Miracle-dz/UniFAR-FTUs huggingface dataset:
Joint CLT for eigenvalue statistics from several dependent large dimensional sample covariance matrices with application

Let $\mathbf{X}_n=(x_{ij})$ be a $k \times n$ data matrix with complex-valued, independent and standardized entries satisfying a Lindeberg-type moment condition. We consider simultaneously $R$ sample covariance matrices $\mathbf{B}_{nr}=\frac1n \mathbf{Q}_r \mathbf{X}_n \mathbf{X}_n^*\mathbf{Q}_r^\top,~1\le r\le R$, where the $\mathbf{Q}_{r}$'s are nonrandom real matrices with common dimensions $p\times k~(k\geq p)$. Assuming that both the dimension $p$ and the sample size $n$ grow to infinity, the limiting distributions of the eigenvalues of the matrices $\{\mathbf{B}_{nr}\}$ are identified, and as the main result of the paper, we establish a joint central limit theorem for linear spectral statistics of the $R$ matrices $\{\mathbf{B}_{nr}\}$. Next, this new CLT is applied to the problem of testing a high dimensional white noise in time series modelling. In experiments the derived test has a controlled size and is significantly faster than the classical permutation test, though it does have lower power. This application highlights the necessity of such joint CLT in the presence of several dependent sample covariance matrices. In contrast, all the existing works on CLT for linear spectral statistics of large sample covariance matrices deal with a single sample covariance matrix ($R=1$).
Bayesian Sparse Global-Local Shrinkage Regression for Selection of Grouped Variables

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of attention in the problem of estimating sparse, high-dimensional linear models. This paper extends these ideas, and presents a Bayesian grouped model with continuous global-local shrinkage priors to handle complex group hierarchies that include overlapping and multilevel group structures. As the posterior mean is never a sparse estimate of the linear model coefficients, we extend the recently proposed decoupled shrinkage and selection (DSS) technique to the problem of selecting groups of variables from posterior samples. To choose a final, sparse model, we also adapt generalised information criteria approaches to the DSS framework. To ensure that sparse groups, in which only a few predictors are active, can be effectively identified, we provide an alternative degrees of freedom estimator for sparse Bayesian linear models that takes into account the effects of shrinkage on the model coefficients. Simulations and real data analysis using our proposed method show promising performance in terms of correct identification of active and inactive groups, and prediction, in comparison with a Bayesian grouped slab-and-spike approach.
A similarity measure for second order properties of non-stationary functional time series with applications to clustering and testing

Due to the surge of data storage techniques, the need for the development of appropriate techniques to identify patterns and to extract knowledge from the resulting enormous data sets, which can be viewed as collections of dependent functional data, is of increasing interest in many scientific areas. We develop a similarity measure for spectral density operators of a collection of functional time series, which is based on the aggregation of Hilbert-Schmidt differences of the individual time-varying spectral density operators. Under fairly general conditions, the asymptotic properties of the corresponding estimator are derived and asymptotic normality is established. The introduced statistic lends itself naturally to quantify (dis)-similarity between functional time series, which we subsequently exploit in order to build a spectral clustering algorithm. Our algorithm is the first of its kind in the analysis of non-stationary (functional) time series and enables to discover particular patterns by grouping together `similar' series into clusters, thereby reducing the complexity of the analysis considerably. The algorithm is simple to implement and computationally feasible. As a further application we provide a simple test for the hypothesis that the second order properties of two non-stationary functional time series coincide.
Subgroup balancing propensity score

This paper concerns estimation of subgroup treatment effects with observational data. Existing propensity score methods are mostly developed for estimating overall treatment effect. Although the true propensity scores balance covariates in any subpopulations, the estimated propensity scores may result in severe imbalance in subgroup samples. Indeed, subgroup analysis amplifies a bias-variance tradeoff, whereby increasing complexity of the propensity score model may help to achieve covariate balance within subgroups, but it also increases variance. We propose a new method, the subgroup balancing propensity score, to ensure good subgroup balance as well as to control the variance inflation. For each subgroup, the subgroup balancing propensity score chooses to use either the overall sample or the subgroup (sub)sample to estimate the propensity scores for the units within that subgroup, in order to optimize a criterion accounting for a set of covariate-balancing moment conditions for both the overall sample and the subgroup samples. We develop two versions of subgroup balancing propensity score corresponding to matching and weighting, respectively. We devise a stochastic search algorithm to estimate the subgroup balancing propensity score when the number of subgroups is large. We demonstrate through simulations that the subgroup balancing propensity score improves the performance of propensity score methods in estimating subgroup treatment effects. We apply the subgroup balancing propensity score method to the Italy Survey of Household Income and Wealth (SHIW) to estimate the causal effects of having debit card on household consumption for different income groups.
Protocol for an Observational Study on the Effects of Early-Life Participation in Contact Sports on Later-Life Cognition in a Sample of Monozygotic and Dizygotic Swedish Twins Reared Together and Twins Reared Apart

A large body of work links traumatic brain injury (TBI) in adulthood to the onset of Alzheimer's disease (AD). AD is the chief cause of dementia, leading to reduced cognitive capacity and autonomy and increased mortality risk. More recently, researchers have sought to investigate whether TBI experienced in early-life may influence trajectories of cognitive dysfunction in adulthood. It has been speculated that early-life participation in collision sports may lead to poor cognitive and mental health outcomes. However, to date, the few studies to investigate this relationship have produced mixed results. We propose to extend this literature by conducting a prospective study on the effects of early-life participation in collision sports on later-life cognitive health using the Swedish Adoption/Twin Study on Aging (SATSA). The SATSA is unique in its sampling of monozygotic and dizygotic twins reared together (respectively MZT, DZT) and twins reared apart (respectively MZA, DZA). The proposed analysis is a prospective study of 660 individuals comprised of 270 twin pairs and 120 singletons. Seventy-eight (11.8% individuals reported participation in collision sports. Our primary outcome will be an indicator of cognitive impairment determined by scores on the Mini-Mental State Examination (MMSE). We will also consider several secondary cognitive outcomes including verbal and spatial ability, memory, and processing speed. Our sample will be restricted to individuals with at least one MMSE score out of seven repeated assessments spaced approximately three years apart. We will adjust for age, sex, and education in each of our models.
Informed Machine Learning - Towards a Taxonomy of Explicit Integration of Knowledge into Machine Learning

Despite the great successes of machine learning, it can have its limits when dealing with insufficient training data.A potential solution is to incorporate additional knowledge into the training process which leads to the idea of informed machine learning. We present a research survey and structured overview of various approaches in this field. We aim to establish a taxonomy which can serve as a classification framework that considers the kind of additional knowledge, its representation,and its integration into the machine learning pipeline. The evaluation of numerous papers on the bases of the taxonomy uncovers key methods in this field.
Community detection with dependent connectivity

In network analysis, within-community members are more likely to be connected than between-community members, which is reflected in that the edges within a community are intercorrelated. However, existing probabilistic models for community detection such as the stochastic block model (SBM) are not designed to capture the dependence among edges. In this paper, we propose a new community detection approach to incorporate within-community dependence of connectivities through the Bahadur representation. The proposed method does not require specifying the likelihood function, which could be intractable for correlated binary connectivities. In addition, the proposed method allows for heterogeneity among edges between different communities. In theory, we show that incorporating correlation information can lower estimation bias and accelerate algorithm convergence. Our simulation studies show that the proposed algorithm outperforms the popular variational EM algorithm assuming conditional independence among edges. We also demonstrate the application of the proposed method to agricultural product trading networks from different countries.
Making Recursive Bayesian Inference Accessible

Abstract Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior distributions resulting from former studies. Two existing Recursive Bayesian methods are: Prior- and Proposal-Recursive Bayes. Prior-Recursive Bayes uses Bayesian updating, fitting models to partitions of data sequentially, and provides a way to accommodate new data as they become available using the posterior from the previous stage as the prior in the new stage based on the latest data. Proposal-Recursive Bayes is intended for use with hierarchical Bayesian models and uses a set of transient priors in first stage independent analyses of the data partitions. The second stage of Proposal-Recursive Bayes uses the posteriors from the first stage as proposals in a Markov chain Monte Carlo algorithm to fit the full model. We combine Prior- and Proposal-Recursive concepts to fit any Bayesian model, and often with computational improvements. We demonstrate our method with two case studies. Our approach has implications for big data, streaming data, and optimal adaptive design situations.
More powerful post-selection inference, with application to the Lasso

Investigators often use the data to generate interesting hypotheses and then perform inference for the generated hypotheses. P-values and confidence intervals must account for this explorative data analysis. A fruitful method for doing so is to condition any inferences on the components of the data used to generate the hypotheses, thus preventing information in those components from being used again. Some currently popular methods "over-condition", leading to wide intervals. We show how to perform the minimal conditioning in a computationally tractable way. In high dimensions, even this minimal conditioning can lead to intervals that are too wide to be useful, suggesting that up to now the cost of hypothesis generation has been underestimated. We show how to generate hypotheses in a strategic manner that sharply reduces the cost of data exploration and results in useful confidence intervals. Our discussion focuses on the problem of post-selection inference after fitting a lasso regression model, but we also outline its extension to a much more general setting.
LARGE SAMPLE THEORY OF INTRINSIC AND EXTRINSIC SAMPLE MEANS ON MANIFOLDS—II

This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Frechet sample means is derived leading to an asymptotic distribution theory of intrinsic sample means on Riemannian manifolds. Central limit theorems are also obtained for extrinsic sample means w.r. t. an arbitrary embedding of a differentiable manifold in a Euclidean space. Bootstrap methods particularly suitable for these problems are presented. Applications are given to distributions on the sphere S d (directional spaces), real projective space RP N-1 (axial spaces), complex projective space CP k-2 (planar shape spaces) w.r. t. Veronese-Whitney embeddings and a three-dimensional shape space Σ 4 3 .
Statistical post‐processing of ensemble forecasts of temperature in Santiago de Chile

Modelling forecast uncertainty is a difficult task in any forecasting problem. In weather forecasting a possible solution is the use of forecast ensembles, which are obtained from multiple runs of numerical weather prediction models with various initial conditions and model parametrizations to provide information about the expected uncertainty. Currently all major meteorological centres issue forecasts using their operational ensemble prediction systems. However, it is a general problem that the spread of the ensemble is too small compared to observations at specific sites resulting in under‐dispersive forecasts, leading to a lack of calibration. In order to correct this problem, various statistical calibration techniques have been developed in the last two decades. In the present work different post‐processing techniques were tested for calibrating nine member ensemble forecasts of temperature for Santiago de Chile, obtained by the Weather Research and Forecasting model using different planetary boundary layer and land surface model parametrizations. In particular, the ensemble model output statistics and Bayesian model averaging techniques were implemented and, since the observations are characterized by large altitude differences, the estimation of model parameters was adapted to the actual conditions at hand. Compared to the raw ensemble, all tested post‐processing approaches significantly improve the calibration of probabilistic forecasts and the accuracy of point forecasts. The ensemble model output statistics method using parameter estimation based on expert clustering of stations (according to their altitudes) shows the best forecast skill.
Uniform Consistency of the Highly Adaptive Lasso Estimator of Infinite Dimensional Parameters

Consider the case that we observe $n$ independent and identically distributed copies of a random variable with a probability distribution known to be an element of a specified statistical model. We are interested in estimating an infinite dimensional target parameter that minimizes the expectation of a specified loss function. In \cite{generally_efficient_TMLE} we defined an estimator that minimizes the empirical risk over all multivariate real valued cadlag functions with variation norm bounded by some constant $M$ in the parameter space, and selects $M$ with cross-validation. We referred to this estimator as the Highly-Adaptive-Lasso estimator due to the fact that the constrained can be formulated as a bound $M$ on the sum of the coefficients a linear combination of a very large number of basis functions. Specifically, in the case that the target parameter is a conditional mean, then it can be implemented with the standard LASSO regression estimator. In \cite{generally_efficient_TMLE} we proved that the HAL-estimator is consistent w.r. t. the (quadratic) loss-based dissimilarity at a rate faster than $n^{-1/2}$ (i.e., faster than $n^{-1/4}$ w.r.t. a norm), even when the parameter space is completely nonparametric. The only assumption required for this rate is that the true parameter function has a finite variation norm. The loss-based dissimilarity is often equivalent with the square of an $L^2(P_0)$-type norm. In this article, we establish that under some weak continuity condition, the HAL-estimator is also uniformly consistent.
Modal clustering asymptotics with applications to bandwidth selection

Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem in a standard inferential setting, where the concept of ideal population clustering is defined as the partition induced by the true density function. The nonparametric formulation of this approach, known as modal clustering, draws a correspondence between the groups and the domains of attraction of the density modes. Operationally, a nonparametric density estimate is required and a proper selection of the amount of smoothing, governing the shape of the density and hence possibly the modal structure, is crucial to identify the final partition. In this work, we address the issue of density estimation for modal clustering from an asymptotic perspective. A natural and easy to interpret metric to measure the distance between density-based partitions is discussed, its asymptotic approximation explored, and employed to study the problem of bandwidth selection for nonparametric modal clustering.
Bouncy Hybrid Sampler as a Unifying Device

This work introduces a class of rejection-free Markov chain Monte Carlo (MCMC) samplers, named the Bouncy Hybrid Sampler, which unifies several existing methods from the literature. Examples include the Bouncy Particle Sampler of Peters and de With (2012), Bouchard-Cote et al. (2015) and the Hamiltonian MCMC. Following the introduced general framework, we derive a new sampler called the Quadratic Bouncy Hybrid Sampler. We apply this novel sampler to the problem of sampling from a truncated Gaussian distribution.
Machine learning accelerated likelihood-free event reconstruction in dark matter direct detection

Reconstructing the position of an interaction for any dual-phase time projection chamber (TPC) with the best precision is key to directly detecting Dark Matter. Using the likelihood-free framework, a new algorithm to reconstruct the 2-D (x,y) position and the size of the charge signal (e) of an interaction is presented. The algorithm uses the secondary scintillation light distribution (S2) obtained by simulating events using a waveform generator. To deal with the computational effort required by the likelihood-free approach, we employ the Bayesian Optimization for Likelihood-Free Inference (BOLFI) algorithm. Together with BOLFI, prior distributions for the parameters of interest (x,y,e) and highly informative discrepancy measures to perform the analyses are introduced. We evaluate the quality of the proposed algorithm by a comparison against the currently existing alternative methods using a large-scale simulation study. BOLFI provides a natural probabilistic uncertainty measure for the reconstruction and it improved the accuracy of the reconstruction over the next best algorithm by up to 15% when focusing on events at large radii (R > 30 cm, the outer 37% of the detector). In addition, BOLFI provides the smallest uncertainties among all the tested methods.
Scalable Monte Carlo inference for state-space models

We present an original simulation-based method to estimate likelihood ratios efficiently for general state-space models. Our method relies on a novel use of the conditional Sequential Monte Carlo (cSMC) algorithm introduced in \citet{Andrieu_et_al_2010} and presents several practical advantages over standard approaches. The ratio is estimated using a unique source of randomness instead of estimating separately the two likelihood terms involved. Beyond the benefits in terms of variance reduction one may expect in general from this type of approach, an important point here is that the variance of this estimator decreases as the distance between the likelihood parameters decreases. We show how this can be exploited in the context of Monte Carlo Markov chain (MCMC) algorithms, leading to the development of a new class of exact-approximate MCMC methods to perform Bayesian static parameter inference in state-space models. We show through simulations that, in contrast to the Particle Marginal Metropolis-Hastings (PMMH) algorithm of Andrieu_et_al_2010, the computational effort required by this novel MCMC scheme scales very favourably for large data sets.
Improving linear quantile regression for replicated data

ABSTRACT This paper deals with improvement of linear quantile regression, when there are a few distinct values of the covariates but many replicates. One can improve asymptotic efficiency of the estimated regression coefficients by using suitable weights in quantile regression, or simply by using weighted least squares regression on the conditional sample quantiles. The asymptotic variances of the unweighted and weighted estimators coincide only in some restrictive special cases, e.g., when the density of the conditional response has identical values at the quantile of interest over the support of the covariate. The dominance of the weighted estimators is demonstrated in a simulation study, and through the analysis of a data set on tropical cyclones.
Modeling Brain Connectivity with Graphical Models on Frequency Domain

Multichannel electroencephalograms (EEGs) have been widely used to study cortical connectivity during acquisition of motor skills. In this paper, we introduce copula Gaussian graphical models on spectral domain to characterize dependence in oscillatory activity between channels. To obtain a simple and robust representation of brain connectivity that can explain the most variation in the observed signals, we propose a framework based on maximizing penalized likelihood with Lasso regularization to search for the sparse precision matrix. To address the optimization problem, graphical Lasso, Ledoit-Wolf and sparse estimation of a covariance matrix (SPCOV) algorithms were modified and implemented. Simulations show the benefit of using the proposed algorithms in terms of robustness and small estimation errors. Furthermore, analysis of the EEG data in a motor skill task conducted using algorithms of modified graphical LASSO and Ledoit-Wolf, reveal a sparse pattern of brain connectivity among cortices which is consistent with the results from other work in the literature.
Only closed testing procedures are admissible for controlling false discovery proportions

We consider the class of all multiple testing methods controlling tail probabilities of the false discovery proportion, either for one random set or simultaneously for many such sets. This class encompasses methods controlling familywise error rate, generalized familywise error rate, false discovery exceedance, joint error rate, simultaneous control of all false discovery proportions, and others, as well as seemingly unrelated methods such as gene set testing in genomics and cluster inference methods in neuroimaging. We show that all such methods are either equivalent to a closed testing method, or are uniformly improved by one. Moreover, we show that a closed testing method is admissible as a method controlling tail probabilities of false discovery proportions if and only if all its local tests are admissible. This implies that, when designing such methods, it is sufficient to restrict attention to closed testing methods only. We demonstrate the practical usefulness of this design principle by constructing a uniform improvement of a recently proposed method.