Miracle-dz/UniFAR-FTUs huggingface dataset:
Adaptive Non-parametric Estimation of Mean and Autocovariance in Regression with Dependent Errors

We develop a fully automatic non-parametric approach to simultaneous estimation of mean and autocovariance functions in regression with dependent errors. Our empirical Bayesian approach is adaptive, numerically efficient and allows for the construction of confidence sets for the regression function. Consistency of the estimators is shown and small sample performance is demonstrated in simulations and real data analysis. The method is implemented in the R package eBsc that accompanies the paper.
High-temperature structure detection in ferromagnets

This paper studies structure detection problems in high-temperature ferromagnetic (positive interaction only) Ising models. The goal is to distinguish whether the underlying graph is empty, i.e., the model consists of independent Rademacher variables, vs. the alternative that the underlying graph contains a subgraph of a certain structure. We give matching upper and lower minimax bounds under which testing this problem is possible/impossible, respectively. Our results reveal that a key quantity called graph arboricity drives the testability of the problem. On the computational front, under a conjecture of the computational hardness of sparse principal component analysis, we prove that, unless the signal is strong enough, there are no polynomial time tests which are capable of testing this problem. In order to prove this result, we exhibit a way to give sharp inequalities for the even moments of sums of i.i. d. Rademacher random variables which may be of independent interest.
Practical Coreset Constructions for Machine Learning

We investigate coresets - succinct, small summaries of large data sets - so that solutions found on the summary are provably competitive with solution found on the full data set. We provide an overview over the state-of-the-art in coreset construction for machine learning. In Section 2, we present both the intuition behind and a theoretically sound framework to construct coresets for general problems and apply it to $k$-means clustering. In Section 3 we summarize existing coreset construction algorithms for a variety of machine learning problems such as maximum likelihood estimation of mixture models, Bayesian non-parametric models, principal component analysis, regression and general empirical risk minimization.
Integrated Principal Components Analysis

Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration method named Integrated Principal Components Analysis (iPCA), which is a model-based generalization of PCA and serves as a practical tool to find and visualize common patterns that occur in multiple data sets. The key idea driving iPCA is the matrix-variate normal model, whose Kronecker product covariance structure captures both individual patterns within each data set and joint patterns shared by multiple data sets. Building upon this model, we develop several penalized (sparse and non-sparse) covariance estimators for iPCA and study their theoretical properties. We show that our sparse iPCA estimator consistently estimates the underlying joint subspace, and using geodesic convexity, we prove that our non-sparse iPCA estimator converges to the global solution of a non-convex problem. We also demonstrate the practical advantages of iPCA through simulations and a case study application to integrative genomics for Alzheimer's Disease. In particular, we show that the joint patterns extracted via iPCA are highly predictive of a patient's cognition and Alzheimer's diagnosis.
Adversarial Soft-detection-based Aggregation Network for Image Retrieval

In recent year, the compact representations based on activations of Convolutional Neural Network (CNN) achieve remarkable performance in image retrieval. However, retrieval of some interested object that only takes up a small part of the whole image is still a challenging problem. Therefore, it is significant to extract the discriminative representations that contain regional information of the pivotal small object. In this paper, we propose a novel adversarial soft-detection-based aggregation (ASDA) method free from bounding box annotations for image retrieval, based on adversarial detector and soft region proposal layer. Our trainable adversarial detector generates semantic maps based on adversarial erasing strategy to preserve more discriminative and detailed information. Computed based on semantic maps corresponding to various discriminative patterns and semantic contents, our soft region proposal is arbitrary shape rather than only rectangle and it reflects the significance of objects. The aggregation based on trainable soft region proposal highlights discriminative semantic contents and suppresses the noise of background. We conduct comprehensive experiments on standard image retrieval datasets. Our weakly supervised ASDA method achieves state-of-the-art performance on most datasets. The results demonstrate that the proposed ASDA method is effective for image retrieval.
The effect of a Durbin–Watson pretest on confidence intervals in regression

Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin–Watson pretest of the null hypothesis of zero first‐order autocorrelation of the random errors against the alternative hypothesis of positive first‐order autocorrelation. If this null hypothesis is accepted then the confidence interval centered on the ordinary least squares estimator is used; otherwise the confidence interval centered on the feasible generalized least squares estimator is used. For any given design matrix and parameter of interest, we compare the confidence interval resulting from this two‐stage procedure and the confidence interval that is always centered on the feasible generalized least squares estimator, as follows. First, we compare the coverage probability functions of these confidence intervals. Second, we compute the scaled expected length of the confidence interval resulting from the two‐stage procedure, where the scaling is with respect to the expected length of the confidence interval centered on the feasible generalized least squares estimator, with the same minimum coverage probability. These comparisons are used to choose the better confidence interval, prior to any examination of the observed response vector.
The distances to star clusters hosting Red Supergiants: χ Per, NGC 7419, and Westerlund 1

Galactic, young massive star clusters are approximately coeval aggregates of stars, close enough to resolve the individual stars, massive enough to have produced large numbers of massive stars, and young enough for these stars to be in a pre-supernova state. As such these objects represent powerful natural laboratories in which to study the evolution of massive stars. To be used in this way, it is crucial that accurate and precise distances are known, since this affects both the inferred luminosities of the cluster members and the age estimate for the cluster itself. Here we present distance estimates for three star clusters rich in Red Supergiants ($\chi$ Per, NGC 7419 and Westerlund 1) based on their average astrometric parallaxes $\bar{\pi}$ in Gaia Data Release 2, where the measurement of $\bar{\pi}$ is obtained from a proper-motion screened sample of spectroscopically-confirmed cluster members. We determine distances of $d=2.25^{+0.16}_{-0.14}$kpc, $d=3.00^{+0.35}_{-0.29}$kpc, and $d=3.87^{+0.95}_{-0.64}$kpc for the three clusters respectively. We find that the dominant source of error is that in Gaia's zero-point parallax offset $\pi_{\rm ZP}$, and we argue that more precise distances cannot be determined without an improved characterization of this quantity.
Estimating Individualized Decision Rules with Tail Controls

With the emergence of precision medicine, estimating optimal individualized decision rules (IDRs) has attracted tremendous attentions in many scientific areas. Most existing literature has focused on finding optimal IDRs that can maximize the expected outcome for each individual. Motivated by complex individualized decision making procedures and popular conditional value at risk (CVaR) measures, we propose two new robust criteria to estimate optimal IDRs: one is to control the average lower tail of the subjects' outcomes and the other is to control the individualized lower tail of each subject's outcome. In addition to optimizing the individualized expected outcome, our proposed criteria take risks into consideration, and thus the resulting IDRs can prevent adverse events caused by the heavy lower tail of the outcome distribution. Interestingly, from the perspective of duality theory, the optimal IDR under our criteria can be interpreted as the decision rule that maximizes the "worst-case" scenario of the individualized outcome within a probability constrained set. The corresponding estimating procedures are implemented using two proposed efficient non-convex optimization algorithms, which are based on the recent developments of difference-of-convex (DC) and majorization-minimization (MM) algorithms that can be shown to converge to the sharpest stationary points of the criteria. We provide a comprehensive statistical analysis for our estimated optimal IDRs under the proposed criteria such as consistency and finite sample error bounds. Simulation studies and a real data application are used to further demonstrate the robust performance of our methods.
Modeling Frequency and Severity of Claims with the Zero-Inflated Generalized Cluster-Weighted Models

In this paper, we propose two important extensions to cluster-weighted models (CWMs). First, we extend CWMs to have generalized cluster-weighted models (GCWMs) by allowing modeling of non-Gaussian distribution of the continuous covariates, as they frequently occur in insurance practice. Secondly, we introduce a zero-inflated extension of GCWM (ZI-GCWM) for modeling insurance claims data with excess zeros coming from heterogenous sources. Additionally, we give two expectation-optimization (EM) algorithms for parameter estimation given the proposed models. An appropriate simulation study shows that, for various settings and in contrast to the existing mixture-based approaches, both extended models perform well. Finally, a real data set based on French auto-mobile policies is used to illustrate the application of the proposed extensions.
Measuring Diffusion over a Large Network

This paper introduces a measure of the diffusion of binary outcomes over a large, sparse network, when the diffusion is observed in two time periods. The measure captures the aggregated spillover effect of the state-switches in the initial period on their neighbors’ outcomes in the second period. This paper introduces a causal network that captures the causal connections among the cross-sectional units over the two periods. It shows that when the researcher's observed network contains the causal network as a subgraph, the measure of diffusion is identified as a simple, spatio-temporal dependence measure of observed outcomes. When the observed network does not satisfy this condition, but the spillover effect is nonnegative, the spatio-temporal dependence measure serves as a lower bound for diffusion. Using this, a lower confidence bound for diffusion is proposed and its asymptotic validity is established. The Monte Carlo simulation studies demonstrate the finite sample stability of the inference across a range of network configurations. The paper applies the method to data on Indian villages to measure the diffusion of microfinancing decisions over households’ social networks.
Distributed inference for quantile regression processes

The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big data, we propose a two-step procedure: (i) estimate conditional quantile functions at different levels in a parallel computing environment; (ii) construct a conditional quantile regression process through projection based on these estimated quantile curves. Our general quantile regression framework covers both linear models with fixed or growing dimension and series approximation models. We prove that the proposed procedure does not sacrifice any statistical inferential accuracy provided that the number of distributed computing units and quantile levels are chosen properly. In particular, a sharp upper bound for the former and a sharp lower bound for the latter are derived to capture the minimal computational cost from a statistical perspective. As an important application, the statistical inference on conditional distribution functions is considered. Moreover, we propose computationally efficient approaches to conducting inference in the distributed estimation setting described above. Those approaches directly utilize the availability of estimators from sub-samples and can be carried out at almost no additional computational cost. Simulations confirm our statistical inferential theory.
Quantile Regression Modeling of Recurrent Event Risk

Progression of chronic disease is often manifested by repeated occurrences of disease-related events over time. Delineating the heterogeneity in the risk of such recurrent events can provide valuable scientific insight for guiding customized disease management. In this paper, we present a new modeling framework for recurrent event data, which renders a flexible and robust characterization of individual multiplicative risk of recurrent event through quantile regression that accommodates both observed covariates and unobservable frailty. The proposed modeling requires no distributional specification of the unobservable frailty, while permitting the exploration of dynamic covariate effects. We develop estimation and inference procedures for the proposed model through a novel adaptation of the principle of conditional score. The asymptotic properties of the proposed estimator, including the uniform consistency and weak convergence, are established. Extensive simulation studies demonstrate satisfactory finite-sample performance of the proposed method. We illustrate the practical utility of the new method via an application to a diabetes clinical trial that explores the risk patterns of hypoglycemia in Type 2 diabetes patients.
Cross-Component Registration for Multivariate Functional Data with Application to Longitudinal Growth Curves

Multivariate functional data are becoming ubiquitous with the advance of modern technology. Multivariate functional data are substantially more complex than univariate functional data. In particular, we study a novel model for multivariate functional data where the component processes exhibit mutual time warping. That is, the component processes exhibit a similar shape but are subject to time warping across their domains. To address this previously unconsidered mode of warping, we propose new registration methodology which is based on a shift-warping model. Our method differs from existing registration methods in several major ways. Namely, instead of focusing on individual-specific registration, we focus on registering across components on a population-wide level. By doing so our proposed estimates for these shifts enjoy parametric rates of convergence and often have intuitive physical interpretations. We exemplify these interpretations by applying our methodology to the Zurich Longitudinal Growth data. We also demonstrate the conditions under which our methodology works via simulation.
Model reparametrization for improving variational inference

In this article, we propose a strategy to improve variational Bayes inference for a class of models whose variables can be classified as global (common across all observations) or local (observation specific) by using a model reparametrization. In particular, an invertible affine transformation is applied on the local variables so that their posterior dependency on the global variables is minimized. The functional form of this transformation is deduced by approximating the conditional posterior distribution of each local variable given the global variables by a Gaussian distribution via a second order Taylor expansion. Variational inference for the reparametrized model is then obtained using stochastic approximation techniques. Our approach can be readily extended to large datasets via a divide and recombine strategy. Application of the methods is illustrated using generalized linear mixed models.
Relevant change points in high dimensional time series

This paper investigates the problem of detecting relevant change points in the mean vector, say $\mu_t =(\mu_{1,t},\ldots ,\mu_{d,t})^T$ of a high dimensional time series $(Z_t)_{t\in \mathbb{Z}}$. While the recent literature on testing for change points in this context considers hypotheses for the equality of the means $\mu_h^{(1)}$ and $\mu_h^{(2)}$ before and after the change points in the different components, we are interested in a null hypothesis of the form $$ H_0: |\mu^{(1)}_{h} - \mu^{(2)}_{h} | \leq \Delta_h ~~~\mbox{ for all } ~~h=1,\ldots ,d $$ where $\Delta_1, \ldots , \Delta_d$ are given thresholds for which a smaller difference of the means in the $h$-th component is considered to be non-relevant. We propose a new test for this problem based on the maximum of squared and integrated CUSUM statistics and investigate its properties as the sample size $n$ and the dimension $d$ both converge to infinity. In particular, using Gaussian approximations for the maximum of a large number of dependent random variables, we show that on certain points of the boundary of the null hypothesis a standardised version of the maximum converges weakly to a Gumbel distribution.
Estimating the Probability that a Function Observed with Noise Is Convex

Consider a real-valued function that can only be observed with stochastic simulation noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function values at the design points. We develop an asymptotically consistent Bayesian sequential sampling procedure that estimates the posterior probability of this being true. In each iteration, the posterior probability is estimated using Monte Carlo simulation. We offer three variance reduction methods -- change of measure, acceptance-rejection, and conditional Monte Carlo. Numerical experiments suggest that the conditional Monte Carlo method should be preferred.
A maximum-mean-discrepancy goodness-of-fit test for censored data

We introduce a kernel-based goodness-of-fit test for censored data, where observations may be missing in random time intervals: a common occurrence in clinical trials and industrial life-testing. The test statistic is straightforward to compute, as is the test threshold, and we establish consistency under the null. Unlike earlier approaches such as the Log-rank test, we make no assumptions as to how the data distribution might differ from the null, and our test has power against a very rich class of alternatives. In experiments, our test outperforms competing approaches for periodic and Weibull hazard functions (where risks are time dependent), and does not show the failure modes of tests that rely on user-defined features. Moreover, in cases where classical tests are provably most powerful, our test performs almost as well, while being more general.
Bias-Aware Confidence Intervals for Empirical Bayes Analysis

In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of when and why empirical Bayes point estimates accurately recover oracle Bayes behavior. In this paper, we develop confidence intervals that provide asymptotic frequentist coverage of empirical Bayes estimands. Our intervals include an honest assessment of bias even in situations where empirical Bayes point estimates may converge very slowly. Applied to multiple testing situations, our approach provides flexible and practical confidence statements about the local false sign rate. As an intermediate step in our approach, we develop methods for inference about linear functionals of the effect size distribution in the Bayes deconvolution problem that may be of independent interest.
Uniform estimation of a class of random graph functionals

We consider estimation of certain functionals of random graphs. The random graph is generated by a stochastic block model (SBM). The number of classes is fixed or grows with the number of vertices. Minimax lower and upper bounds of estimation along specific submodels are derived. The results are nonasymptotic and imply that uniform estimation of a single connectivity parameter is much slower than the expected asymptotic pointwise rate. Specifically, the uniform quadratic rate does not scale as the number of edges, but only as the number of vertices. The lower bounds are local around any possible SBM. An analogous result is derived for functionals of a class of smooth graphons.
SMARTp: A SMART design for nonsurgical treatments of chronic periodontitis with spatially referenced and nonrandomly missing skewed outcomes

This paper proposes dynamic treatment regimes (DTRs) as effective individualized treatment strategies for managing chronic periodontitis. The proposed DTRs are studied via SMARTp—a two‐stage sequential multiple assignment randomized trial (SMART) design. For this design, we propose a statistical analysis plan and a novel cluster‐level sample size calculation method that factors in typical features of periodontal responses such as non‐Gaussianity, spatial clustering, and nonrandom missingness. Here, each patient is viewed as a cluster, and a tooth within a patient's mouth is viewed as an individual unit inside the cluster, with the tooth‐level covariance structure described by a conditionally autoregressive structure. To accommodate possible skewness and tail behavior, the tooth‐level clinical attachment level (CAL) response is assumed to be skew‐t, with the nonrandomly missing structure captured via a shared parameter model corresponding to the missingness indicator. The proposed method considers mean comparison for the regimes with or without sharing an initial treatment, where the expected values and corresponding variances or covariance for the sample means of a pair of DTRs are derived by the inverse probability weighting and method of moments. Simulation studies are conducted to investigate the finite‐sample performance of the proposed sample size formulas under a variety of outcome‐generating scenarios. An R package SMARTp implementing our sample size formula is available at the Comprehensive R Archive Network for free download.