arXiv subjects

David Ruppert

Publications and source records attributed to David Ruppert.

At least 19 recordsLinked to original sources

arXiv2025

Bayesian analysis of regression discontinuity designs with heterogeneous treatment effects

Regression Discontinuity Design (RDD) is a popular framework for estimating a causal effect in settings where treatment is assigned if an observed covariate exceeds a fixed threshold. We consider estimation and inference in the common setting where the sample consists of multiple known sub-populations with potentially heterogeneous treatment effects. In the applied literature, it is common to account for heterogeneity by either fitting a parametric model or considering each sub-population separately. In contrast, we develop a Bayesian hierarchical model using Gaussian process regression which allows for non-parametric regression while borrowing information across sub-populations. We derive the posterior distribution, prove posterior consistency, and develop a Metropolis-Hastings within Gibbs sampling algorithm. In extensive simulations, we show that the proposed procedure outperforms existing methods in both estimation and inferential tasks. Finally, we apply our procedure to U.S. Senate election data and discover an incumbent party advantage which is heterogeneous over different time periods.

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arXiv2024

Bayesian functional data analysis in astronomy

Cosmic demographics -- the statistical study of populations of astrophysical objects -- has long relied on *multivariate statistics*, providing methods for analyzing data comprising fixed-length vectors of properties of objects, as might be compiled in a tabular astronomical catalog (say, with sky coordinates, and brightness measurements in a fixed number of spectral passbands). But beginning with the emergence of automated digital sky surveys, ca. ~2000, astronomers began producing large collections of data with more complex structure: light curves (brightness time series) and spectra (brightness vs. wavelength). These comprise what statisticians call *functional data* -- measurements of populations of functions. Upcoming automated sky surveys will soon provide astronomers with a flood of functional data. New methods are needed to accurately and optimally analyze large ensembles of light curves and spectra, accumulating information both along and across measured functions. Functional data analysis (FDA) provides tools for statistical modeling of functional data. Astronomical data presents several challenges for FDA methodology, e.g., sparse, irregular, and asynchronous sampling, and heteroscedastic measurement error. Bayesian FDA uses hierarchical Bayesian models for function populations, and is well suited to addressing these challenges. We provide an overview of astronomical functional data, and of some key Bayesian FDA modeling approaches, including functional mixed effects models, and stochastic process models. We briefly describe a Bayesian FDA framework combining FDA and machine learning methods to build low-dimensional parametric models for galaxy spectra.

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arXiv2023

Maximizing Portfolio Predictability with Machine Learning

We construct the maximally predictable portfolio (MPP) of stocks using machine learning. Solving for the optimal constrained weights in the multi-asset MPP gives portfolios with a high monthly coefficient of determination, given the sample covariance matrix of predicted return errors from a machine learning model. Various models for the covariance matrix are tested. The MPPs of S&P 500 index constituents with estimated returns from Elastic Net, Random Forest, and Support Vector Regression models can outperform or underperform the index depending on the time period. Portfolios that take advantage of the high predictability of the MPP's returns and employ a Kelly criterion style strategy consistently outperform the benchmark.

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arXiv2023

Splines 'n Lines: Rest-frame galaxy spectral energy distributions via Bayesian functional data analysis

Survey-based measurements of the spectral energy distributions (SEDs) of galaxies have flux density estimates on badly misaligned grids in rest-frame wavelength. The shift to rest frame wavelength also causes estimated SEDs to have differing support. For many galaxies, there are sizeable wavelength regions with missing data. Finally, dim galaxies dominate typical samples and have noisy SED measurements, many near the limiting signal-to-noise level of the survey. These limitations of SED measurements shifted to the rest frame complicate downstream analysis tasks, particularly tasks requiring computation of functionals (e.g., weighted integrals) of the SEDs, such as synthetic photometry, quantifying SED similarity, and using SED measurements for photometric redshift estimation. We describe a hierarchical Bayesian framework, drawing on tools from functional data analysis, that models SEDs as a random superposition of smooth continuum basis functions (B-splines) and line features, comprising a finite-rank, nonstationary Gaussian process, measured with additive Gaussian noise. We apply this *Splines 'n Lines* (SnL) model to a collection of 678,239 galaxy SED measurements comprising the Main Galaxy Sample from the Sloan Digital Sky Survey, Data Release 17, demonstrating capability to provide continuous estimated SEDs that reliably denoise, interpolate, and extrapolate, with quantified uncertainty, including the ability to predict line features where there is missing data by leveraging correlations between line features and the entire continuum.

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arXiv2023

Smoothness-Penalized Deconvolution (SPeD) of a Density Estimate

This paper addresses the deconvolution problem of estimating a square-integrable probability density from observations contaminated with additive measurement errors having a known density. The estimator begins with a density estimate of the contaminated observations and minimizes a reconstruction error penalized by an integrated squared $m$-th derivative. Theory for deconvolution has mainly focused on kernel- or wavelet-based techniques, but other methods including spline-based techniques and this smoothness-penalized estimator have been found to outperform kernel methods in simulation studies. This paper fills in some of these gaps by establishing asymptotic guarantees for the smoothness-penalized approach. Consistency is established in mean integrated squared error, and rates of convergence are derived for Gaussian, Cauchy, and Laplace error densities, attaining some lower bounds already in the literature. The assumptions are weak for most results; the estimator can be used with a broader class of error densities than the deconvoluting kernel. Our application example estimates the density of the mean cytotoxicity of certain bacterial isolates under random sampling; this mean cytotoxicity can only be measured experimentally with additive error, leading to the deconvolution problem. We also describe a method for approximating the solution by a cubic spline, which reduces to a quadratic program.

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arXiv2023

Measurement Errors in Semiparametric Generalized Regression Models

Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian nonparametric regression. This problem becomes tremendously more difficult when considering other families such as logistic regression, Poisson and negative-binomial. For the first time, we present a method aiming to correct for measurement error when estimating regression functions flexibly covering virtually all distributions and link functions regularly considered in generalized linear models. This approach depends on approximating the first and the second moment of the response after integrating out the true unobserved predictors in a semiparametric generalized linear model. Unlike previous methods, this method is not restricted to truncated splines and can utilize various basis functions. Through extensive simulation studies, we study the performance of our method under many scenarios.

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arXiv2021

Machine Learning Portfolio Allocation

We find economically and statistically significant gains when using machine learning for portfolio allocation between the market index and risk-free asset. Optimal portfolio rules for time-varying expected returns and volatility are implemented with two Random Forest models. One model is employed in forecasting the sign probabilities of the excess return with payout yields. The second is used to construct an optimized volatility estimate. Reward-risk timing with machine learning provides substantial improvements over the buy-and-hold in utility, risk-adjusted returns, and maximum drawdowns. This paper presents a new theoretical basis and unifying framework for machine learning applied to both return- and volatility-timing.

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arXiv2021

Copula-based functional Bayes classification with principal components and partial least squares

We present a new functional Bayes classifier that uses principal component (PC) or partial least squares (PLS) scores from the common covariance function, that is, the covariance function marginalized over groups. When the groups have different covariance functions, the PC or PLS scores need not be independent or even uncorrelated. We use copulas to model the dependence. Our method is semiparametric; the marginal densities are estimated nonparametrically by kernel smoothing and the copula is modeled parametrically. We focus on Gaussian and t-copulas, but other copulas could be used. The strong performance of our methodology is demonstrated through simulation, real data examples, and asymptotic properties.

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arXiv2021

Adaptive Ridge-Penalized Functional Local Linear Regression

We introduce an original method of multidimensional ridge penalization in functional local linear regressions. The nonparametric regression of functional data is extended from its multivariate counterpart, and is known to be sensitive to the choice of $J$, where $J$ is the dimension of the projection subspace of the data. Under multivariate setting, a roughness penalty is helpful for variance reduction. However, among the limited works covering roughness penalty under the functional setting, most only use a single scalar for tuning. Our new approach proposes a class of data-adaptive ridge penalties, meaning that the model automatically adjusts the structure of the penalty according to the data sets. This structure has $J$ free parameters and enables a quadratic programming search for optimal tuning parameters that minimize the estimated mean squared error (MSE) of prediction, and is capable of applying different roughness penalty levels to each of the $J$ basis. The strength of the method in prediction accuracy and variance reduction with finite data is demonstrated through multiple simulation scenarios and two real-data examples. Its asymptotic performance is proved and compared to the unpenalized functional local linear regressions.

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arXiv2021

Bootstrap inference for quantile-based modal regression

In this paper, we develop uniform inference methods for the conditional mode based on quantile regression. Specifically, we propose to estimate the conditional mode by minimizing the derivative of the estimated conditional quantile function defined by smoothing the linear quantile regression estimator, and develop two bootstrap methods, a novel pivotal bootstrap and the nonparametric bootstrap, for our conditional mode estimator. Building on high-dimensional Gaussian approximation techniques, we establish the validity of simultaneous confidence rectangles constructed from the two bootstrap methods for the conditional mode. We also extend the preceding analysis to the case where the dimension of the covariate vector is increasing with the sample size. Finally, we conduct simulation experiments and a real data analysis using U.S. wage data to demonstrate the finite sample performance of our inference method.

math.ST↗

arXiv2021

Bayesian Functional Principal Components Analysis via Variational Message Passing

Functional principal components analysis is a popular tool for inference on functional data. Standard approaches rely on an eigendecomposition of a smoothed covariance surface in order to extract the orthonormal functions representing the major modes of variation. This approach can be a computationally intensive procedure, especially in the presence of large datasets with irregular observations. In this article, we develop a Bayesian approach, which aims to determine the Karhunen-Loève decomposition directly without the need to smooth and estimate a covariance surface. More specifically, we develop a variational Bayesian algorithm via message passing over a factor graph, which is more commonly referred to as variational message passing. Message passing algorithms are a powerful tool for compartmentalizing the algebra and coding required for inference in hierarchical statistical models. Recently, there has been much focus on formulating variational inference algorithms in the message passing framework because it removes the need for rederiving approximate posterior density functions if there is a change to the model. Instead, model changes are handled by changing specific computational units, known as fragments, within the factor graph. We extend the notion of variational message passing to functional principal components analysis. Indeed, this is the first article to address a functional data model via variational message passing. Our approach introduces two new fragments that are necessary for Bayesian functional principal components analysis. We present the computational details, a set of simulations for assessing accuracy and speed and an application to United States temperature data.

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arXiv2020

Density Estimation on a Network

This paper develops a novel approach to density estimation on a network. We formulate nonparametric density estimation on a network as a nonparametric regression problem by binning. Nonparametric regression using local polynomial kernel-weighted least squares have been studied rigorously, and its asymptotic properties make it superior to kernel estimators such as the Nadaraya-Watson estimator. When applied to a network, the best estimator near a vertex depends on the amount of smoothness at the vertex. Often, there are no compelling reasons to assume that a density will be continuous or discontinuous at a vertex, hence a data driven approach is proposed. To estimate the density in a neighborhood of a vertex, we propose a two-step procedure. The first step of this pretest estimator fits a separate local polynomial regression on each edge using data only on that edge, and then tests for equality of the estimates at the vertex. If the null hypothesis is not rejected, then the second step re-estimates the regression function in a small neighborhood of the vertex, subject to a joint equality constraint. Since the derivative of the density may be discontinuous at the vertex, we propose a piecewise polynomial local regression estimate to model the change in slope. We study in detail the special case of local piecewise linear regression and derive the leading bias and variance terms using weighted least squares theory. We show that the proposed approach will remove the bias near a vertex that has been noted for existing methods, which typically do not allow for discontinuity at vertices. For a fixed network, the proposed method scales sub-linearly with sample size and it can be extended to regression and varying coefficient models on a network. We demonstrate the workings of the proposed model by simulation studies and apply it to a dendrite network data set.

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arXiv2020

Optimal Sampling for Generalized Linear Models under Measurement Constraints

Under "measurement constraints," responses are expensive to measure and initially unavailable on most of records in the dataset, but the covariates are available for the entire dataset. Our goal is to sample a relatively small portion of the dataset where the expensive responses will be measured and the resultant sampling estimator is statistically efficient. Measurement constraints require the sampling probabilities can only depend on a very small set of the responses. A sampling procedure that uses responses at most only on a small pilot sample will be called "response-free." We propose a response-free sampling procedure \mbox{(OSUMC)} for generalized linear models (GLMs). Using the A-optimality criterion, i.e., the trace of the asymptotic variance, the resultant estimator is statistically efficient within a class of sampling estimators. We establish the unconditional asymptotic distribution of a general class of response-free sampling estimators. This result is novel compared with the existing conditional results obtained by conditioning on both covariates and responses. Under our unconditional framework, the subsamples are no longer independent and new martingale techniques are developed for our asymptotic theory. We further derive the A-optimal response-free sampling distribution. Since this distribution depends on population level quantities, we propose the Optimal Sampling Under Measurement Constraints (OSUMC) algorithm to approximate the theoretical optimal sampling. Finally, we conduct an intensive empirical study to demonstrate the advantages of OSUMC algorithm over existing methods in both statistical and computational perspectives.

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arXiv2019

Sample Splitting as an M-Estimator with Application to Physical Activity Scoring

Sample splitting is widely used in statistical applications, including classically in classification and more recently for inference post model selection. Motivating by problems in the study of diet, physical activity, and health, we consider a new application of sample splitting. Physical activity researchers wanted to create a scoring system to quickly assess physical activity levels. A score is created using a large cohort study. Then, using the same data, this score serves as a covariate in a model for the risk of disease or mortality. Since the data are used twice in this way, standard errors and confidence intervals from fitting the second model are not valid. To allow for proper inference, sample splitting can be used. One builds the score with a random half of the data and then uses the score when fitting a model to the other half of the data. We derive the limiting distribution of the estimators. An obvious question is what happens if multiple sample splits are performed. We show that as the number of sample splits increases, the combination of multiple sample splits is effectively equivalent to solving a set of estimating equations.

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arXiv2019

Finite Sample Hypothesis Tests for Stacked Estimating Equations

Suppose there are two unknown parameters, each parameter is the solution to an estimating equation, and the estimating equation of one parameter depends on the other parameter. The parameters can be jointly estimated by "stacking" their estimating equations and solving for both parameters simultaneously. Asymptotic confidence intervals are readily available for stacked estimating equations. We introduce a bootstrap-based hypothesis test for stacked estimating equations which does not rely on asymptotic approximations. Test statistics are constructed by splitting the sample in two, estimating the first parameter on a portion of the sample then plugging the result into the second estimating equation to solve for the next parameter using the remaining sample. To reduce simulation variability from a single split, we repeatedly split the sample and take the sample mean of all the estimates. For parametric models, we derive the limiting distribution of sample splitting estimator and show they are equivalent to stacked estimating equations.

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arXiv2018

Density Deconvolution with Additive Measurement Errors using Quadratic Programming

Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can achieve better estimation than kernel density deconvolution methods. The QP approach appears to have a more favorable regularization tradeoff between oversmoothing vs. oscillation, especially at the tails of the distribution. An additional advantage is that it is straightforward to incorporate a number of common density constraints such as nonnegativity, integration-to-one, unimodality, tail convexity, tail monotonicity, and support constraints. We demonstrate that the QP approach has outstanding estimation performance relative to existing methods. Its performance is superior when only the universally applicable nonnegativity and integration-to-one constraints are incorporated, and incorporating additional common constraints when applicable (e.g., nonnegative support, unimodality, tail monotonicity or convexity, etc.) can further substantially improve the estimation.

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arXiv2018

Dynamic Shrinkage Processes

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon a global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence among the local scale parameters. The resulting processes inherit the desirable shrinkage behavior of popular global-local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modeling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólya-Gamma scale mixture representation of the proposed process. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than competing methods, and apply the model for irregular curve-fitting of minute-by-minute Twitter CPU usage data. In addition, we develop an adaptive time-varying parameter regression model to assess the efficacy of the Fama-French five-factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that with the exception of the market risk, no other risk factors are significant except for brief periods.

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arXiv2017

Linear Non-Gaussian Component Analysis via Maximum Likelihood

Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA (PCA+ICA), which could remove important information. The problem is that interesting independent components (ICs) could be mixed in several principal components that are discarded and then these ICs cannot be recovered. We formulate a linear non-Gaussian component model with Gaussian noise components. To estimate this model, we propose likelihood component analysis (LCA), in which dimension reduction and latent variable estimation are achieved simultaneously. Our method orders components by their marginal likelihood rather than ordering components by variance as in PCA. We present a parametric LCA using the logistic density and a semi-parametric LCA using tilted Gaussians with cubic B-splines. Our algorithm is scalable to datasets common in applications (e.g., hundreds of thousands of observations across hundreds of variables with dozens of latent components). In simulations, latent components are recovered that are discarded by PCA+ICA methods. We apply our method to multivariate data and demonstrate that LCA is a useful data visualization and dimension reduction tool that reveals features not apparent from PCA or PCA+ICA. We also apply our method to an fMRI experiment from the Human Connectome Project and identify artifacts missed by PCA+ICA. We present theoretical results on identifiability of the linear non-Gaussian component model and consistency of LCA.

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