The Mixture-of-Experts (MoE) paradigm attempts to learn complex models by combining several “experts” via probabilistic mixture models. Each expert in the MoE model handles a small area of the data space in which a gating function controls the data-to-expert assignment. The MoE framework has been used extensively in designing nonlinear models in machine learning and statistics to model the heterogeneity

The estimation of the average treatment effect on the treated (ATT) plays an essential role when the effect of an intervention or a treatment on those participants who actually received it is focused. However, the validity of conventional estimation methods relies on the precise measurement of variables. Misclassified category outcome variable may cause non-negligible bias when estimating ATT. In this

Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering algorithm to the resulting altered dataset. Here, we develop clustering methodology through a model-based approach using the marginal density for the observed values, assuming

The Stein paradox has played an influential role in the field of high dimensional statistics. This result warns that the sample mean, classically regarded as the “usual estimator”, may be suboptimal in high dimensions. The development of the James-Stein estimator, that addresses this paradox, has by now inspired a large literature on the theme of “shrinkage” in statistics. In this direction, we develop

In this paper, an F-type test is proposed for the functional association between a functional covariate and a scalar response in functional linear models (FLM). The proposed F test is based on the order statistics of functional principal components (fPCs), which is motivated by the phenomena that the power of the classical F test is sensitive to the choice of thresholds. Theoretical properties of the

Many machine learning models have tuning parameters to be determined by the training data, and cross-validation (CV) is perhaps the most commonly used method for selecting tuning parameters. This work concerns the problem of estimating the generalization error of a CV-tuned predictive model. We propose to use an honest leave-one-out cross-validation framework to produce a nearly unbiased estimator

In this short note, we prove an asymptotic expansion for the ratio of the Dirichlet density to the multivariate normal density with the same mean and covariance matrix. The expansion is then used to derive an upper bound on the total variation between the corresponding probability measures and rederive the asymptotic variance of the Dirichlet kernel estimators introduced by Aitchison and Lauder (1985)

Building efficient sampling procedures to provide more accurate results with smaller sample size is one of the main goals in sampling surveys. Ranked Set Sampling (RSS) is a well-known procedure for selecting representative samples and improving parametric estimation by employing ranking on observations. In order to have a more efficient sampling procedure, new sampling procedures are proposed and

With the rapid advancement of biotechnology, there arise new challenges to discover regulatory and co-action relationships among heterogeneous biological features as well as to capture significant topological changes when data is observed across time. This paper is devoted to joint structural estimation of time-varying mixed graphical models based on multivariate data over a series of time points.

Network clustering is a fundamental task that discovers innate communities or groups in networks. Hence, network clustering methods such as spectral clustering and regularized spectral clustering have been applied in a wide range of realms. On top of a network structure, it is known in social network analysis that incorporating information from each vertex can be beneficial. This has led to development

A correctly specified working correlation structure ensures the efficiency in inferences for marginal regressions based on estimating equations. When there are measurement errors in covariates, however, correct specification of working correlation structure may lead to more severe bias and higher mean squared error than working independence. We report this lesser-known phenomenon and explain it in

Longitudinal data on patient reported outcomes (PROs), such as quality of life of patients, are frequently collected in clinical trials and other medical studies. Joint analysis of these data with survival times may improve the accuracy of statistical inferences, especially when PRO measurements may be missing after the death of patients. Classical linear mixed models are often used as the models for

Locally stationary time series is frequently appeared in the fields of finance and environmental science, such as daily air pollutants concentration or financial returns, but how to construct the multi-step-ahead prediction interval for such time series remains an open question. We handle this issue by extending the nonparametric regression model with auto-regressive errors for equally spaced design

The coronavirus disease 2019 (COVID-19) pandemic has led to tremendous loss of human life and has severe social and economic impacts worldwide. The spread of the disease has also caused dramatic uncertainty in financial markets, especially in the early stages of the pandemic. In this paper, we adopt the stochastic actor-oriented model (SAOM) to model dynamic/longitudinal financial networks with the

The receiver operator characteristic (ROC) curve is one of the most popular tools to evaluate the performance of binary classifiers in a variety of applications. Rakotomamonjy (2004) proposed the ROC-SVM that directly optimizes the area under the ROC curve instead of the prediction accuracy. In this article, we study the L1-penalized ROC-SVM that directly optimizes the ROC curve. We first show that

In this paper, the composite hypothesis that lifetimes follow an exponential distribution is tested based on observed randomly right censored data. Testing this hypothesis is complicated by the presence of this censoring, due to the fact that not all lifetimes are observed. To account for this complication, we propose modifications to tests based on the empirical characteristic function and Laplace

We consider the problem of recovering a subhypergraph based on an observed adjacency tensor corresponding to a uniform hypergraph. The uniform hypergraph is assumed to contain a subset of vertices called as subhypergraph. The edges restricted to the subhypergraph are assumed to follow a different probability distribution than other edges. We consider both weak recovery and exact recovery of the subhypergraph

Mapper is a popular topological data analysis method to analyse structure of complex high-dimensional data sets. As the Mapper algorithm can be applied to clustering and feature selection with visualization, it is used in various fields such as biology and chemistry. However, some resolution parameters have to be chosen by the user before applying the Mapper algorithm, and the results are sensitive

We propose a new low-dimensional registration procedure that exploits the relationship between the response and the predictor in a function-on-function regression. In this context, functional covariance components (FCCs) provide a flexible and powerful tool to represent the data in a low-dimensional space, capturing the most meaningful modes of dependency between the two set of curves. Based on this

In this paper, a hidden Markov model for modelling matrix-variate time series data is developed. It relies on matrix-variate distribution and presents a promising alternative to the existing methods. Simulation study is carefully conducted and uses benchmark tests with pre-specified overlapping values. Compared with the existing methods, the proposed model demonstrates rather high accuracy in state

Point processes are popular models for data consisting of a random configuration of points, such as positions of trees of a given species in a forest stand, locations of earthquakes' epicentres or positions of proteins in a cell membrane. Pair correlation function is a functional summary characteristic quantifying the interactions between pairs of points of the process at different distances. In practice

Accelerated life test is currently the main method of assessing product reliability rapidly, and the design of efficient test plans is a critical step to ensure that accelerated life tests can assess the product reliability accurately, quickly and economically. In these tests, the samples are tested at stress levels higher than normal. Then, the product life at the normal stress level can be estimated

Recent advances in information technology have led to the appearance of high-dimensional and complex data sets which necessitates in-depth investigation on high-dimensional data analysis and modelling. The current study introduces five approaches to fit a functional linear regression model on interval-valued functional data. The proposed approaches are based on the functional linear regression models

In this work, we propose a deep neural networks-based method to perform non-parametric regression for functional data. The proposed estimators are based on sparsely connected deep neural networks with rectifier linear unit (ReLU) activation function. We provide the convergence rate of the proposed deep neural networks estimator in terms of the empirical norm. Through Monte Carlo simulation studies

Personalized optimal decision making, finding the optimal decision rule (ODR) based on individual characteristics, has attracted increasing attention recently in many fields, such as education, economics, and medicine. Current ODR methods usually require the primary outcome of interest in samples for assessing treatment effects, namely, the experimental sample. However, in many studies, treatments

Empirical Bayesian analysis is a well-known approach that incorporates an estimator into a Bayesian analysis. In this article, we offer another approach, which has several useful properties. Our solution is based on the framework introduced by Yekutieli (2012) to account for the variability introduced by selecting parameters. Specifically, we assume that the unknown parameter is contained within a

This paper studies the problem of classifying longitudinal structural brain networks to identify meaningful substructures and their time-varying effects. The problem is motivated by a subpopulation of healthy older adults who can maintain excellent cognitive functions across time, while others usually have cognitive decline in aging. It is of substantial scientific interest to study neurological mechanisms

In this paper, we describe a method that can be used to obtain UE(s2)-optimal two-level supersaturated designs. A major advantage of the proposed approach is the information it provides on the correlation structure of the generated UE(s2)-optimal supersaturated design and on the pairs of its orthogonal (or nearly orthogonal) columns. Therefore, it can be used to further distinguish between competitive

In this paper, we consider the problem of obtaining appropriate weights for model averaging in the face of model uncertainty and outliers. Most of the current model averaging methods are based on ordinary least squares (OLS) estimators, which are very sensitive to outliers or departures from the normality assumption on the error distribution. To overcome this problem, we propose an outlier robust Sp-type

Statistical models for extreme values are generally derived from non-degenerate probabilistic limits that can be used to approximate the distribution of events that exceed a selected high threshold. If convergence to the limit distribution is slow, then the approximation may describe observed extremes poorly, and bias can only be reduced by choosing a very high threshold at the cost of unacceptably

Our main, novel, result is that a certain non-central chi-squared mixture of non-central chi-squared distributions is itself a scaled non-central chi-squared distribution. From this and a link to a known result on a mixture representation for a scaled central chi-squared distribution, numerous further mixture results, both old and new, ensue. These include mixture results for central F, non-central

We study the effects of rounding on the moments of random variables. Specifically, given a random variable X and its rounded counterpart rd(X), we study|E[Xk]-E[rd(X)k]|for non-negative integer k. We consider the case that the rounding function rd: R → F corresponds either to (i) rounding to the nearest point in some discrete set F or (ii) rounding randomly to either the nearest larger or smaller point

Function-on-function linear regression is an essential tool in characterizing the linear relationship between a functional response and a functional predictor. However, most of the estimation methods for this model are based on the least-squares procedure, which is sensitive to atypical observations. In this paper, we present a robust method for the function-on-function linear model using M-estimation

Network data are becoming increasingly available, and so there is a need to develop a suitable methodology for statistical analysis. Networks can be represented as graph Laplacian matrices, which are a type of manifold‐valued data. Our main objective is to estimate a regression curve from a sample of graph Laplacian matrices conditional on a set of Euclidean covariates, for example, in dynamic networks

We propose a constrained minimum method for converting a hypothesis test into a model selection criterion that pursues consistency and sparsity of the selected model explicitly. The method achieves consistency by letting the significance level of the test go to zero at a certain speed depending on the sample size. It maximizes the sparsity by choosing the most sparse model among models not rejected

Sliced uniform designs are useful for generating experimental data with batch structures. In this paper, we employ the discrete discrepancy as the measure of uniformity to construct sliced uniform designs. The construction method is based on an important class of combinatorial configurations, namely, resolvable balanced incomplete block designs; hence, the construction method does not require any computer

Quantile regression estimate gives more complete information about the response distribution but is more costly to compute than mean regression. When the dimension is large, a ridge penalty is conventionally used to stabilize the estimate and achieve better bias-variance trade-off. We investigate a random projection approach to ease the computational burden and establish its statistical properties

This paper derives a criterion for deciding conditional independence that is consistent with small-sample corrections of Akaike's information criterion but is easier to apply to such problems as selecting variables in canonical correlation analysis and selecting graphical models. The criterion reduces to mutual information when the assumed distribution equals the true distribution; hence, it is called

In binary classification, class imbalance is undesirable in that it may worsen the performance of a classifier. One of the remedies to handle this problem is rebalancing with the optimal rate. Theoretical derivation of the rate is not usually considered and often empirically detected, because it is complex and depends on the classifier. To simplify this, we used a linear discriminant classifier, deriving

Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often, a few parameters are sufficient to parameterize the covariance function, and maximum likelihood (ML) methods can be used to estimate these parameters from data. ML methods, however, are computationally demanding. For example

We pursue the problem of modelling and analysing latent space dynamics in collections of networks. Towards this end, we pose and study latent space generative models for signed networks that are amenable to inference via spectral methods. Permitting signs, rather than restricting to unsigned networks, enables richer latent space structure and permissible dynamic mechanisms that can be provably inferred

Determination of optimal individual treatment rules (ITR) is a rapidly growing area in precision medicine; various parametric and non‐parametric methods have been proposed. Existing methods, however, focus on the mean outcome and thus are sensitive to outliers, skewed and heavy‐tailed outcome distributions. In this paper, we propose an optimal ITR estimation framework using a weighted classifier with

Many applications of regression study the predictors with complex forms such as tensors. Besides low dimensional assumption, the effects of predictors with a tensor structure typically show clustered or smooth phenomena in the sense that adjacent elements have a similar effect on the response. To simultaneously incorporate the low‐rank and smoothness in tensor regression, we generalize the CANDECOMP/PARAFAC

When the null hypothesis constrains parameters to the boundary of the parameter space, the asymptotic null distribution of the composite likelihood ratio statistic is often a mixture of weighted chi‐squared distributions. The mixing weights depend on the true unknown parameter and can be very difficult to calculate, except in a few special cases. We propose a Monte Carlo algorithm to estimate the mixing

Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we provide a new result on the size of the error in first- and higher-order Laplace approximations, in terms of the rate of growth of information about each of the integrated

Delayed rewards problem in contextual bandits has been of interest in various practical settings. We study randomized allocation strategies and provide an understanding on how the exploration–exploitation trade‐off is affected by delays in observing the rewards. In randomized strategies, the extent of exploration–exploitation is controlled by a user‐determined exploration probability sequence. In the

We propose a generalized non‐linear state‐space model for count‐valued time series of COVID‐19 fatalities. To capture the dynamic changes in daily COVID‐19 death counts, we specify a latent state process that involves second‐order differencing and an AR(1)‐ARCH(1) model. These modelling choices are motivated by the application and validated by model assessment. We consider and fit a progression of

Clustering with Bregman divergence has been used in literature to unify centroid‐based parametric clustering approaches and to allow the detection of nonspherical clusters within the data. Although empirically useful, the large sample theoretical aspects of Bregman clustering techniques remain largely unexplored. In this paper, we attempt to bridge the gap between the theory and practice of centroid‐based

Multi‐layer networks are often used to represent multiple types of relationships between nodes in network studies. In this paper, we investigate the community detection problem in multi‐layer networks. Specifically, we consider the multi‐layer stochastic block model (MLSBM), which assumes that the community memberships are shared across all network layers, while other model parameters can be different

We propose Dirichlet process mixture (DPM) models for prediction and cluster‐wise variable selection, based on two choices of shrinkage baseline prior distributions for the linear regression coefficients, namely, the Horseshoe prior and the Normal‐Gamma prior. We show in a simulation study that each of the two proposed DPM models tends to outperform the standard DPM model based on the non‐shrinkage

We introduce a Bayesian nonparametric regression model for data with multiway (tensor) structure, motivated by an application to periodontal disease (PD) data. Our outcome is the number of diseased sites measured over four different tooth types for each subject, with subject-specific covariates available as predictors. The outcomes are not well characterized by simple parametric models, so we use a

We study a variant of user‐item recommendation where each item has a set of attributes, such as tags on an image, user reactions to a post or foods in a meal. We focus on the latter example, with the goal of building a meal recommender for a diet tracking app. Meal recommendation is challenging: (i) each item (meal) is rarely logged by more than a handful of users, (ii) the database of attributes (foods)

In this article, we revisit the problem of how to construct better nonparametric confidence intervals for the conditional quantile function from an optimization perspective. We apply the fully data‐driven bias correction procedure based on local polynomial smoothing to estimate the conditional quantile. To account for the effect of the estimated bias, we apply an asymptotic framework that the ratio

Quantile regression has emerged as an important analytical alternative to the classical mean regression model. However, the analysis could be complicated by the presence of censored measurements due to a detection limit of equipment in combination with unavoidable missing values arising when, for instance, a researcher is simply unable to collect an observation. Another complication arises when measures

More than 720,000 patients with end‐stage renal disease in the United States require life‐sustaining dialysis treatment. In this population of typically older patients with a high morbidity burden, hospitalization is frequent at a rate of about twice per patient‐year. Aside from frequent hospitalizations, which is a major source of death risk, overall mortality in dialysis patients is higher than other

In this study, we propose a design for a control chart for the normal distribution using a modified double sampling scheme. The probability of in control, out of control, the average run length (ARL), and the standard deviation of run length (SDRL) of the proposed control chart is derived. The proposed control chart using the modified double sampling scheme is found to be more efficient in detecting

A test of the concavity of a distribution function with support contained in the unit interval may be based on a statistic constructed from the Lp-norm of the difference between an empirical distribution function and its least concave majorant. It is shown here that the uniform distribution is least favourable for such a test, in the sense that the limiting distribution of the statistic obtained under

Finite mixture models can be interpreted as a model representing heterogeneous subpopulations within the whole population. However, more care is needed when associating a mixture component with a cluster, because a mixture model may fit more components than the number of clusters. Modal merging via the mean shift algorithm can help identify such multicomponent clusters. So far, most of the related

In this paper, we propose to use sufficient dimension reduction (SDR) in conjunction with nonparametric techniques to estimate the average treatment effect on the treated (ATT), a parameter of common interest in causal inference. The proposed method is applicable under a general low‐dimensional structure in the data, and avoids both the risk of model misspecification and the “curse of dimensionality

We study the implicit bias of gradient descent methods in solving a binary classification problem over a linearly separable data set. The classifier is described by a non‐linear ReLU model and the objective function adopts the exponential loss function. We first characterize the landscape of the loss function and show that there can exist spurious asymptotic local minima besides asymptotic global minima