Miracle-dz/UniFAR-FTUs huggingface dataset:
A note on using Bayes priors for Weibull distribution

In this note, the practical use of priors for Bayes estimators, of the two parameters of the Weibull reliability model, is discussed in a technological context. The meaning of the priors as expression of virtual data samples is analyzed. The implications of physics of failures are also highlighted. The whole analysis shows a rational way to convert a really available technological knowledge into prior information, effectively and without a long elicitation process. A large Monte Carlo study, on both complete and censored samples of small size, shows the good properties of some estimators, which can exploit such a new approach.
A goodness-of-fit test based on the empirical characteristic function and a comparison of tests for normality

The normal distribution has the unique property that the cumulant generating function has only two terms, namely those involving the mean and the variance. This property is used to construct a simple by using the log of the modulus of the empirical characteristic function to what would be expected under normality. The test statistic is easy to calculate. Using a simulation study the proposed test is shown to have excellent power, especially in large samples.
On Using Control Variates with Stochastic Approximation for Variational Bayes and its Connection to Stochastic Linear Regression

Recently, we and several other authors have written about the possibilities of using stochastic approximation techniques for fitting variational approximations to intractable Bayesian posterior distributions. Naive implementations of stochastic approximation suffer from high variance in this setting. Several authors have therefore suggested using control variates to reduce this variance, while we have taken a different but analogous approach to reducing the variance which we call stochastic linear regression. In this note we take the former perspective and derive the ideal set of control variates for stochastic approximation variational Bayes under a certain set of assumptions. We then show that using these control variates is closely related to using the stochastic linear regression approximation technique we proposed earlier. A simple example shows that our method for constructing control variates leads to stochastic estimators with much lower variance compared to other approaches.
Consistency of spectral clustering in stochastic block models

We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\log n$, with $n$ the number of nodes. This result applies to some popular polynomial time spectral clustering algorithms and is further extended to degree corrected stochastic block models using a spherical $k$-median spectral clustering method. A key component of our analysis is a combinatorial bound on the spectrum of binary random matrices, which is sharper than the conventional matrix Bernstein inequality and may be of independent interest.
A Survival Copula Mixture Model for Comparing Two Genomic Rank Lists

Analyses of high-throughput genomic data often lead to ranked lists of genomic loci. How to characterize concordant signals between two rank lists is a common problem with many applications. One example is measuring the reproducibility between two replicate experiments. Another is to characterize the interaction and co-binding between two transcription factors (TF) based on the overlap between their binding sites. As an exploratory tool, the simple Venn diagram approach can be used to show the common loci between two lists. However, this approach does not account for changes in overlap with decreasing ranks, which may contain useful information for studying similarities or dissimilarities of the two lists. The recently proposed irreproducible discovery rate (IDR) approach compares two rank lists using a copula mixture model. This model considers the rank correlation between two lists. However, it only analyzes the genomic loci that appear in both lists, thereby only measuring signal concordance in the overlapping set of the two lists. When two lists have little overlap but loci in their overlapping set have high concordance in terms of rank, the original IDR approach may misleadingly claim that the two rank lists are highly reproducible when they are indeed not. In this article, we propose to address the various issues above by translating the problem into a bivariate survival problem. A survival copula mixture model is developed to characterize concordant signals in two rank lists. The effectiveness of this approach is demonstrated using both simulations and real data.
Margin conditions for vector quantization

In this report, oracle inequalities on the excess risk of the empirical risk minimizer in the quantization framework are derived. These inequalities are based on conditions which may be thought of as margin type conditions, such as one derived in the statistical learning framework. Furthermore, these inequalities derive from innovative chaining techniques and its use for Dudley's entropy integral.
Local Digital Estimators of Intrinsic Volumes for Boolean Models and in the Design-Based Setting

In order to estimate the specific intrinsic volumes of a planar Boolean model from a binary image, we consider local digital algorithms based on weighted sums of 2×2 configuration counts. For Boolean models with balls as grains, explicit formulas for the bias of such algorithms are derived, resulting in a set of linear equations that the weights must satisfy in order to minimize the bias in high resolution. These results generalize to larger classes of random sets, as well as to the design-based situation, where a fixed set is observed on a stationary isotropic lattice. Finally, the formulas for the bias obtained for Boolean models are applied to existing algorithms in order to compare their accuracy.
Nearly unbiased variable selection under minimax concave penalty

We propose MC+, a fast, continuous, nearly unbiased and accurate method of penalized variable selection in high-dimensional linear regression. The LASSO is fast and continuous, but biased. The bias of the LASSO may prevent consistent variable selection. Subset selection is unbiased but computationally costly. The MC+ has two elements: a minimax concave penalty (MCP) and a penalized linear unbiased selection (PLUS) algorithm. The MCP provides the convexity of the penalized loss in sparse regions to the greatest extent given certain thresholds for variable selection and unbiasedness. The PLUS computes multiple exact local minimizers of a possibly nonconvex penalized loss function in a certain main branch of the graph of critical points of the penalized loss. Its output is a continuous piecewise linear path encompassing from the origin for infinite penalty to a least squares solution for zero penalty. We prove that at a universal penalty level, the MC+ has high probability of matching the signs of the unknowns, and thus correct selection, without assuming the strong irrepresentable condition required by the LASSO. This selection consistency applies to the case of p » n, and is proved to hold for exactly the MC+ solution among possibly many local minimizers. We prove that the MC+ attains certain minimax convergence rates in probability for the estimation of regression coefficients in l r balls. We use the SURE method to derive degrees of freedom and C p -type risk estimates for general penalized LSE, including the LASSO and MC+ estimators, and prove their unbiasedness. Based on the estimated degrees of freedom, we propose an estimator of the noise level for proper choice of the penalty level. For full rank designs and general sub-quadratic penalties, we provide necessary and sufficient conditions for the continuity of the penalized LSE. Simulation results overwhelmingly support our claim of superior variable selection properties and demonstrate the computational efficiency of the proposed method.
Non-Local means est un algorithme de d\'ebruitage local (Non-Local means is a local image denoising algorithm)

The Non-Local Means (NLM) image denoising algorithm pushed the limits of denoising. But it introduced a new paradigm, according to which one could capture the similarity of images with the NLM weights. We show that, contrary to the prevailing opinion, the NLM weights do not allow to get a reliable measure of the similarity in a noisy image, unless one add a locality constraint. As an image denoising method, the Non-Local Means prove to be local. Some works had already pointed out that to get the best denoising performances with the NLM algorithm, one should run it locally. But no general conclusion has been yet proposed and the only explanation that was proposed to justify the experimental results is not sufficient. Our study based on experimental evidence proves that, on average on natural images, the bias of the NLM estimator is an increasing function of the radius of the similarity searching zone. The reason for this phenomenon is that noise disrupts the order of similarity between patches. Hence the mean squared error between the original image and the NLM estimation, which is the sum of the bias, the variance and the covariance of the estimator, has an absolute minimum for a disk of radius 3 to 4 pixels.
Stochastic Dual Coordinate Ascent with Alternating Direction Multiplier Method

We propose a new stochastic dual coordinate ascent technique that can be applied to a wide range of regularized learning problems. Our method is based on Alternating Direction Multiplier Method (ADMM) to deal with complex regularization functions such as structured regularizations. Although the original ADMM is a batch method, the proposed method offers a stochastic update rule where each iteration requires only one or few sample observations. Moreover, our method can naturally afford mini-batch update and it gives speed up of convergence. We show that, under mild assumptions, our method converges exponentially. The numerical experiments show that our method actually performs efficiently.
Bayes Model Selection with Path Sampling: Factor Models and Other Examples

We prove a theorem justifying the regularity conditions which are needed for Path Sampling in Factor Models. We then show that the remaining ingredient, namely, MCMC for calculating the integrand at each point in the path, may be seriously flawed, leading to wrong estimates of Bayes factors. We provide a new method of Path Sampling (with Small Change) that works much better than standard Path Sampling in the sense of estimating the Bayes factor better and choosing the correct model more often. When the more complex factor model is true, PS-SC is substantially more accurate. New MCMC diagnostics is provided for these problems in support of our conclusions and recommendations. Some of our ideas for diagnostics and improvement in computation through small changes should apply to other methods of computation of the Bayes factor for model selection.
Discovering and Visualizing Hierarchy in the Data

How to extract useful insights from data in a human perceivable manner is always a challenge when the dimension and amount of the data is large. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or from the information and phenomena carried by the data itself. The current study attempts to discover and visualize these underlying hierarchies. Regarding each observation as a draw from a (hypothetical) multidimensional joint density, our first goal is to approximate this unknown density with a piecewise constant function over the binary partitioned sample space; our non-parametric approach makes no assumptions on the form of the density, such as assuming that it is Multivariate Gaussian, or that it is a mixture of a small number of Gaussians. Given the piecewise constant density function and its corresponding partitions of the sample space, our second goal is to construct a connected graph and build up a tree representation of the data from sub-level sets. To demonstrate that our method is a general data mining and visualization tool which can provide "multi-resolution" summaries and reveal different levels of information of the data, we apply it to two real data sets from different fields.
Hierarchical Testing in the High-Dimensional Setting With Correlated Variables

We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model. In presence of highly correlated variables, as is very common in high-dimensional data, it seems indispensable to go beyond an approach of inferring individual regression coefficients, and we show that detecting smallest groups of variables (MTDs: minimal true detections) is realistic. Thanks to the hierarchy among the groups of variables, powerful multiple testing adjustment is possible which leads to a data-driven choice of the resolution level for the groups. Our procedure, based on repeated sample splitting, is shown to asymptotically control the familywise error rate and we provide empirical results for simulated and real data which complement the theoretical analysis. Supplementary materials for this article are available online.
Approximate D-optimal Experimental Design with Simultaneous Size and Cost Constraints

Consider an experiment with a finite set of design points representing permissible trial conditions. Suppose that each trial is associated with a cost that depends on the selected design point. In this paper, we study the problem of constructing an approximate D-optimal experimental design with simultaneous restrictions on the size and on the total cost. For the problem of size-and-cost constrained D-optimality, we formulate an equivalence theorem and rules for the removal of redundant design points. We also propose a simple monotonically convergent "barycentric" algorithm that allows us to numerically compute a size-and-cost constrained approximate D-optimal design.
Inferring Team Strengths Using a Discrete Markov Random Field

We propose an original model for inferring team strengths using a Markov Random Field, which can be used to generate historical estimates of the offensive and defensive strengths of a team over time. This model was designed to be applied to sports such as soccer or hockey, in which contest outcomes take value in a limited discrete space. We perform inference using a combination of Expectation Maximization and Loopy Belief Propagation. The challenges of working with a non-convex optimization problem and a high-dimensional parameter space are discussed. The performance of the model is demonstrated on professional soccer data from the English Premier League.
Nonparametric Estimation for Jump-Diffusion CIR Model

We study the nonparametric estimation for the intensity of Poisson random measure in jump-diffusion CIR model based on the low frequency observations. This is given in terms of the minimization of norms on a nonempty, closed and convex subset of some special Hilbert space. We establish the measurability of the estimator and derive its consistency and asymptotic risk bound.
Dense graph limits under respondent-driven sampling.

We consider certain respondent-driven sampling procedures on dense graphs. We show that if the sequence of the vertex-sets is ergodic then the limiting graph can be expressed in terms of the original dense graph via a transformation related to the invariant measure of the ergodic sequence. For specific sampling procedures, we describe the transformation explicitly.
Metastatistics of Extreme Values and its Application in Hydrology

We present a novel statistical treatment, the "metastatistics of extreme events", for calculating the frequency of extreme events. This approach, which is of general validity, is the proper statistical framework to address the problem of data with statistical inhomogeneities. By use of artificial sequences, we show that the metastatistics produce the correct predictions while the traditional approach based on the generalized extreme value distribution does not. An application of the metastatistics methodology to the case of extreme event to rainfall daily precipitation is also presented.
Mixtures of Variance-Gamma Distributions

A mixture of variance-gamma distributions is introduced and developed for model-based clustering and classification. The latest in a growing line of non-Gaussian mixture approaches to clustering and classification, the proposed mixture of variance-gamma distributions is a special case of the recently developed mixture of generalized hyperbolic distributions, and a restriction is required to ensure identifiability. Our mixture of variance-gamma distributions is perhaps the most useful such special case and, we will contend, may be more useful than the mixture of generalized hyperbolic distributions in some cases. In addition to being an alternative to the mixture of generalized hyperbolic distributions, our mixture of variance-gamma distributions serves as an alternative to the ubiquitous mixture of Gaussian distributions, which is a special case, as well as several non-Gaussian approaches, some of which are special cases. The mathematical development of our mixture of variance-gamma distributions model relies on its relationship with the generalized inverse Gaussian distribution; accordingly, the latter is reviewed before our mixture of variance-gamma distributions is presented. Parameter estimation carried out within the expectation-maximization framework.
Approximate tests for the equality of two cumulative incidence functions of a competing risk

ABSTRACT In the context of a competing risks set-up, we discuss different inference procedures for testing equality of two cumulative incidence functions, where the data may be subject to independent right-censoring or left-truncation. To this end, we compare two-sample Kolmogorov–Smirnov- and Cramér–von Mises-type test statistics. Since, in general, their corresponding asymptotic limit distributions depend on unknown quantities, we utilize wild bootstrap resampling as well as approximation techniques to construct adequate test decisions. Here, the latter procedures are motivated from tests for heteroscedastic factorial designs but have not yet been proposed in the survival context. A simulation study shows the performance of all considered tests under various settings and finally a real data example about bloodstream infection during neutropenia is used to illustrate their application.
Convergence of hybrid slice sampling via spectral gap

It is known that the simple slice sampler has very robust convergence properties, however the class of problems where it can be implemented is limited. In contrast, we consider hybrid slice samplers which are easily implementable and where another Markov chain approximately samples the uniform distribution on each slice. Under appropriate assumptions on the Markov chain on the slice we show a lower bound and an upper bound of the spectral gap of the hybrid slice sampler in terms of the spectral gap of the simple slice sampler. An immediate consequence of this is that spectral gap and geometric ergodicity of the hybrid slice sampler can be concluded from spectral gap and geometric ergodicity of its simple version which is very well understood. These results indicate that robustness properties of the simple slice sampler are inherited by (appropriately designed) easily implementable hybrid versions and provide the first theoretical underpinning of their use in applications. We apply the developed theory and analyse a number of specific algorithms such as the stepping-out shrinkage slice sampling, hit-and-run slice sampling on very general multidimensional targets and an easily implementable combination of both procedures on fairly general and realistic multidimensional bimodal densities.
On Geometric Ergodicity of Additive and Multiplicative Transformation Based Markov Chain Monte Carlo in High Dimensions

Recently Dutta and Bhattacharya (2013) introduced a novel Markov Chain Monte Carlo methodology that can simultaneously update all the components of high dimensional parameters using simple deterministic transformations of a one-dimensional random variable drawn from any arbitrary distribution defined on a relevant support. The methodology, which the authors refer to as Transformation-based Markov Chain Monte Carlo (TMCMC), greatly enhances computational speed and acceptance rate in high-dimensional problems. Two significant transformations associated with TMCMC are additive and multiplicative transformations. Combinations of additive and multiplicative transformations are also of much interest. In this work we investigate geometric ergodicity associated with additive and multiplicative TMCMC, along with their combinations, and illustrate their efficiency in practice with simulation studies.
Nonparametric graphon estimation

We propose a nonparametric framework for the analysis of networks, based on a natural limit object termed a graphon. We prove consistency of graphon estimation under general conditions, giving rates which include the important practical setting of sparse networks. Our results cover dense and sparse stochastic blockmodels with a growing number of classes, under model misspecification. We use profile likelihood methods, and connect our results to approximation theory, nonparametric function estimation, and the theory of graph limits.
Using the bootstrap for statistical inference on random graphs

In this paper we propose a new nonparametric approach to network inference that may be viewed as a fusion of block sampling procedures for temporally and spatially dependent processes with the classical network methodology. We develop estimation and uncertainty quantification procedures for network mean degree using a “patchwork” sample and nonparametric bootstrap, under the assumption of unknown degree distribution. We provide a heuristic justification of asymptotic properties of the proposed “patchwork” sampling and present cross‐validation methodology for selecting an optimal “patch” size. We validate the new “patchwork” bootstrap on simulated networks with short‐ and long‐tailed mean degree distributions, and revisit the Erdös collaboration data to illustrate the proposed methodology. The Canadian Journal of Statistics 44: 3–24; 2016 © 2015 Statistical Society of Canada
Asymptotic behavior of unregularized and ridge-regularized high-dimensional robust regression estimators : rigorous results

We study the behavior of high-dimensional robust regression estimators in the asymptotic regime where $p/n$ tends to a finite non-zero limit. More specifically, we study ridge-regularized estimators, i.e $\widehat{\beta}=\text{argmin}_{\beta \in \mathbb{R}^p} \frac{1}{n}\sum_{i=1}^n \rho(\varepsilon_i-X_i' \beta)+\frac{\tau}{2}\lVert\beta\rVert^2$. In a recently published paper, we had developed with collaborators probabilistic heuristics to understand the asymptotic behavior of $\widehat{\beta}$. We give here a rigorous proof, properly justifying all the arguments we had given in that paper. Our proof is based on the probabilistic heuristics we had developed, and hence ideas from random matrix theory, measure concentration and convex analysis. While most the work is done for $\tau>0$, we show that under some extra assumptions on $\rho$, it is possible to recover the case $\tau=0$ as a limiting case. We require that the $X_i$'s be i.i. d with independent entries, but our proof handles the case where these entries are not Gaussian. A 2-week old paper of Donoho and Montanari [arXiv:1310.7320] studied a similar problem by a different method and with a different point of view. At this point, their interesting approach requires Gaussianity of the design matrix.