Miracle-dz/UniFAR-FTUs huggingface dataset:
On spike and slab empirical Bayes multiple testing

This paper explores a connection between empirical Bayes posterior distributions and false discovery rate (FDR) control. In the Gaussian sequence model, this work shows that empirical Bayes-calibrated spike and slab posterior distributions allow a correct FDR control under sparsity. Doing so, it offers a frequentist theoretical validation of empirical Bayes methods in the context of multiple testing. Our theoretical results are illustrated with numerical experiments.
Max‐infinitely divisible models and inference for spatial extremes

For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max‐stable models are inadequate to capture the rate of joint tail decay, and to estimate joint extremal probabilities beyond observed levels. We here develop a more flexible modeling framework based on the class of max‐infinitely divisible processes, which extend max‐stable processes while retaining dependence properties that are natural for maxima. We propose two parametric constructions for max‐infinitely divisible models, which relax the max‐stability property but remain close to some popular max‐stable models obtained as special cases. The first model considers maxima over a finite, random number of independent observations, while the second model generalizes the spectral representation of max‐stable processes. Inference is performed using a pairwise likelihood. We illustrate the benefits of our new modeling framework on Dutch wind gust maxima calculated over different time units. Results strongly suggest that our proposed models outperform other natural models, such as the Student‐t copula process and its max‐stable limit, even for large block sizes.
Pivotal Estimation Via Self-Normalization for High-Dimensional Linear Models with Errors in Variables

We propose a new estimator for the high-dimensional linear regression model with measurement error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the choice of penalty parameters is pivotal. The estimator is based on applying a self-normalization to the constraints that characterize the estimator. Importantly, we show how to cast the computation of the estimator as the solution of a convex program with second order cone constraints. This allows the use of algorithms with theoretical guarantees and enables reliable implementation. Under sparsity assumptions, we derive lq-rates of convergence and show that consistency can be achieved even if the number of regressors exceeds the sample size. We further provide a simple thresholded estimator that yields a provably sparse estimator with similar l2 and l1-rates of convergence.
Gaussian Processes for Individualized Continuous Treatment Rule Estimation

Individualized treatment rule (ITR) recommends treatment on the basis of individual patient characteristics and the previous history of applied treatments and their outcomes. Despite the fact there are many ways to estimate ITR with binary treatment, algorithms for continuous treatment have only just started to emerge. We propose a novel approach to continuous ITR estimation based on explicit modelling of uncertainty in the subject's outcome as well as direct estimation of the mean outcome using gaussian process regression. Our method incorporates two intuitively appealing properties - it is more inclined to give a treatment with the outcome of higher expected value and lower variance. Experiments show that this direct incorporation of the uncertainty into ITR estimation process allows to select better treatment than standard indirect approach that just models the average. Compared to the competitors (including OWL), the proposed method shows improved performance in terms of value function maximization, has better interpretability, and could be easier generalized to multiple interdependent continuous treatments setting.
“Robust-Squared” Imputation Models Using Bart

Examples of “doubly robust” estimators for missing data include augmented inverse probability weighting (AIPWT) and penalized splines of propensity prediction (PSPP). Doubly robust estimators have the property that, if either the response propensity or the mean is modeled correctly, a consistent estimator of the population mean is obtained. However, doubly robust estimators can perform poorly when modest misspecification is present in both models. Here we consider extensions of the AIPWT and PSPP that use Bayesian additive regression trees (BART) to provide highly robust propensity and mean model estimation. We term these “robust-squared” in the sense that the propensity score, the means, or both can be estimated with minimal model misspecification, and applied to the doubly robust estimator. We consider their behavior via simulations where propensities and/or mean models are misspecified. We apply our proposed method to impute missing instantaneous velocity (delta-v) values from the 2014 National Automotive Sampling System Crashworthiness Data System dataset and missing Blood Alcohol Concentration values from the 2015 Fatality Analysis Reporting System dataset. We found that BART, applied to PSPP and AIPWT, provides a more robust estimate compared with PSPP and AIPWT.
Greater Data Science at Baccalaureate Institutions

Donoho's JCGS (in press) paper is a spirited call to action for statisticians, who he points out are losing ground in the field of data science by refusing to accept that data science is its own domain. (Or, at least, a domain that is becoming distinctly defined.) He calls on writings by John Tukey, Bill Cleveland, and Leo Breiman, among others, to remind us that statisticians have been dealing with data science for years, and encourages acceptance of the direction of the field while also ensuring that statistics is tightly integrated. As faculty at baccalaureate institutions (where the growth of undergraduate statistics programs has been dramatic), we are keen to ensure statistics has a place in data science and data science education. In his paper, Donoho is primarily focused on graduate education. At our undergraduate institutions, we are considering many of the same questions.
Sample size determination in superiority or non-inferiority clinical trials with time-to-event data under exponential, Weibull and Gompertz distributions

Abstract To examine the effect of exponential, Weibull and Gompertz distributions on sample size determination for superiority trials (STs) or non-inferiority trials (NTs) with time-to-event data based on proportional hazard model, we present two sample size formulas for STs or NTs based on Weibull and Gompertz distributions, respectively. The formulas are compared with the current exponential formula to examine their performance. The simulation results show that the sample size formula based on the Weibull distribution is the most robust among the three formulas in STs or NTs. We suggest that recognizing the appropriate distribution in advance is beneficial for proper project planning and that assuming a Weibull distributed survival time is most advantageous in STs or NTs.
On Noisy Negative Curvature Descent: Competing with Gradient Descent for Faster Non-convex Optimization

The Hessian-vector product has been utilized to find a second-order stationary solution with strong complexity guarantee (e.g., almost linear time complexity in the problem's dimensionality). In this paper, we propose to further reduce the number of Hessian-vector products for faster non-convex optimization. Previous algorithms need to approximate the smallest eigen-value with a sufficient precision (e.g., $\epsilon_2\ll 1$) in order to achieve a sufficiently accurate second-order stationary solution (i.e., $\lambda_{\min}(\nabla^2 f(\x))\geq -\epsilon_2)$. In contrast, the proposed algorithms only need to compute the smallest eigen-vector approximating the corresponding eigen-value up to a small power of current gradient's norm. As a result, it can dramatically reduce the number of Hessian-vector products during the course of optimization before reaching first-order stationary points (e.g., saddle points). The key building block of the proposed algorithms is a novel updating step named the NCG step, which lets a noisy negative curvature descent compete with the gradient descent. We show that the worst-case time complexity of the proposed algorithms with their favorable prescribed accuracy requirements can match the best in literature for achieving a second-order stationary point but with an arguably smaller per-iteration cost. We also show that the proposed algorithms can benefit from inexact Hessian by developing their variants accepting inexact Hessian under a mild condition for achieving the same goal. Moreover, we develop a stochastic algorithm for a finite or infinite sum non-convex optimization problem. To the best of our knowledge, the proposed stochastic algorithm is the first one that converges to a second-order stationary point in {\it high probability} with a time complexity independent of the sample size and almost linear in dimensionality.
Region-Referenced Spectral Power Dynamics of EEG Signals: A Hierarchical Modeling Approach

Functional brain imaging through electroencephalography (EEG) relies upon the analysis and interpretation of high-dimensional, spatially organized time series. We propose to represent time-localized frequency domain characterizations of EEG data as region-referenced functional data. This representation is coupled with a hierarchical modeling approach to multivariate functional observations. Within this familiar setting, we discuss how several prior models relate to structural assumptions about multivariate covariance operators. An overarching modeling framework, based on infinite factorial decompositions, is finally proposed to balance flexibility and efficiency in estimation. The motivating application stems from a study of implicit auditory learning, in which typically developing (TD) children, and children with autism spectrum disorder (ASD) were exposed to a continuous speech stream. Using the proposed model, we examine differential band power dynamics as brain function is interrogated throughout the duration of a computer-controlled experiment. Our work offers a novel look at previous findings in psychiatry, and provides further insights into the understanding of ASD. Our approach to inference is fully Bayesian and implemented in a highly optimized Rcpp package.
Structured Shrinkage Priors

In many regression settings the unknown coefficients may have some known structure, for instance they may be ordered in space or correspond to a vectorized matrix or tensor. At the same time, the unknown coefficients may be sparse, with many nearly or exactly equal to zero. However, many commonly used priors and corresponding penalties for coefficients do not encourage simultaneously structured and sparse estimates. In this paper we develop structured shrinkage priors that generalize multivariate normal, Laplace, exponential power and normal-gamma priors. These priors allow the regression coefficients to be correlated a priori without sacrificing elementwise sparsity or shrinkage. The primary challenges in working with these structured shrinkage priors are computational, as the corresponding penalties are intractable integrals and the full conditional distributions that are needed to approximate the posterior mode or simulate from the posterior distribution may be non-standard. We overcome these issues using a flexible elliptical slice sampling procedure, and demonstrate that these priors can be used to introduce structure while preserving sparsity of the corresponding penalized estimate given by the posterior mode.
Self-testing of unsharp measurements

We consider unsharp quantum measurements as a recourse in scenarios where one faces the trade-off between information gain and disturbance. We analyse in detail the case of two-outcome qubit measurements and show that generalized measurements allow for a strict advantage over their probabilistic realization with projective measurements. Based on that, we propose a scheme for self-testing of unsharp measurements and show that all binary qubit measurements can be self-tested in a robust way. We apply our results to the analysis of semi-device-independent one-way quantum key distribution and present new monogamy relations for guessing probabilities of the receiver and the eavesdropper for the case of individual attacks. In particular, we find the exact threshold on the critical guessing probability of the receiver for which the security can be still proven.
Variance Reduced Methods for Non-Convex Composition Optimization

This paper explores the non-convex composition optimization consisting of inner and outer finite-sum functions with a large number of component functions. This problem arises in important applications such as nonlinear embedding and reinforcement learning. Although existing approaches such as stochastic gradient descent (SGD) and stochastic variance reduced gradient (SVRG) descent can be applied to solve this problem, their query complexities tend to be high, especially when the number of inner component functions is large. Therefore, to significantly improve the query complexity of current approaches, we have devised the stochastic composition via variance reduction (SCVR). What's more, we analyze the query complexity under different numbers of inner function and outer function. Based on different kinds of estimation of inner component function, we also present the SCVRII algorithm, though the order of query complexities are the same with SCVR. Additionally, we propose an extension to handle the mini-batch cases, which improve the query complexity under the optimal mini-batch size. The experimental results validate our proposed algorithms and theoretical analyses.
Impact of Inter-Country Distances on International Tourism

Tourism is a worldwide practice with international tourism revenues increasing from US\$495 billion in 2000 to US\$1340 billion in 2017. Its relevance to the economy of many countries is obvious. Even though the World Airline Network (WAN) is global and has a peculiar construction, the International Tourism Network (ITN) is very similar to a random network and barely global in its reach. To understand the impact of global distances on local flows, we map the flow of tourists around the world onto a complex network and study its topological and dynamical balance. We find that although the WAN serves as infrastructural support for the ITN, the flow of tourism does not correlate strongly with the extent of flight connections worldwide. Instead, unidirectional flows appear locally forming communities that shed light on global travelling behaviour inasmuch as there is only a 15% probability of finding bidirectional tourism between a pair of countries. We conjecture that this is a consequence of one-way cyclic tourism by analyzing the triangles that are formed by the network of flows in the ITN. Finally, we find that most tourists travel to neighbouring countries and mainly cover larger distances when there is a direct flight, irrespective of the time it takes.
Reallocating and Resampling: A Comparison for Inference

Simulation-based inference plays a major role in modern statistics, and often employs either reallocating (as in a randomization test) or resampling (as in bootstrapping). Reallocating mimics random allocation to treatment groups, while resampling mimics random sampling from a larger population; does it matter whether the simulation method matches the data collection method? Moreover, do the results differ for testing versus estimation? Here we answer these questions in a simple setting by exploring the distribution of a sample difference in means under a basic two group design and four different scenarios: true random allocation, true random sampling, reallocating, and resampling. For testing a sharp null hypothesis, reallocating is superior in small samples, but reallocating and resampling are asymptotically equivalent. For estimation, resampling is generally superior, unless the effect is truly additive. Moreover, these results hold regardless of whether the data were collected by random sampling or random allocation.
Cytometry inference through adaptive atomic deconvolution

ABSTRACT In this paper, we consider a statistical estimation problem known as atomic deconvolution. Introduced in reliability, this model has a direct application when considering biological data produced by flow cytometers. From a statistical point of view, we aim at inferring the percentage of cells expressing the selected molecule and the probability distribution function associated with its fluorescence emission. We propose here an adaptive estimation procedure based on a previous deconvolution procedure introduced by Es, Gugushvili, and Spreij [(2008), ‘Deconvolution for an atomic distribution’, Electronic Journal of Statistics, 2, 265–297] and Gugushvili, Es, and Spreij [(2011), ‘Deconvolution for an atomic distribution: rates of convergence’, Journal of Nonparametric Statistics, 23, 1003–1029]. For both estimating the mixing parameter and the mixing density automatically, we use the Lepskii method based on the optimal choice of a bandwidth using a bias-variance decomposition. We then derive some convergence rates that are shown to be minimax optimal (up to some log terms) in Sobolev classes. Finally, we apply our algorithm on the simulated and real biological data.
Maximum likelihood estimation of the Latent Class Model through model boundary decomposition

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of the latent class model in order to understand the behavior of the maximum likelihood estimator. In particular, we characterize the boundary stratification of the binary latent class model with a binary hidden variable. For small models, such as for three binary observed variables, we show that this stratification allows exact computation of the maximum likelihood estimator. In this case we use simulations to study the maximum likelihood estimation attraction basins of the various strata. Our theoretical study is complemented with a careful analysis of the EM fixed point ideal which provides an alternative method of studying the boundary stratification and maximizing the likelihood function. In particular, we compute the minimal primes of this ideal in the case of a binary latent class model with a binary or ternary hidden random variable.
Overpruning in Variational Bayesian Neural Networks

The motivations for using variational inference (VI) in neural networks differ significantly from those in latent variable models. This has a counter-intuitive consequence; more expressive variational approximations can provide significantly worse predictions as compared to those with less expressive families. In this work we make two contributions. First, we identify a cause of this performance gap, variational over-pruning. Second, we introduce a theoretically grounded explanation for this phenomenon. Our perspective sheds light on several related published results and provides intuition into the design of effective variational approximations of neural networks.
A sharp oracle inequality for Graph-Slope

Following recent success on the analysis of the Slope estimator, we provide a sharp oracle inequality in term of prediction error for Graph-Slope, a generalization of Slope to signals observed over a graph. In addition to improving upon best results obtained so far for the Total Variation denoiser (also referred to as Graph-Lasso or Generalized Lasso), we propose an efficient algorithm to compute Graph-Slope. The proposed algorithm is obtained by applying the forward-backward method to the dual formulation of the Graph-Slope optimization problem. We also provide experiments showing the interest of the method.
A Spatio-Temporal Modeling Approach for Weather Radar Reflectivity Data and Its Applications in Tropical Southeast Asia

Weather radar echoes, correlated in both space and time, are the most important input data for short-term precipitation forecast. Motivated by real datasets, this paper is concerned with the spatio-temporal modeling of two-dimensional radar reflectivity fields from a sequence of radar images. Under a Lagrangian integration scheme, we model the radar reflectivity data by a spatio-temporal conditional autoregressive process which is driven by two hidden sub-processes. The first sub-process is the dynamic velocity field which determines the motion of the weather system, while the second sub-process governs the growth or decay of the strength of radar reflectivity. The proposed method is demonstrated, and compared with existing methods, using the real radar data collected from the tropical southeast Asia. Note that, since the tropical storms are known to be highly chaotic and extremely difficult to be predicted, we only focus on the modeling of reflectivity data within a short-period of time and consider the short-term prediction problem based on the proposed model. This is often referred to as the nowcasting issue in the meteorology society.
Optimal rates for community estimation in the weighted stochastic block model

Community identification in a network is an important problem in fields such as social science, neuroscience, and genetics. Over the past decade, stochastic block models (SBMs) have emerged as a popular statistical framework for this problem. However, SBMs have an important limitation in that they are suited only for networks with unweighted edges; in various scientific applications, disregarding the edge weights may result in a loss of valuable information. We study a weighted generalization of the SBM, in which observations are collected in the form of a weighted adjacency matrix and the weight of each edge is generated independently from an unknown probability density determined by the community membership of its endpoints. We characterize the optimal rate of misclustering error of the weighted SBM in terms of the Renyi divergence of order 1/2 between the weight distributions of within-community and between-community edges, substantially generalizing existing results for unweighted SBMs. Furthermore, we present a computationally tractable algorithm based on discretization that achieves the optimal error rate. Our method is adaptive in the sense that the algorithm, without assuming knowledge of the weight densities, performs as well as the best algorithm that knows the weight densities.