Miracle-dz/UniFAR-FTUs huggingface dataset:
Optimal Estimation for the Functional Cox Model

Functional covariates are common in many medical, biodemographic, and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study the asymptotic properties of the maximum partial likelihood estimator and establish the asymptotic normality and efficiency of the estimator of the finite-dimensional estimator. Under the framework of reproducing kernel Hilbert space, the estimator of the coefficient function for a functional covariate achieves the minimax optimal rate of convergence under a weighted $L_2$-risk. This optimal rate is determined jointly by the censoring scheme, the reproducing kernel and the covariance kernel of the functional covariates. Implementation of the estimation approach and the selection of the smoothing parameter are discussed in detail. The finite sample performance is illustrated by simulated examples and a real application.
Lipschitz partition processes

We introduce a family of Markov processes on set partitions with a bounded number of blocks, called Lipschitz partition processes. We construct these processes explicitly by a Poisson point process on the space of Lipschitz continuous maps on partitions. By this construction, the Markovian consistency property is readily satisfied; that is, the finite restrictions of any Lipschitz partition process comprise a compatible collection of finite state space Markov chains. We further characterize the class of exchangeable Lipschitz partition processes by a novel set-valued matrix operation.
On the evolution by fractional mean curvature

In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric quantities that yield preservation of certain quantities (such as positive fractional curvature) and smoothness of graphical evolutions.
Forecast dominance testing via sign randomization

We propose randomization tests of whether forecast 1 outperforms forecast 2 across a class of scoring functions. This hypothesis is of applied interest: While the prediction context often prescribes a certain class of scoring functions, it is typically hard to motivate a specific choice on statistical or substantive grounds. We investigate the asymptotic behavior of the test statistics under mild conditions, avoiding the need to assume particular dynamic properties of forecasts and realizations. The properties of the one-sided tests depend on a corresponding version of Anderson's inequality, which we state as a conjecture of independent interest. Numerical experiments and a data example indicate that the tests have good size and power properties in practically relevant situations.
On the quasi-stationary distribution of the Shiryaev–Roberts diffusion

ABSTRACT We consider the diffusion generated by the equation with fixed, and where μ≠0 is given, and is standard Brownian motion. We assume that is stopped at with A>0 preset, and obtain a closed-from formula for the quasi-stationary distribution of , i.e., the limit , x∈[0,A]. Further, we also prove QA(x) to be unimodal for any A>0, and obtain its entire moment series. More importantly, the pair with r≥0 and A>0 is the well-known Generalized Shiryaev–Roberts change-point detection procedure, and its characteristics for r∼QA(x) are of particular interest, especially when A>0 is large. In view of this circumstance, we offer an order-three large-A asymptotic approximation of QA(x) valid for all x∈[0,A]. The approximation is rather accurate even if A is lower than what would be considered “large” in practice.
Goodness-of-fit statistics for approximate Bayesian computation

Approximate Bayesian computation is a statistical framework that uses numerical simulations to calibrate and compare models. Instead of computing likelihood functions, Approximate Bayesian computation relies on numerical simulations, which makes it applicable to complex models in ecology and evolution. As usual for statistical modeling, evaluating goodness-of-fit is a fundamental step for Approximate Bayesian Computation. Here, we introduce a goodness-of-fit approach based on hypothesis-testing. We introduce two test statistics based on the mean distance between numerical summaries of the data and simulated ones. One test statistic relies on summaries simulated with the prior predictive distribution whereas the other one relies on simulations from the posterior predictive distribution. For different coalescent models, we find that the statistics are well calibrated, meaning that the type I error can be controlled. However, the statistical power of the two statistics is extremely variable across models ranging from 20% to 100%. The difference of power between the two statistics is negligible in models of demographic inference but substantial in an additional and purely statistical example. When analyzing resequencing data to evaluate models of human demography, the two statistics confirm that an out-of-Africa bottleneck cannot be rejected for Asiatic and European data. We also consider two speciation models in the context of a butterfly species complex. One goodness-of-fit statistic indicates a poor fit for both models, and the numerical summaries causing the poor fit were identified using posterior predictive checks. Statistical tests for goodness-of-fit should foster evaluation of model fit in Approximate Bayesian Computation. The test statistic based on simulations from the prior predictive distribution is implemented in the gfit function of the R abc package.
Transfer Learning via Latent Factor Modeling to Improve Prediction of Surgical Complications

We aim to create a framework for transfer learning using latent factor models to learn the dependence structure between a larger source dataset and a target dataset. The methodology is motivated by our goal of building a risk-assessment model for surgery patients, using both institutional and national surgical outcomes data. The national surgical outcomes data is collected through NSQIP (National Surgery Quality Improvement Program), a database housing almost 4 million patients from over 700 different hospitals. We build a latent factor model with a hierarchical prior on the loadings matrix to appropriately account for the different covariance structure in our data. We extend this model to handle more complex relationships between the populations by deriving a scale mixture formulation using stick-breaking properties. Our model provides a transfer learning framework that utilizes all information from both the source and target data, while modeling the underlying inherent differences between them.
Regularization and Variable Selection with Copula Prior

In this work, we show that under specific choices of the copula, the lasso, elastic net, and $g$-prior are particular cases of `copula prior,' for regularization and variable selection method. We present `lasso with Gauss copula prior' and `lasso with t-copula prior. ' The simulation study and real-world data for regression, classification, and large time-series data show that the `copula prior' often outperforms the lasso and elastic net while having a comparable sparsity of representation. Also, the copula prior encourages a grouping effect. The strongly correlated predictors tend to be in or out of the model collectively under the copula prior. The `copula prior' is a generic method, which can be used to define the new prior distribution. The application of copulas in modeling prior distribution for Bayesian methodology has not been explored much. We present the resampling-based optimization procedure to handle big data with copula prior.
Microwave breast cancer detection using Empirical Mode Decomposition features

Microwave-based breast cancer detection has been proposed as a complementary approach to compensate for some drawbacks of existing breast cancer detection techniques. Among the existing microwave breast cancer detection methods, machine learning-type algorithms have recently become more popular. These focus on detecting the existence of breast tumours rather than performing imaging to identify the exact tumour position. A key step of the machine learning approaches is feature extraction. One of the most widely used feature extraction method is principle component analysis (PCA). However, it can be sensitive to signal misalignment. This paper presents an empirical mode decomposition (EMD)-based feature extraction method, which is more robust to the misalignment. Experimental results involving clinical data sets combined with numerically simulated tumour responses show that combined features from EMD and PCA improve the detection performance with an ensemble selection-based classifier.
A Consistent Bayesian Formulation for Stochastic Inverse Problems Based on Push-forward Measures

We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is derived using a Bayesian updating approach for measurable maps that finds a posterior probability measure, that when propagated through the deterministic model produces a push-forward measure that exactly matches the observed probability measure on the data. Our approach for finding such posterior measures, which we call consistent Bayesian inference, is simple and only requires the computation of the push-forward probability measure induced by the combination of a prior probability measure and the deterministic model. We establish existence and uniqueness of observation-consistent posteriors and present stability and error analysis. We also discuss the relationships between consistent Bayesian inference, classical/statistical Bayesian inference, and a recently developed measure-theoretic approach for inference. Finally, analytical and numerical results are presented to highlight certain properties of the consistent Bayesian approach and the differences between this approach and the two aforementioned alternatives for inference.
Robust and scalable Bayesian analysis of spatial neural tuning function data

A common analytical problem in neuroscience is the interpretation of neural activity with respect to sensory input or behavioral output. This is typically achieved by regressing measured neural activity against known stimuli or behavioral variables to produce a "tuning function" for each neuron. Unfortunately, because this approach handles neurons individually, it cannot take advantage of simultaneous measurements from spatially adjacent neurons that often have similar tuning properties. On the other hand, sharing information between adjacent neurons can errantly degrade estimates of tuning functions across space if there are sharp discontinuities in tuning between nearby neurons. In this paper, we develop a computationally efficient block Gibbs sampler that effectively pools information between neurons to de-noise tuning function estimates while simultaneously preserving sharp discontinuities that might exist in the organization of tuning across space. This method is fully Bayesian and its computational cost per iteration scales sub-quadratically with total parameter dimensionality. We demonstrate the robustness and scalability of this approach by applying it to both real and synthetic datasets. In particular, an application to data from the spinal cord illustrates that the proposed methods can dramatically decrease the experimental time required to accurately estimate tuning functions.
Predictive Characterization of Mixtures of Markov Chains

Predictive constructions are a powerful way of characterizing the probability law of stochastic processes with certain forms of invariance, such as exchangeability or Markov exchangeability. When de Finetti-like representation theorems are available, the predictive characterization implicitly defines the prior distribution, starting from assumptions on the observables; moreover, it often helps designing efficient computational strategies. In this paper we give necessary and sufficient conditions on the sequence of predictive distributions such that they characterize a Markov exchangeable probability law for a discrete valued process X. Under recurrence, Markov exchangeable processes are mixtures of Markov chains. Thus, our results help checking when a predictive scheme characterizes a prior for Bayesian inference on the unknown transition matrix of a Markov chain. Our predictive conditions are in some sense minimal sufficient conditions for Markov exchangeability; we also provide predictive conditions for recurrence. We illustrate their application in relevant examples from the literature and in novel constructions.
Confidence regions for high-dimensional generalized linear models under sparsity

We study asymptotically normal estimation and confidence regions for low-dimensional parameters in high-dimensional sparse models. Our approach is based on the $\ell_1$-penalized M-estimator which is used for construction of a bias corrected estimator. We show that the proposed estimator is asymptotically normal, under a sparsity assumption on the high-dimensional parameter, smoothness conditions on the expected loss and an entropy condition. This leads to uniformly valid confidence regions and hypothesis testing for low-dimensional parameters. The present approach is different in that it allows for treatment of loss functions that we not sufficiently differentiable, such as quantile loss, Huber loss or hinge loss functions. We also provide new results for estimation of the inverse Fisher information matrix, which is necessary for the construction of the proposed estimator. We formulate our results for general models under high-level conditions, but investigate these conditions in detail for generalized linear models and provide mild sufficient conditions. As particular examples, we investigate the case of quantile loss and Huber loss in linear regression and demonstrate the performance of the estimators in a simulation study and on real datasets from genome-wide association studies. We further investigate the case of logistic regression and illustrate the performance of the estimator on simulated and real data.
Integrating multiple random sketches for singular value decomposition

The singular value decomposition (SVD) of large-scale matrices is a key tool in data analytics and scientific computing. The rapid growth in the size of matrices further increases the need for developing efficient large-scale SVD algorithms. Randomized SVD based on one-time sketching has been studied, and its potential has been demonstrated for computing a low-rank SVD. Instead of exploring different single random sketching techniques, we propose a Monte Carlo type integrated SVD algorithm based on multiple random sketches. The proposed integration algorithm takes multiple random sketches and then integrates the results obtained from the multiple sketched subspaces. So that the integrated SVD can achieve higher accuracy and lower stochastic variations. The main component of the integration is an optimization problem with a matrix Stiefel manifold constraint. The optimization problem is solved using Kolmogorov-Nagumo-type averages. Our theoretical analyses show that the singular vectors can be induced by population averaging and ensure the consistencies between the computed and true subspaces and singular vectors. Statistical analysis further proves a strong Law of Large Numbers and gives a rate of convergence by the Central Limit Theorem. Preliminary numerical results suggest that the proposed integrated SVD algorithm is promising.
A Decision Theoretic Approach to A/B Testing

A/B testing is ubiquitous within the machine learning and data science operations of internet companies. Generically, the idea is to perform a statistical test of the hypothesis that a new feature is better than the existing platform---for example, it results in higher revenue. If the p value for the test is below some pre-defined threshold---often, 0.05---the new feature is implemented. The difficulty of choosing an appropriate threshold has been noted before, particularly because dependent tests are often done sequentially, leading some to propose control of the false discovery rate (FDR) rather than use of a single, universal threshold. However, it is still necessary to make an arbitrary choice of the level at which to control FDR. Here we suggest a decision-theoretic approach to determining whether to adopt a new feature, which enables automated selection of an appropriate threshold. Our method has the basic ingredients of any decision-theory problem: a loss function, action space, and a notion of optimality, for which we choose Bayes risk. However, the loss function and the action space differ from the typical choices made in the literature, which has focused on the theory of point estimation. We give some basic results for Bayes-optimal thresholding rules for the feature adoption decision, and give some examples using eBay data. The results suggest that the 0.05 p-value threshold may be too conservative in some settings, but that its widespread use may reflect an ad-hoc means of controlling multiplicity in the common case of repeatedly testing variants of an experiment when the threshold is not reached.
SAGA and Restricted Strong Convexity

SAGA is a fast incremental gradient method on the finite sum problem and its effectiveness has been tested on a vast of applications. In this paper, we analyze SAGA on a class of non-strongly convex and non-convex statistical problem such as Lasso, group Lasso, Logistic regression with $\ell_1$ regularization, linear regression with SCAD regularization and Correct Lasso. We prove that SAGA enjoys the linear convergence rate up to the statistical estimation accuracy, under the assumption of restricted strong convexity (RSC). It significantly extends the applicability of SAGA in convex and non-convex optimization.
Segmentation of multiple series using a Lasso strategy

We propose a new semi-parametric approach to the joint segmentation of multiple series corrupted by a functional part. This problem appears in particular in geodesy where GPS permanent station coordinate series are affected by undocumented artificial abrupt changes and additionally show prominent periodic variations. Detecting and estimating them are crucial, since those series are used to determine averaged reference coordinates in geosciences and to infer small tectonic motions induced by climate change. We propose an iterative procedure based on Dynamic Programming for the segmentation part and Lasso estimators for the functional part. Our Lasso procedure, based on the dictionary approach, allows us to both estimate smooth functions and functions with local irregularity, which permits more flexibility than previous proposed methods. This yields to a better estimation of the bias part and improvements in the segmentation. The performance of our method is assessed using simulated and real data. In particular, we apply our method to data from four GPS stations in Yarragadee, Australia. Our estimation procedure results to be a reliable tool to assess series in terms of change detection and periodic variations estimation giving an interpretable estimation of the functional part of the model in terms of known functions.
A Non-Gaussian, Nonparametric Structure for Gene-Gene and Gene-Environment Interactions in Case-Control Studies Based on Hierarchies of Dirichlet Processes

It is becoming increasingly clear that complex interactions among genes and environmental factors play crucial roles in triggering complex diseases. Thus, understanding such interactions is vital, which is possible only through statistical models that adequately account for such intricate, albeit unknown, dependence structures. Bhattacharya & Bhattacharya (2016b) attempt such modeling, relating finite mixtures composed of Dirichlet processes that represent unknown number of genetic sub-populations through a hierarchical matrix-normal structure that incorporates gene-gene interactions, and possible mutations, induced by environmental variables. However, the product dependence structure implied by their matrix-normal model seems to be too simple to be appropriate for general complex, realistic situations. In this article, we propose and develop a novel nonparametric Bayesian model for case-control genotype data using hierarchies of Dirichlet processes that offers a more realistic and nonparametric dependence structure between the genes, induced by the environmental variables. In this regard, we propose a novel and highly parallelisable MCMC algorithm that is rendered quite efficient by the combination of modern parallel computing technology, effective Gibbs sampling steps, retrospective sampling and Transformation based Markov Chain Monte Carlo (TMCMC). We use appropriate Bayesian hypothesis testing procedures to detect the roles of genes and environment in case-control studies. We apply our ideas to 5 biologically realistic case-control genotype datasets simulated under distinct set-ups, and obtain encouraging results in each case. We finally apply our ideas to a real, myocardial infarction dataset, and obtain interesting results on gene-gene and gene-environment interaction, while broadly agreeing with the results reported in the literature.
Main and Interaction Effects Selection for Quadratic Discriminant Analysis via Penalized Linear Regression

Discriminant analysis is a useful classification method. Variable selection for discriminant analysis is becoming more and more im- portant in a high-dimensional setting. This paper is concerned with the binary-class problems of main and interaction effects selection for the quadratic discriminant analysis. We propose a new penalized quadratic discriminant analysis (QDA) for variable selection in binary classification. Under sparsity assumption on the relevant variables, we conduct a penalized liner regression to derive sparse QDA by plug- ging the main and interaction effects in the model. Then the QDA problem is converted to a penalized sparse ordinary least squares op- timization by using the composite absolute penalties (CAP). Coor- dinate descent algorithm is introduced to solve the convex penalized least squares. The penalized linear regression can simultaneously se- lect the main and interaction effects, and also conduct classification. Compared with the existing methods of variable selection in QDA, the extensive simulation studies and two real data analyses demon- strate that our proposed method works well and is robust in the performance of variable selection and classification.
Nonconvex Penalization in Sparse Estimation: An Approach Based on the Bernstein Function

In this paper we study nonconvex penalization using Bernstein functions whose first-order derivatives are completely monotone. The Bernstein function can induce a class of nonconvex penalty functions for high-dimensional sparse estimation problems. We derive a thresholding function based on the Bernstein penalty and discuss some important mathematical properties in sparsity modeling. We show that a coordinate descent algorithm is especially appropriate for regression problems penalized by the Bernstein function. We also consider the application of the Bernstein penalty in classification problems and devise a proximal alternating linearized minimization method. Based on theory of the Kurdyka-Lojasiewicz inequality, we conduct convergence analysis of these alternating iteration procedures. We particularly exemplify a family of Bernstein nonconvex penalties based on a generalized Gamma measure and conduct empirical analysis for this family.