Miracle-dz/UniFAR-FTUs huggingface dataset:
Autoregressive Kernels For Time Series

We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the likelihood function p_{\theta}(x) of different parameters \theta in the VAR model as features to describe x. To compare two time series x and x', we form the product of their features p_{\theta}(x) p_{\theta}(x') which is integrated out w.r. t \theta using a matrix normal-inverse Wishart prior. Among other properties, this kernel can be easily computed when the dimension d of the time series is much larger than the lengths of the considered time series x and x'. It can also be generalized to time series taking values in arbitrary state spaces, as long as the state space itself is endowed with a kernel \kappa. In that case, the kernel between x and x' is a a function of the Gram matrices produced by \kappa on observations and subsequences of observations enumerated in x and x'. We describe a computationally efficient implementation of this generalization that uses low-rank matrix factorization techniques. These kernels are compared to other known kernels using a set of benchmark classification tasks carried out with support vector machines.
Quantiles Equivariance

It is widely claimed that the quantile function is equivariant under increasing transformations. We show by a counterexample that this is not true (even for strictly increasing transformations). However, we show that the quantile function is equivariant under left continuous increasing transformations. We also provide an equivariance relation for continuous decreasing transformations. In the case that the transformation is not continuous, we show that while the transformed quantile at p can be arbitrarily far from the quantile of the transformed at p (in terms of absolute difference), the probability mass between the two is zero. We also show by an example that weighted definition of the median is not equivariant under even strictly increasing continuous transformations.
Geometric kernel smoothing of tensor fields

In this paper, we study a kernel smoothing approach for denoising a tensor field. Particularly, both simulation studies and theoretical analysis are conducted to understand the effects of the noise structure and the structure of the tensor field on the performance of different smoothers arising from using different metrics, viz., Euclidean, log-Euclidean and affine invariant metrics. We also study the Rician noise model and compare two regression estimators of diffusion tensors based on raw diffusion weighted imaging data at each voxel.
Robust Tests in Genome-Wide Scans under Incomplete Linkage Disequilibrium

Under complete linkage disequilibrium (LD), robust tests often have greater power than Pearson's chi-square test and trend tests for the analysis of case-control genetic association studies. Robust statistics have been used in candidate-gene and genome-wide association studies (GWAS) when the genetic model is unknown. We consider here a more general incomplete LD model, and examine the impact of penetrances at the marker locus when the genetic models are defined at the disease locus. Robust statistics are then reviewed and their efficiency and robustness are compared through simulations in GWAS of 300,000 markers under the incomplete LD model. Applications of several robust tests to the Wellcome Trust Case-Control Consortium [Nature 447 (2007) 661--678] are presented.
emcee: The MCMC Hammer

We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (). The code is open source and has already been used in several published projects in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to ∼N2 for a traditional algorithm in an N-dimensional parameter space. In this document, we describe the algorithm and the details of our implementation. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort. The code is available online at http://dan.iel. fm/emcee under the GNU General Public License v2.
Highly efficient stepped wedge designs for clusters of unequal size

The stepped wedge design (SWD) is a form of cluster randomized trial, usually comparing two treatments, which is divided into time periods and sequences, with clusters allocated to sequences. Typically all sequences start with the standard treatment and end with the new treatment, with the change happening at different times in the different sequences. The clusters will usually differ in size but this is overlooked in much of the existing literature. This paper considers the case when clusters have different sizes and determines how efficient designs can be found. The approach uses an approximation to the variance of the treatment effect, which is expressed in terms of the proportions of clusters and of individuals allocated to each sequence of the design. The roles of these sets of proportions in determining an efficient design are discussed and illustrated using two SWDs, one in the treatment of sexually transmitted diseases and one in renal replacement therapy. Cluster‐balanced designs, which allocate equal numbers of clusters to each sequence, are shown to have excellent statistical and practical properties; suggestions are made about the practical application of the results for these designs. The paper concentrates on the cross‐sectional case, where subjects are measured once, but it is briefly indicated how the methods can be extended to the closed‐cohort design.
The Stick-Breaking Construction of the Beta Process as a Poisson Process

We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tighter than those in the literature. We also develop a new MCMC inference algorithm for beta processes, based in part on our new Poisson process construction.
A quantile variant of the expectation–maximization algorithm and its application to parameter estimation with interval data

The expectation–maximization algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The expectation–maximization is best suited for situations where the expectation in each E-step and the maximization in each M-step are straightforward. A difficulty with the implementation of the expectation–maximization algorithm is that each E-step requires the integration of the log-likelihood function in closed form. The explicit integration can be avoided by using what is known as the Monte Carlo expectation–maximization algorithm. The Monte Carlo expectation–maximization uses a random sample to estimate the integral at each E-step. But the problem with the Monte Carlo expectation–maximization is that it often converges to the integral quite slowly and the convergence behavior can also be unstable, which causes computational burden. In this paper, we propose what we refer to as the quantile variant of the expectation–maximization algorithm. We prove that the proposed method has an accuracy of O ( 1 / K 2 ) , while the Monte Carlo expectation–maximization method has an accuracy of O p ( 1 / K ) . Thus, the proposed method possesses faster and more stable convergence properties when compared with the Monte Carlo expectation–maximization algorithm. The improved performance is illustrated through the numerical studies. Several practical examples illustrating its use in interval-censored data problems are also provided.
Hub discovery in partial correlation graphical models

This paper treats the problem of screening a p-variate sample for strongly and multiply connected vertices in the partial correlation graph associated with the the partial correlation matrix of the sample. This problem, called hub screening, is important in many applications ranging from network security to computational biology to finance to social networks. In the area of network security, a node that becomes a hub of high correlation with neighboring nodes might signal anomalous activity such as a coordinated flooding attack. In the area of computational biology the set of hubs of a gene expression correlation graph can serve as potential targets for drug treatment to block a pathway or modulate host response. In the area of finance a hub might indicate a vulnerable financial instrument or sector whose collapse might have major repercussions on the market. In the area of social networks a hub of observed interactions between criminal suspects could be an influential ringleader. The techniques and theory presented in this paper permit scalable and reliable screening for such hubs. This paper extends our previous work on correlation screening [arXiv:1102.1204] to the more challenging problem of partial correlation screening for variables with a high degree of connectivity. In particular we consider 1) extension to the more difficult problem of screening for partial correlations exceeding a specified magnitude; 2) extension to screening variables whose vertex degree in the associated partial correlation graph, often called the concentration graph, exceeds a specified degree.
Moments Calculation for the Double Truncated Multivariate Normal Density

In the present article, we derive an explicit expression for the truncated mean and variance for the multivariate normal distribution with arbitrary rectangular double truncation. We use the moment generating approach of Tallis (1961) and extend it to general μ, Σ and all combinations of truncation. As part of the solution, we also give a formula for the bivariate marginal density of truncated multinormal variates. We also prove an invariance property of some elements of the inverse covariance after truncation. Computer algorithms for computing the truncated mean, variance and the bivariate marginal probabilities for doubly truncated multivariate normal variates have been written in R and are presented along with three examples.
Sufficient dimension reduction based on an ensemble of minimum average variance estimators

We introduce a class of dimension reduction estimators based on an ensemble of the minimum average variance estimates of functions that characterize the central subspace, such as the characteristic functions, the Box―Cox transformations and wavelet basis. The ensemble estimators exhaustively estimate the central subspace without imposing restrictive conditions on the predictors, and have the same convergence rate as the minimum average variance estimates. They are flexible and easy to implement, and allow repeated use of the available sample, which enhances accuracy. They are applicable to both univariate and multivariate responses in a unified form. We establish the consistency and convergence rate of these estimators, and the consistency of a cross validation criterion for order determination. We compare the ensemble estimators with other estimators in a wide variety of models, and establish their competent performance.
Efficient estimators : the use of neural networks to construct pseudo panels

Pseudo panels constituted with repeated cross-sections are good substitutes to true panel data. But individuals grouped in a cohort are not the same for successive periods, and it results in a measurement error and inconsistent estimators. The solution is to constitute cohorts of large numbers of individuals but as homogeneous as possible. This paper explains a new way to do this: by using a self-organizing map, whose properties are well suited to achieve these objectives. It is applied to a set of Canadian surveys, in order to estimate income elasticities for 18 consumption functions.
Bootstrap independence test for functional linear models

Functional data have been the subject of many research works over the last years. Functional regression is one of the most discussed issues. Specifically, significant advances have been made for functional linear regression models with scalar response. Let $(\mathcal{H}, )$ be a separable Hilbert space. We focus on the model $Y= +b+\varepsilon$, where $Y$ and $\varepsilon$ are real random variables, $X$ is an $\mathcal{H}$-valued random element, and the model parameters $b$ and $\Theta$ are in $\mathbb{R}$ and $\mathcal{H}$, respectively. Furthermore, the error satisfies that $E(\varepsilon|X)=0$ and $E(\varepsilon^2|X)=\sigma^2<\infty$. A consistent bootstrap method to calibrate the distribution of statistics for testing $H_0: \Theta=0$ versus $H_1: \Theta\neq 0$ is developed. The asymptotic theory, as well as a simulation study and a real data application illustrating the usefulness of our proposed bootstrap in practice, is presented.
Revisiting Guerry’s data: Introducing spatial constraints in multivariate analysis

Standard multivariate analysis methods aim to identify and summarize the main structures in large data sets containing the description of a number of observations by several variables. In many cases, spatial information is also available for each observation, so that a map can be associated to the multivariate data set. Two main objectives are relevant in the analysis of spatial multivariate data: summarizing covariation structures and identifying spatial patterns. In practice, achieving both goals simultaneously is a statistical challenge, and a range of methods have been developed that offer trade-offs between these two objectives. In an applied context, this methodological question has been and remains a major issue in community ecology, where species assemblages (i.e., covariation between species abundances) are often driven by spatial processes (and thus exhibit spatial patterns). In this paper we review a variety of methods developed in community ecology to investigate multivariate spatial patterns. We present different ways of incorporating spatial constraints in multivariate analysis and illustrate these different approaches using the famous data set on moral statistics in France published by Andr\'{e}-Michel Guerry in 1833. We discuss and compare the properties of these different approaches both from a practical and theoretical viewpoint.
A weighting method for simultaneous adjustment for confounding and joint exposure-outcome misclassifications

Joint misclassification of exposure and outcome variables can lead to considerable bias in epidemiological studies of causal exposure-outcome effects. In this paper, we present a new maximum likelihood based estimator for marginal causal effects that simultaneously adjusts for confounding and several forms of joint misclassification of the exposure and outcome variables. The proposed method relies on validation data for the construction of weights that account for both sources of bias. The weighting estimator, which is an extension of the outcome misclassification weighting estimator proposed by Gravel and Platt (Weighted estimation for confounded binary outcomes subject to misclassification. Stat Med 2018; 37: 425–436), is applied to reinfarction data. Simulation studies were carried out to study its finite sample properties and compare it with methods that do not account for confounding or misclassification. The new estimator showed favourable large sample properties in the simulations. Further research is needed to study the sensitivity of the proposed method and that of alternatives to violations of their assumptions. The implementation of the estimator is facilitated by a new R function (ipwm) in an existing R package (mecor).
Statistical challenges in microrheology

Microrheology is the study of the properties of a complex fluid through the diffusion dynamics of small particles, typically latex beads, moving through that material. Currently, it is the dominant technique in the study of the physical properties of biological fluids, of the material properties of membranes or the cytoplasm of cells, or of the entire cell. The theoretical underpinning of microrheology was given in Mason and Weitz (Physical Review Letters; 1995), who introduced a framework for the use of path data of diffusing particles to infer viscoelastic properties of its fluid environment. The multi‐particle tracking techniques that were subsequently developed have presented numerous challenges for experimentalists and theoreticians. This study describes some specific challenges that await the attention of statisticians and applied probabilists. We describe relevant aspects of the physical theory, current inferential efforts and simulation aspects of a central model for the dynamics of nano‐scale particles in viscoelastic fluids, the generalized Langevin equation.
Semiparametric Mixed Model for Evaluating Pathway-Environment Interaction

A biological pathway represents a set of genes that serves a particular cellular or a physiological function. The genes within the same pathway are expected to function together and hence may interact with each other. It is also known that many genes, and so pathways, interact with other environmental variables. However, no formal procedure has yet been developed to evaluate the pathway-environment interaction. In this article, we propose a semiparametric method to model the pathway-environment interaction. The method connects a least square kernel machine and a semiparametric mixed effects model. We model nonparametrically the environmental effect via a natural cubic spline. Both a pathway effect and an interaction between a pathway and an environmental effect are modeled nonparametrically via a kernel machine, and we estimate variance component representing an interaction effect under a semiparametric mixed effects model. We then employ a restricted likelihood ratio test and a score test to evaluate the main pathway effect and the pathway-environment interaction. The approach was applied to a genetic pathway data of Type II diabetes, and pathways with either a significant main pathway effect, an interaction effect or both were identified. Other methods previously developed determined many as having a significant main pathway effect only. Furthermore, among those significant pathways, we discovered some pathways having a significant pathway-environment interaction effect, a result that other methods would not be able to detect.
Self-exciting hurdle models for terrorist activity

A predictive model of terrorist activity is developed by examining the daily number of terrorist attacks in Indonesia from 1994 through 2007. The dynamic model employs a shot noise process to explain the self-exciting nature of the terrorist activities. This estimates the probability of future attacks as a function of the times since the past attacks. In addition, the excess of nonattack days coupled with the presence of multiple coordinated attacks on the same day compelled the use of hurdle models to jointly model the probability of an attack day and corresponding number of attacks. A power law distribution with a shot noise driven parameter best modeled the number of attacks on an attack day. Interpretation of the model parameters is discussed and predictive performance of the models is evaluated.
Stochastic model selection for Mixtures of Matrix-Normals

Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be estimated through the EM algorithm under the assumption that the number of components is known and fixed. In this work we introduce, develop and explore a Bayesian analysis of the model in order to provide a tool for simultaneous model estimation and model selection. The effectiveness of the proposed method is illustrated on a simulation study and on a real example.
Estimated VC dimension for risk bounds

Vapnik-Chervonenkis (VC) dimension is a fundamental measure of the generalization capacity of learning algorithms. However, apart from a few special cases, it is hard or impossible to calculate analytically. Vapnik et al. [10] proposed a technique for estimating the VC dimension empirically. While their approach behaves well in simulations, it could not be used to bound the generalization risk of classifiers, because there were no bounds for the estimation error of the VC dimension itself. We rectify this omission, providing high probability concentration results for the proposed estimator and deriving corresponding generalization bounds.
An alternative to the Baum-Welch recursions for hidden Markov models

We develop a recursion for hidden Markov model of any order h, which allows us to obtain the posterior distribution of the latent state at every occasion, given the previous h states and the observed data. With respect to the well-known Baum-Welch recursions, the proposed recursion has the advantage of being more direct to use and, in particular, of not requiring dummy renormalizations to avoid numerical problems. We also show how this recursion may be expressed in matrix notation, so as to allow for an efficient implementation, and how it may be used to obtain the manifest distribution of the observed data and for parameter estimation within the Expectation-Maximization algorithm. The approach is illustrated by an application to financial data which is focused on the study of the dynamics of the volatility level of log-returns.
Estimation and Inference for High Dimensional Generalized Linear Models: A Splitting and Smoothing Approach

The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into prevention strategies or treatment decisions for both patients and physicians. High dimensional inference, including confidence intervals and hypothesis testing, has sparked much interest. While much work has been done in the linear regression setting, there is lack of literature on inference for high dimensional generalized linear models. We propose a novel and computationally feasible method, which accommodates a variety of outcome types, including normal, binomial, and Poisson data. We use a “splitting and smoothing” approach, which splits samples into two parts, performs variable selection using one part and conducts partial regression with the other part. Averaging the estimates over multiple random splits, we obtain the smoothed estimates, which are numerically stable. We show that the estimates are consistent, asymptotically normal, and construct confidence intervals with proper coverage probabilities for all predictors. We examine the finite sample performance of our method by comparing it with the existing methods and applying it to analyze a lung cancer cohort study.