated by a non-parametric data-driven statistical model, based on the phase-randomized Fourier transform. The model, tested on both 10-min and 1-min resolution real-world datasets, yields average non-stationarities in synthetic wind speed with the accuracy close to the computing precision.

The MACE-SCREEN – Screening for Abuse and Neglect Across Developmental Stages

ABSTRACT Few high-quality instruments are available to comprehensively screen for multiple interpersonal traumatic childhood experiences differentiated by developmental stage. One instrument assessing various forms of childhood trauma is the Maltreatment and Abuse Chronology of Exposure (MACE-X, Teicher & Parigger, 2015), which allows for the assessment of age at exposure for every item. The aim of this study is the development of a shorter version, which is suitable for screening. In- and out-patients (n = 719) of a somatic clinic were assessed with the German version of the 75-item MACE. Descriptive statistics, a nonparametric item response theory model (Mokken Scale Analysis), and factor analysis were combined to select items for a screening version. A screener (MACE-SCREEN) with 39 items allocated to five scales was developed. Scales differentiate between abuse types and neglect, direct experience vs. witnessing violence, and the age of the perpetrator (adults vs. peers). The scales showed good internal consistency (Alpha .78 to .91) and the total score a strong correlation with the total score of the long version (r = .96). This screening version is still comprehensive as it assesses exposure to various forms of interpersonal traumatic events, including peer violence and witnessing domestic abuse. As it also allows for the concurrent assessment of age at exposure, it lends itself to assessing exposure across developmental stages.

Hierarchical Bayesian spectral regression with shape constraints for multi-group data

We propose a hierarchical Bayesian (HB) model for multi-group analysis with group–specific, flexible regression functions. The lower–level (within group) and upper–level (between groups) regression functions have hierarchical Gaussian process priors. HB smoothing priors are developed for the spectral coefficients. The HB priors smooth the estimated functions within and between groups. The HB model is particularly useful when data within groups are sparse because it shares information across groups, and provides more accurate estimates than fitting separate nonparametric models to each group. The proposed model also allows shape constraints, such as monotone, U and S–shaped, and multi-modal constraints. When appropriate, shape constraints improve estimation by recognizing violations of the shape constraints as noise. The model is illustrated by two examples: monotone growth curves for children, and happiness as a convex, U-shaped function of age in multiple countries. Various basis functions could also be used, and the paper also implements versions with B-splines and orthogonal polynomials.

Robust tests for equality of regression curves based on characteristic functions

This paper focuses on the problem of testing the null hypothesis that the regression functions of several populations are equal under a general nonparametric homoscedastic regression model. It is well known that linear kernel regression estimators are sensitive to atypical responses. These distorted estimates will influence the test statistic constructed from them so the conclusions obtained when testing equality of several regression functions may also be affected. In recent years, the use of testing procedures based on empirical characteristic functions has shown good practical properties. For that reason, to provide more reliable inferences, we construct a test statistic that combines characteristic functions and residuals obtained from a robust smoother under the null hypothesis. The asymptotic distribution of the test statistic is studied under the null hypothesis and under root − n contiguous alternatives. A Monte Carlo study is performed to compare the finite sample behaviour of the proposed test with the classical one obtained using local averages. The reported numerical experiments show the advantage of the proposed methodology over the one based on Nadaraya–Watson estimators for finite samples. An illustration to a real data set is also provided and enables to investigate the sensitivity of the p − value to the bandwidth selection.

Applying machine learning approach in predicting short-term rockburst risks using microseismic information: a comparison of parametric and non-parametric models

Applying machine learning approach in predicting short-term rockburst risks using microseismic information: a comparison of parametric and non-parametric models

MODELING DHF IN CENTRAL JAVA USING HYBRID NONPARAMETRIC SPLINE TRUNCATED-FOURIER SERIES APPROACH

Regression analysis aims to determine the relationship and influence of predictor variables on response variables through regression curve. The problem with nonparametric regression research so far is that it only uses one approach, causing the estimation results to be biased, even though each data sub-pattern has its own suitability depending on the approach method used. Therefore, the hybrid method emerged as a development of nonparametric regression. Hybrid models are models that combine approach methods, with the hope of increasing accuracy in modeling analysis. This research was carried out using two non-parametric approaches, namely Spline Truncated and Fourier Series. Dengue Hemorrhagic Fever (DHF) is a disease caused by the dengue virus. DHF is endemic and occurs throughout the year, especially during the rainy season because mosquitoes reproduce optimally. The aim of this research is to estimate the Hybrid Nonparametric Spline Truncated -Fourier Series model and apply the estimation results to data on DHF cases in Central Java. The data used to apply the hybrid nonparametric Spline Truncated-Fourier series regression model is DHF in the city/districts of Central Java. Estimation smoothing parameters uses the GCV (Generalized Cross Validation) method. The best model is selected based on largest R-Square and the smallest MSE. Modeling the disease of DHF cases in Central Java using the Spline Truncated-Fourier Series hybrid estimator produced the best model from the Spline Truncated model with two knot points for each predictor and the Fourier Series model with value of 9. Based on the results obtained, it can be compared that the Truncated Spline-Fourier Series hybrid model is better than the Spline Truncated model, this can be seen from the largest R-square, namely 99.94% and the smallest MSE.

Nonparametric inference of higher order interaction patterns in networks

Local interaction patterns play an important role in the structural and functional organization of complex networks. Here we propose a method for obtaining parsimonious decompositions of networks into higher order interactions which can take the form of arbitrary motifs. The method is based on a class of analytically solvable generative models which in combination with non-parametric priors allow us to infer higher order interactions from dyadic graph data without any prior knowledge on the types or frequencies of such interactions. We test the presented approach on simulated data for which we recover the set of underlying higher order interactions to a high degree of accuracy. For empirical networks the method identifies concise sets of atomic subgraphs from within thousands of candidates that cover a large fraction of edges and include higher order interactions of known structural and functional significance. Being based on statistical inference the method also produces a fit of the network to analytically tractable higher order models opening new avenues for the systematic study of higher order interactions.

Spiritual needs and influencing factors among people with stroke in China: a cross-sectional study

BackgroundStroke is one of the primary causes of disability in China and around the world, having an impact on the health and well-being of stroke patients. The importance of spiritual needs for stroke patients has always been a controversial topic internationally, partly because related research was mostly qualitative and may not directly reflect the degree of spiritual needs. In addition, most studies focus on the same cultural background, there is a lack of research that delves into the nuances of Chinese culture and background. The goal of this study is to evaluate the level of spiritual needs and influencing factors in Chinese stroke patients and to explore the mediating role and pathways of these variables on spiritual needs.MethodsFrom August 2022 to January 2023, we conducted a cross-sectional questionnaire survey of 422 stroke patients in the affiliated hospitals of Hunan University of Chinese Medicine in Changsha Province by cluster sampling. We measured the patient’s spiritual needs, quality of life, anxiety and depression levels, and family support using the Spiritual Needs Questionnaire (SPNQ), the MOS36 item Short Form Health Survey (SF-36), the Hospital Anxiety and Depression Scale (HADS), and the Family Support Self Rating Scale (PSS-Fa). We used the General Information Questionnaire to gain insight into the sociodemographic characteristics of the patients. Nonparametric tests and multiple linear regression models were used to analyze the independent relationship between spiritual needs and quality of life, anxiety, depression, and family support. The mediation model in AMOS 24.0 software was used to analyze the mediating role among the five variables.ResultsThe score of spiritual needs of people with stroke included in this study was 37 points [IQR 33 to 40)]. The influencing factors of spiritual needs included primary economic sources for disease-related expenditures (p = 0.044), number of stroke occurrences (p = 0.001), duration of illness (p = 0.023), activities of daily living (p = 0.006), depression scores(p = 0.034), and family support scores(p = 0.008). Anxiety (β = 0.347, p = 0.004), depression (β = 0.368, p = 0.005), and family support (β = 0.167, p = 0.023) had directly or indirectly affected the spiritual needs of people with stroke. Quality of life (β=-0.202, p = 0.017) had a direct effect on spiritual needs.ConclusionsThe spiritual needs of people with stroke were at an intermediate level. Our findings highlight that the SPNQ score is associated with anxiety, depression, quality of life, and family support. Therefore, nurses should identify the spiritual needs of patients and provide them with effective and comprehensive spiritual care by reducing negative emotions and enhancing social support, promoting the development and progress of spiritual care in China. This study offers a theoretical basis for the spiritual care of clinical people with stroke and constructing a stroke spiritual care model.

NHSMM-MAR-sdNC: A novel data-driven computational framework for state-dependent effective connectivity analysis

The brain exhibits intrinsic dynamics characterized by spontaneous spatiotemporal reorganization of neural activity or metastability, which is associated closely with functional integration and segregation. Compared to dynamic functional connectivity, state-dependent effective connectivity (i.e., dynamic effective connectivity) is more suitable for exploring the metastability as its ability to infer causalities between brain regions. However, methods for state-dependent effective connectivity are scarce and urgently needed. In this study, a novel data-driven computational framework, named NHSMM-MAR-sdNC integrating nonparametric hidden semi-Markov model combined with multivariate autoregressive model and state-dependent new causality, is proposed to investigate the state-dependent effective connectivity. The framework is not constrained by any biological assumptions. Furthermore, state number can be inferred from the observed data directly and the state duration distributions will be estimated explicitly rather than restricted by geometric form, which overcomes limitations of hidden Markov model. Experimental results of synthetic data show that the framework can identify the state number adaptively and the state-dependent causality networks accurately. The dynamics of state-related causality networks are also revealed by the new method on real-world resting-state fMRI data. Our method provides a new data-driven computational framework for identifying state-dependent effective connectivity, which will facilitate the identification and assessment of metastability and itinerant dynamics of the brain.

A Hybrid Data Envelopment Analysis–Random Forest Methodology for Evaluating Green Innovation Efficiency in an Asymmetric Environment

The accurate evaluation of green innovation efficiency is a critical prerequisite for enterprises to achieve sustainable development goals and improve environmental performance and economic efficiency. This paper evaluates the green innovation efficiency of 72 new-energy enterprises by using a hybrid method of Data Envelopment Analysis (DEA) and a random forest model. The non-parametric DEA model is combined with the parametric SFA model to analyze the real green innovation efficiency on the basis of removing environmental factors and random factors. Then, the random forest model based on a nonlinear relationship is used to evaluate factors impacting green innovation efficiency. This paper proposes a comprehensive evaluation method designed to assess the green innovation efficiency of new-energy enterprises. By applying this method, companies can gain a comprehensive understanding of the current performance in green innovation, facilitating informed decision-making and accelerating sustainable development.

Bayesian mixture models (in)consistency for the number of clusters

AbstractBayesian nonparametric mixture models are common for modeling complex data. While these models are well‐suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of components is finite, for the Dirichlet process and Pitman–Yor process mixture models. We extend these results to additional Bayesian nonparametric priors such as Gibbs‐type processes and finite‐dimensional representations thereof. The latter include the Dirichlet multinomial process, the recently proposed Pitman–Yor, and normalized generalized gamma multinomial processes. We show that mixture models based on these processes are also inconsistent in the number of clusters and discuss possible solutions. Notably, we show that a postprocessing algorithm introduced for the Dirichlet process can be extended to more general models and provides a consistent method to estimate the number of components.

The Berry-Esseen bounds of wavelet estimator for nonparametric regression models whose errors form a linear process based on ANA sequences

In this paper, we consider the nonparametric regression model Y ni = g ( t ni ) + ϵ i ( 1 ≤ i ≤ n ), where ϵ i = ∑ j = − ∞ ∞ a j e i − j and e i are identically distributed and asymptotically negatively associated (ANA or ρ − , for short) sequences. This paper obtains the Berry-Esseen bounds of the wavelet estimator of g ( ⋅ ) , and the rate of the normal approximation is shown as O ( n − 1 / 4 ) under certain conditions. Finally, the simulation study is provided to verify the validity of the theoretical results.

Nonparametric Regression Modeling with Multivariable Fourier Series Estimator on Average Length of Schooling in Central Java in 2023

Nonparametric Regression Modeling with Multivariable Fourier Series Estimator on Average Length of Schooling in Central Java in 2023

Reconciling shared versus context-specific information in a neural network model of latent causes

It has been proposed that, when processing a stream of events, humans divide their experiences in terms of inferred latent causes (LCs) to support context-dependent learning. However, when shared structure is present across contexts, it is still unclear how the “splitting” of LCs and learning of shared structure can be simultaneously achieved. Here, we present the Latent Cause Network (LCNet), a neural network model of LC inference. Through learning, it naturally stores structure that is shared across tasks in the network weights. Additionally, it represents context-specific structure using a context module, controlled by a Bayesian nonparametric inference algorithm, which assigns a unique context vector for each inferred LC. Across three simulations, we found that LCNet could (1) extract shared structure across LCs in a function learning task while avoiding catastrophic interference, (2) capture human data on curriculum effects in schema learning, and (3) infer the underlying event structure when processing naturalistic videos of daily events. Overall, these results demonstrate a computationally feasible approach to reconciling shared structure and context-specific structure in a model of LCs that is scalable from laboratory experiment settings to naturalistic settings.

Observation vector reconstruction-based nonparametric nonlinear restoring force identification for granules-structures coupled vibrating system

The nonlinear restoring force (NRF) generated by the collision and friction between particles and structures is the leading cause of the complex dynamic response of the granules-structures coupled vibrating system (GSCVS). Identification of NRF can provide critical information for post-event damage diagnosis and structural design of immersed structures. However, the spatial distribution and dynamic response of the particles near the structures are diverse and complex, making it difficult to describe the NRF with an accurate mathematical model. This paper proposed a data-based nonparametric method to estimate the NRF in the GSCVS. A nonparametric model of NRF that considered the additional effects of particles on both sides of the structures and consisted of system response and undetermined coefficients was developed. The observation vector of the conventional Extended Kalman Filter (EKF) was reconstructed by the sparse measurement of the strain response. The reconstructed observation vector contains three response components: translational displacement, translational acceleration, and rotational acceleration, in which the rotational acceleration response is difficult to measure in engineering applications. The proposed EKF based on observation vector reconstruction (EKF-OVR) can identify the undetermined coefficients in the nonparametric model, and then the NRF can be calculated. Numerical studies showed that EKF-OVR achieved higher accuracy and noise robustness than the conventional EKF and the data fusion based EKF. A dynamic experimental study on granules-beam coupled vibrating system (GBCVS) was conducted, and the proposed algorithm was employed to identify the NRF of the GBCVS. The effects of excitation amplitude, particle size, and immersed depth on NRF are analyzed, and it is found that higher harmonic components in the NRF led to period doubling and chaos of the beam response.

Stochastic prior for non-parametric star-formation histories

ABSTRACT The amount of power contained in the variations in galaxy star-formation histories (SFHs) across a range of time-scales encodes key information about the physical processes which modulate star formation. Modelling the SFHs of galaxies as stochastic processes allows the relative importance of different time-scales to be quantified via the power spectral density (PSD). In this paper, we build upon the PSD framework and develop a physically motivated, ‘stochastic’ prior for non-parametric SFHs in the spectral energy distribution (SED)-modelling code prospector. We test this prior in two different regimes: (1) massive, $z = 0.7$ galaxies with both photometry and spectra, analogous to those observed with the LEGA-C survey, and (2) $z = 8$ galaxies with photometry only, analogous to those observed with NIRCam on JWST. We find that it is able to recover key galaxy parameters (e.g. stellar mass, stellar metallicity) to the same level of fidelity as the commonly used continuity prior. Furthermore, the realistic variability information incorporated by the stochastic SFH model allows it to fit the SFHs of galaxies more accurately and precisely than traditional non-parametric models. In fact, the stochastic prior is $\gtrsim 2\times$ more accurate than the continuity prior in measuring the recent star-formation rates (log SFR$_{100}$ and log SFR$_{10}$) of both the $z = 0.7$ and $z = 8$ mock systems. While the PSD parameters of individual galaxies are difficult to constrain, the stochastic prior implementation presented in this work allows for the development of hierarchical models in the future, i.e. simultaneous SED-modelling of an ensemble of galaxies to measure their underlying PSD.