Miracle-dz/UniFAR-FTUs huggingface dataset:
Inference For High-Dimensional Split-Plot-Designs: A Unified Approach for Small to Large Numbers of Factor Levels

Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries of conventional multivariate data analysis. Such situations occur, e.g., frequently in life sciences whenever it is easier or cheaper to repeatedly generate a large number $d$ of observations per subject than recruiting many, say $N$, subjects. In this paper we discuss inference procedures for such situations in general heteroscedastic split-plot designs with $a$ independent groups of repeated measurements. These will, e.g., be able to answer questions about the occurrence of certain time, group and interactions effects or about particular profiles. The test procedures are based on standardized quadratic forms involving suitably symmetrized U-statistics-type estimators which are robust against an increasing number of dimensions $d$ and/or groups $a$. We then discuss its limit distributions in a general asymptotic framework and additionally propose improved small sample approximations. Finally its small sample performance is investigated in simulations and the applicability is illustrated by a real data analysis.
Discussion on "Random-projection ensemble classification" by T. Cannings and R. Samworth

Discussion on "Random-projection ensemble classification" by T. Cannings and R. Samworth. We believe that the proposed approach can find many applications in economics such as credit scoring (e.g. Altman (1968)) and can be extended to more general type of classifiers. In this discussion we would like to draw authors attention to the copula-based discriminant analysis (Han et al. (2013) and He et al. (2016)).
Tractable Graph Matching via Soft Seeding

The graph matching problem aims to discover a latent correspondence between the vertex sets of two observed graphs. This problem has proven to be quite challenging, with few satisfying methods that are computationally tractable and widely applicable. The FAQ algorithm has proven to have good performance on benchmark problems and works with a indefinite relaxation of the problem. Due to the indefinite relaxation, FAQ is not guaranteed to find the global maximum. However, if prior information is known about the true correspondence, this can be leveraged to initialize the algorithm near the truth. We show that given certain properties of this initial matrix, with high probability the FAQ algorithm will converge in two steps to the truth under a flexible model for pairs of random graphs. Importantly, this result implies that there will be no local optima near the global optima, providing a method to assess performance.
5. Optimality criteria for probabilistic numerical methods

It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that the decision-theoretic framework is neither appropriate nor sufficient. To this end, we consider an alternative optimality criterion from Bayesian experimental design and study its implied optimal information in the numerical context. This information is demonstrated to differ, in general, from the information that would be used in an average-case-optimal numerical method. The explicit connection to Bayesian experimental design suggests several distinct regimes in which optimal probabilistic numerical methods can be developed.
E-Loyalty Networks in Online Auctions

Creating a loyal customer base is one of the most important, and at the same time, most difficult tasks a company faces. Creating loyalty online (e-loyalty) is especially difficult since customers can "switch" to a competitor with the click of a mouse. In this paper we investigate e-loyalty in online auctions. Using a unique data set of over 30,000 auctions from one of the main consumer-to-consumer online auction houses, we propose a novel measure of e-loyalty via the associated network of transactions between bidders and sellers. Using a bipartite network of bidder and seller nodes, two nodes are linked when a bidder purchases from a seller and the number of repeat-purchases determines the strength of that link. We employ ideas from functional principal component analysis to derive, from this network, the loyalty distribution which measures the perceived loyalty of every individual seller, and associated loyalty scores which summarize this distribution in a parsimonious way. We then investigate the effect of loyalty on the outcome of an auction. In doing so, we are confronted with several statistical challenges in that standard statistical models lead to a mis-representation of the data and a violation of the model assumptions. The reason is that loyalty networks result in an extreme clustering of the data, with few high-volume sellers accounting for most of the individual transactions. We investigate several remedies to the clustering problem and conclude that loyalty networks consist of very distinct segments that can best be understood individually.
JMASM 52: Extremely Efficient Permutation and Bootstrap Hypothesis Tests Using R

Re-sampling based statistical tests are known to be computationally heavy, but reliable when small sample sizes are available. Despite their nice theoretical properties not much effort has been put to make them efficient. In this paper we treat the case of Pearson correlation coefficient and two independent samples t-test. We propose a highly computationally efficient method for calculating permutation based p-values in these two cases. The method is general and can be applied or be adopted to other similar two sample mean or two mean vectors cases.
Distributed linear regression by averaging

Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck. In this paper, we study one-step and iterative weighted parameter averaging in statistical linear models under data parallelism. We do linear regression on each machine, send the results to a central server, and take a weighted average of the parameters. Optionally, we iterate, sending back the weighted average and doing local ridge regressions centered at it. How does this work compared to doing linear regression on the full data? Here we study the performance loss in estimation, test error, and confidence interval length in high dimensions, where the number of parameters is comparable to the training data size. We find the performance loss in one-step weighted averaging, and also give results for iterative averaging. We also find that different problems are affected differently by the distributed framework. Estimation error and confidence interval length increase a lot, while prediction error increases much less. We rely on recent results from random matrix theory, where we develop a new calculus of deterministic equivalents as a tool of broader interest.
Numerical techniques for the computation of sample spectral distributions of population mixtures

This note describes some techniques developed for the computation of the sample eigenvalue distribution of random matrices generated by mixtures of populations. Within this model the mapping between the population distributions and the asymptotic sample distribution can be obtained by solving a set of systems of non-linear equations, for which we provide an efficient implementation. This work contributes by describing a method for accelerated fixed point convergence, a homotopy continuation strategy to prevent convergence to non-admissible solutions, a blind non-uniform grid construction for effective distribution support detection and improved approximation at its edges, and a parallel computing architecture. Comparisons are performed with available packages for the single population case and with results obtained by simulation for the more general model implemented here. Results show competitive performance and improved flexibility.
3D mean Projective Shape Difference for Face Differentiation from Multiple Digital Camera Images

We give a nonparametric methodology for hypothesis testing for equality of extrinsic mean objects on a manifold embedded in a numerical spaces. The results obtained in the general setting are detailed further in the case of 3D projective shapes represented in a space of symmetric matrices via the quadratic Veronese-Whitney (VW) embedding. Large sample and nonparametric bootstrap confidence regions are derived for the common VW-mean of random projective shapes for finite 3D configurations. As an example, the VW MANOVA testing methodology is applied to the multi-sample mean problem for independent projective shapes of $3D$ facial configurations retrieved from digital images, via Agisoft PhotoScan technology.
$k$-Sample problem based on generalized maximum mean discrepancy

In this paper we deal with the problem of testing for the quality of $k$ probability distributions. We introduce a generalization of the maximum mean discrepancy that permits to characterize the null hypothesis. Then, an estimator of it is proposed as test statistic, and its asymptotic distribution under the null hypothesis is derived. Simulations show that the introduced procedure outperforms classical ones.
Multiscale change point detection for dependent data

In this article we study the theoretical properties of the simultaneous multiscale change point estimator (SMUCE) in piecewise‐constant signal models with dependent error processes. Empirical studies suggest that in this case the change point estimate is inconsistent, but it is not known if alternatives suggested in the literature for correlated data are consistent. We propose a modification of SMUCE scaling the basic statistic by the long run variance of the error process, which is estimated by a difference‐type variance estimator calculated from local means from different blocks. For this modification we prove model consistency for physical‐dependent error processes and illustrate the finite sample performance by means of a simulation study.
Oracle inequalities for square root analysis estimators with application to total variation penalties

Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan et al. (2017, Bernoulli, 23, 552–581). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularized estimators on graphs and obtain constant-friendly rates, which, up to log terms, match previous results obtained by entropy calculations. We also obtain an oracle inequality for the (square root) total variation regularized estimator over the cycle graph.
Structure Learning of Undirected Graphical Models for Count Data

Biological processes underlying the basic functions of a cell involve complex interactions between genes. From a technical point of view, these interactions can be represented through a graph where genes and their connections are, respectively, nodes and edges. The main objective of this paper is to develop a statistical framework for modelling the interactions between genes when the activity of genes is measured on a discrete scale. In detail, we define a new algorithm for learning the structure of undirected graphs, PC-LPGM, proving its theoretical consistence in the limit of infinite observations. The proposed algorithm shows promising results when applied to simulated data as well as to real data.
Testing for the rank of a covariance operator

How can we discern whether a mean-square continuous stochastic process is finite-dimensional, and if so, what its precise dimension is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional data, which require low-dimensional representations whether by functional PCA or other methods. The difficulty is that the determination is to be made on the basis of iid replications of the process observed discretely and with measurement error contamination. This adds a ridge to the empirical covariance, obfuscating the underlying dimension. We build a matrix-completion inspired test statistic that circumvents this issue by measuring the best possible least square fit of the empirical covariance's off-diagonal elements, optimised over covariances of given finite rank. For a fixed grid of sufficient size, we determine the statistic's asymptotic null distribution as the number of replications grows. We then use it to construct a bootstrap implementation of a stepwise testing procedure controlling the family-wise error rate corresponding to the collection of hypotheses formalising the question at hand. Under minimal regularity assumptions we prove that the procedure is consistent and that its bootstrap implementation is valid. The procedure involves no tuning parameters or pre-smoothing, is indifferent to the homoskedasticity or lack of it in the measurement errors, and does not assume a low-noise regime. An extensive study of the procedure's finite-sample accuracy demonstrates remarkable performance in both real and simulated data, corroborating our theoretical results showing that the test should asymptotically attain near perfect power for any level.
Estimating Bayesian Optimal Treatment Regimes for Dichotomous Outcomes using Observational Data.

Optimal treatment regimes (OTR) are individualised treatment assignment strategies that identify a medical treatment as optimal given all background information available on the individual. We discuss Bayes optimal treatment regimes estimated using a loss function defined on the bivariate distribution of dichotomous potential outcomes. The proposed approach allows considering more general objectives for the OTR than maximization of an expected outcome (e.g., survival probability) by taking into account, for example, unnecessary treatment burden. As a motivating example we consider the case of oropharynx cancer treatment where unnecessary burden due to chemotherapy is to be avoided while maximizing survival chances. Assuming ignorable treatment assignment we describe Bayesian inference about the OTR including a sensitivity analysis on the unobserved partial association of the potential outcomes. We evaluate the methodology by simulations that apply Bayesian parametric and more flexible non-parametric outcome models. The proposed OTR for oropharynx cancer reduces the frequency of the more burdensome chemotherapy assignment by approximately 75% without reducing the average survival probability. This regime thus offers a strong increase in expected quality of life of patients.
On a universality class of anomalous diffusion

We show that when transport is asymptotically dominated by ballistic excursions the momentsof displacement exhibit a universal behaviour, and their values that can be obtained after an appropriate rescaling of the mean square displacement in terms of the asymptotic behaviour of a minimal transport model that be call Fly-and-Die. Furthermore, we show that this universality extends to the displacement correlation function. We obtain the statistical properties defining a universality class to which the details and nature of the dynamics are irrelevant. We support this by studying several models exhibiting strong anomalous diffusion.
Influence of Clustering on Cascading Failures in Interdependent Systems

We study the influence of clustering, more specifically triangles, on cascading failures in interdependent networks or systems, in which we model the dependence between comprising systems using a dependence graph. First, we propose a new model that captures how the presence of triangles in the dependence graph alters the manner in which failures transmit from affected systems to others. Unlike existing models, the new model allows us to approximate the failure propagation dynamics using a multi-type branching process, even with triangles. Second, making use of the model, we provide a simple condition that indicates how increasing clustering will affect the likelihood that a random failure triggers a cascade of failures, which we call the probability of cascading failures (PoCF). In particular, our condition reveals an intriguing observation that the influence of clustering on PoCF depends on the vulnerability of comprising systems to an increasing number of failed neighboring systems and the current PoCF, starting with different types of failed systems. Our numerical studies hint that increasing clustering impedes cascading failures under both (truncated) power law and Poisson degree distributions. Furthermore, our finding suggests that, as the degree distribution becomes more concentrated around the mean degree with smaller variance, increasing clustering will have greater impact on the PoCF. A numerical investigation of networks with Poisson and power law degree distributions reflects this finding and demonstrates that increasing clustering reduces the PoCF much faster under Poisson degree distributions in comparison to power law degree distributions.
On marginal and conditional parameters in logistic regression models

We derive the exact formula linking the parameters of marginal and conditional logistic regression models with binary mediators when no conditional independence assumptions can be made. The formula has the appealing property of being the sum of terms that vanish whenever parameters of the conditional models vanish, thereby recovering well-known results as particular cases. It also permits the disentangling of direct and indirect effects as well as quantifying the distortion induced by the omission of relevant covariates, opening the way to sensitivity analysis. As the parameters of the conditional models are multiplied by terms that are always bounded, the derivations may also be used to construct reasonable bounds on the parameters of interest when relevant intermediate variables are unobserved. We assume that, conditionally on a set of covariates, the data-generating process can be represented by a directed acyclic graph. We also show how the results presented here lead to the extension of path analysis to a system of binary random variables.
Making Tree Ensembles Interpretable

Tree ensembles, such as random forest and boosted trees, are renowned for their high prediction performance, whereas their interpretability is critically limited. In this paper, we propose a post processing method that improves the model interpretability of tree ensembles. After learning a complex tree ensembles in a standard way, we approximate it by a simpler model that is interpretable for human. To obtain the simpler model, we derive the EM algorithm minimizing the KL divergence from the complex ensemble. A synthetic experiment showed that a complicated tree ensemble was approximated reasonably as interpretable.
Sign tests for weak principal directions

We consider inference on the first principal direction of a p -variate elliptical distribution. We do so in challenging double asymptotic scenarios for which this direction eventually fails to be identifiable. In order to achieve robustness not only with respect to such weak identifiability but also with respect to heavy tails, we focus on sign-based statistical procedures, that is, on procedures that involve the observations only through their direction from the center of the distribution. We actually consider the generic problem of testing the null hypothesis that the first principal direction coincides with a given direction of R p. We first focus on weak identifiability setups involving single spikes (that is, involving spectra for which the smallest eigenvalue has multiplicity p-1). We show that, irrespective of the degree of weak identifiability, such setups offer local alternatives for which the corresponding sequence of statistical experiments converges in the Le Cam sense. Interestingly, the limiting experiments depend on the degree of weak identifiability. We exploit this convergence result to build optimal sign tests for the problem considered. In classical asymptotic scenarios where the spectrum is fixed, these tests are shown to be asymptotically equivalent to the sign-based likelihood ratio tests available in the literature. Unlike the latter, however, the proposed sign tests are robust to arbitrarily weak identifiability. We show that our tests meet the asymptotic level constraint irrespective of the structure of the spectrum, hence also in possibly multi-spike setups. Finally, we fully characterize the non-nullasymptotic distributions of the corresponding test statistics under weak identifiability, which allows us to quantify the corresponding local asymptotic powers. Monte Carlo exercises confirm our asymptotic results.
The Reduced Dynamic Chain Event Graph

In this paper we introduce a new class of probabilistic graphical models called the Reduced Dynamic Chain Event Graph (RDCEG) which is a novel mixture of a Chain Event Graph (CEG) and a semi-Markov process (SMP). It has been demonstrated that many real-world scenarios, particularly in the domain of public health and security, can be modelled as an unfolding of events in the life histories of individuals. Our interest not only lies in the future trajectories of an individual with a specified history and set of characteristics but also in the timescale associated with these developments. Such information is critical in developing suitable interventions and informs the prioritisation of policy decisions. The RDCEG was born out of the need for such a model. It is a coloured graph which inherits useful properties like fast conjugate model selection, conditional independence interrogations and a support for causal interventions from the family of probabilistic graphical models. Its novelty lies in its underlying semi-Markov structure which offers the flexibility of the holding time at each state being any arbitrary distribution. We demonstrate this new decision support system with a simulated intervention to reduce falls in the elderly.
Non-Linear Non-Stationary Heteroscedasticity Volatility for Tracking of Jump Processes

In this paper, we introduce a new jump process modeling which involves a particular kind of non-Gaussian stochastic processes with random jumps at random time points. The main goal of this study is to provide an accurate tracking technique based on non-linear non-stationary heteroscedasticity (NNH) time series. It is, in fact, difficult to track jump processes regarding the fact that non-Gaussianity is an inherent feature in these processes. The proposed NNH model is conditionally Gaussian whose conditional variance is time-varying. Therefore, we use Kalman filter for state tracking. We show analytically that the proposed NNH model is superior to the traditional methods. Furthermore, to validate the findings, simulations are performed. Finally, the comparison between the proposed method and other alternatives techniques has been made.
The Gradient Discretisation Method for Linear Advection Problems

Abstract We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence analysis of various numerical schemes, corresponding to the methods known to be GDMs, such as finite elements (conforming or non-conforming, standard or mass-lumped), finite volumes on rectangular or simplicial grids, and other recent methods developed for general polytopal meshes. The scheme is of centred type, with added linear or non-linear numerical diffusion. We complement the convergence analysis with numerical tests based on the mass-lumped ℙ 1 {\mathbb{P}_{1}} conforming and non-conforming finite element and on the hybrid finite volume method.