Miracle-dz/UniFAR-FTUs huggingface dataset:
Prior and Likelihood Choices for Bayesian Matrix Factorisation on Small Datasets

In this paper, we study the effects of different prior and likelihood choices for Bayesian matrix factorisation, focusing on small datasets. These choices can greatly influence the predictive performance of the methods. We identify four groups of approaches: Gaussian-likelihood with real-valued priors, nonnegative priors, semi-nonnegative models, and finally Poisson-likelihood approaches. For each group we review several models from the literature, considering sixteen in total, and discuss the relations between different priors and matrix norms. We extensively compare these methods on eight real-world datasets across three application areas, giving both inter- and intra-group comparisons. We measure convergence runtime speed, cross-validation performance, sparse and noisy prediction performance, and model selection robustness. We offer several insights into the trade-offs between prior and likelihood choices for Bayesian matrix factorisation on small datasets - such as that Poisson models give poor predictions, and that nonnegative models are more constrained than real-valued ones.
A geostatistical framework for combining spatially referenced disease prevalence data from multiple diagnostics

Multiple diagnostic tests are often used due to limited resources or because they provide complementary information on the epidemiology of a disease under investigation. Existing statistical methods to combine prevalence data from multiple diagnostics ignore the potential overdispersion induced by the spatial correlations in the data. To address this issue, we develop a geostatistical framework that allows for joint modelling of data from multiple diagnostics by considering two main classes of inferential problems: (a) to predict prevalence for a gold‐standard diagnostic using low‐cost and potentially biased alternative tests; (b) to carry out joint prediction of prevalence from multiple tests. We apply the proposed framework to two case studies: mapping Loa loa prevalence in Central and West Africa, using miscroscopy, and a questionnaire‐based test called RAPLOA; mapping Plasmodium falciparum malaria prevalence in the highlands of Western Kenya using polymerase chain reaction and a rapid diagnostic test. We also develop a Monte Carlo procedure based on the variogram in order to identify parsimonious geostatistical models that are compatible with the data. Our study highlights (a) the importance of accounting for diagnostic‐specific residual spatial variation and (b) the benefits accrued from joint geostatistical modelling so as to deliver more reliable and precise inferences on disease prevalence.
Sequential model selection method for nonparametric autoregression

Abstract In this article, the nonparametric autoregression estimation problem for quadratic risks is considered. To this end, we develop a new adaptive sequential model selection method based on the efficient sequential kernel estimators proposed by Arkoun and Pergamenshchikov (2016). Moreover, we develop a new analytical tool for general regression models to obtain the non-asymptotic sharp oracle inequalities for both usual quadratic and robust quadratic risks. Then, we show that the constructed sequential model selection procedure is optimal in the sense of oracle inequalities.
A Computer Algebra System for R: Macaulay2 and the m2r Package

Algebraic methods have a long history in statistics. The most prominent manifestation of modern algebra in statistics can be seen in the field of algebraic statistics, which brings tools from commutative algebra and algebraic geometry to bear on statistical problems. Now over two decades old, algebraic statistics has applications in a wide range of theoretical and applied statistical domains. Nevertheless, algebraic statistical methods are still not mainstream, mostly due to a lack of easy off-the-shelf implementations. In this article we debut m2r, an R package that connects R to Macaulay2 through a persistent back-end socket connection running locally or on a cloud server. Topics range from basic use of m2r to applications and design philosophy.
New Risk Bounds for 2D Total Variation Denoising

2D Total Variation Denoising (TVD) is a widely used technique for image denoising. It is also an important nonparametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to be nearly minimax rate optimal for the class of functions with bounded variation. In this paper, we complement these worst case guarantees by investigating the adaptivity of the TVD estimator to functions which are piecewise constant on axis aligned rectangles. We rigorously show that, when the truth is piecewise constant with few pieces, the ideally tuned TVD estimator performs better than in the worst case. We also study the issue of choosing the tuning parameter. In particular, we propose a fully data driven version of the TVD estimator which enjoys similar worst case risk guarantees as the ideally tuned TVD estimator.
Simulation of elliptic and hypo-elliptic conditional diffusions

Abstract Suppose X is a multidimensional diffusion process. Assume that at time zero the state of X is fully observed, but at time $T>0$ only linear combinations of its components are observed. That is, one only observes the vector $L X_T$ for a given matrix L. In this paper we show how samples from the conditioned process can be generated. The main contribution of this paper is to prove that guided proposals, introduced in [35], can be used in a unified way for both uniformly elliptic and hypo-elliptic diffusions, even when L is not the identity matrix. This is illustrated by excellent performance in two challenging cases: a partially observed twice-integrated diffusion with multiple wells and the partially observed FitzHugh–Nagumo model.
Sparse Convolved Multiple Output G aussian Processes

Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appropriate covariance function that, whilst being positive semi-definite, captures the dependencies between all the data points and across all the outputs. One approach to account for non-trivial correlations between outputs employs convolution processes. Under a latent function interpretation of the convolution transform we establish dependencies between output variables. The main drawbacks of this approach are the associated computational and storage demands. In this paper we address these issues. We present different sparse approximations for dependent output Gaussian processes constructed through the convolution formalism. We exploit the conditional independencies present naturally in the model. This leads to a form of the covariance similar in spirit to the so called PITC and FITC approximations for a single output. We show experimental results with synthetic and real data, in particular, we show results in pollution prediction, school exams score prediction and gene expression data.
Diverse correlation structures in gene expression data and their utility in improving statistical inference

It is well known that correlations in microarray data represent a serious nuisance deteriorating the performance of gene selection procedures. This paper is intended to demonstrate that the correlation structure of microarray data provides a rich source of useful information. We discuss distinct correlation substructures revealed in microarray gene expression data by an appropriate ordering of genes. These substructures include stochastic proportionality of expression signals in a large percentage of all gene pairs, negative correlations hidden in ordered gene triples, and a long sequence of weakly dependent random variables associated with ordered pairs of genes. The reported striking regularities are of general biological interest and they also have far-reaching implications for theory and practice of statistical methods of microarray data analysis. We illustrate the latter point with a method for testing differential expression of nonoverlapping gene pairs. While designed for testing a different null hypothesis, this method provides an order of magnitude more accurate control of type I error rate compared to conventional methods of individual gene expression profiling. In addition, this method is robust to the technical noise. Quantitative inference of the correlation structure has the potential to extend the analysis of microarray data far beyond currently practiced methods.
A Quantile-Based g-Computation Approach to Addressing the Effects of Exposure Mixtures

Background: Exposure mixtures frequently occur in data across many domains, particularly in the fields of environmental and nutritional epidemiology. Various strategies have arisen to answer questions about exposure mixtures, including methods such as weighted quantile sum (WQS) regression that estimate a joint effect of the mixture components. Objectives: We demonstrate a new approach to estimating the joint effects of a mixture: quantile g-computation. This approach combines the inferential simplicity of WQS regression with the flexibility of g-computation, a method of causal effect estimation. We use simulations to examine whether quantile g-computation and WQS regression can accurately and precisely estimate the effects of mixtures in a variety of common scenarios. Methods: We examine the bias, confidence interval (CI) coverage, and bias–variance tradeoff of quantile g-computation and WQS regression and how these quantities are impacted by the presence of noncausal exposures, exposure correlation, unmeasured confounding, and nonlinearity of exposure effects. Results: Quantile g-computation, unlike WQS regression, allows inference on mixture effects that is unbiased with appropriate CI coverage at sample sizes typically encountered in epidemiologic studies and when the assumptions of WQS regression are not met. Further, WQS regression can magnify bias from unmeasured confounding that might occur if important components of the mixture are omitted from the analysis. Discussion: Unlike inferential approaches that examine the effects of individual exposures while holding other exposures constant, methods like quantile g-computation that can estimate the effect of a mixture are essential for understanding the effects of potential public health actions that act on exposure sources. Our approach may serve to help bridge gaps between epidemiologic analysis and interventions such as regulations on industrial emissions or mining processes, dietary changes, or consumer behavioral changes that act on multiple exposures simultaneously. https://doi.org/10.1289/EHP5838
Separating common (global and local) and distinct variation in multiple mixed types data sets

Multiple sets of measurements on the same objects obtained from different platforms may reflect partially complementary information of the studied system. The integrative analysis of such data sets not only provides us with the opportunity of a deeper understanding of the studied system but also introduces some new statistical challenges. First, the separation of information that is common across all or some of the data sets and the information that is specific to each data set is problematic. Furthermore, these data sets are often a mix of quantitative and discrete (binary or categorical) data types, while commonly used data fusion methods require all data sets to be quantitative. In this paper, we propose an exponential family simultaneous component analysis (ESCA) model to tackle the potential mixed data types problem of multiple data sets. In addition, a structured sparse pattern of the loading matrix is induced through a nearly unbiased group concave penalty to disentangle the global, local common, and distinct information of the multiple data sets. A Majorization‐Minimization–based algorithm is derived to fit the proposed model. Analytic solutions are derived for updating all the parameters of the model in each iteration, and the algorithm will decrease the objective function in each iteration monotonically. For model selection, a missing value–based cross validation procedure is implemented. The advantages of the proposed method in comparison with other approaches are assessed using comprehensive simulations as well as the analysis of real data from a chronic lymphocytic leukaemia (CLL) study.
High-dimensional Stochastic Inversion via Adjoint Models and Machine Learning

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even with gradient information provided. Moreover, the `nonlinear' mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, characterized by a tight coupling between a gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the `curse-of-dimensionality' via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated spatial random field. Moreover, non-Gaussian full posterior probability distribution functions are estimated via an efficient LMCMC method on both the projected low-dimensional feature space and the recovered high-dimensional parameter space. We demonstrate this computational framework by integrating and adapting recent developments such as data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to solve inverse problems in linear elasticity.
Estimating Population Average Causal Effects in the Presence of Non-Overlap: A Bayesian Approach

Most causal inference studies rely on the assumption of positivity, or overlap, to identify population or sample average causal effects. When this assumption is violated, these estimands are unidentifiable without some degree of reliance on model specifications, due to poor data support. Existing methods to address non-overlap, such as trimming or down-weighting data in regions of poor support, all suffer from the limitation of changing the estimand. The change in estimand may diminish the impact of the study results, particularly for studies intended to influence policy, because estimates may not be representative of effects in the population of interest to policymakers. Researchers may be willing to make additional, minimal modeling assumptions in order to preserve the ability to estimate population average causal effects. We seek to make two contributions on this topic. First, we propose systematic definitions of propensity score overlap and non-overlap regions. Second, we develop a novel Bayesian framework to estimate population average causal effects with nominal model dependence and appropriately large uncertainties in the presence of non-overlap and causal effect heterogeneity. In this approach, the tasks of estimating causal effects in the overlap and non-overlap regions are delegated to two distinct models. Tree ensembles are selected to non-parametrically estimate individual causal effects in the overlap region, where the data can speak for themselves. In the non-overlap region, where insufficient data support means reliance on model specification is necessary, individual causal effects are estimated by extrapolating trends from the overlap region via a spline model. The promising performance of our method is demonstrated in simulations. Finally, we utilize our method to perform a novel investigation of the effect of natural gas compressor station exposure on cancer outcomes.
Implementation of Frequency-Severity Association in BMS Ratemaking

A Bonus-Malus System (BMS) in insurance is a premium adjustment mechanism widely used in a posteriori ratemaking process to set the premium for the next contract period based on a policyholder's claim history. The current practice in BMS implementation relies on the assumption of independence between claim frequency and severity, despite the fact that a series of recent studies report evidence of a significant frequency-severity relationship, particularly in automobile insurance. To address this discrepancy, we propose a copula-based correlated random effects model to accommodate the dependence between claim frequency and severity, and further illustrate how to incorporate such dependence into the current BMS. We derive analytical solutions to the optimal relativities under the proposed framework and provide numerical experiments based on real data analysis to assess the effect of frequency-severity dependence in BMS ratemaking.
A Note on Bayesian Nonparametric Inference for Spherically Symmetric Distribution

In this paper, we describe a Bayesian nonparametric approach to make inference for a bivariate spherically symmetric distribution. We consider a Dirichlet invariant process prior on the set of all bivariate spherically symmetric distributions and we derive the Dirichlet invariant process posterior. Indeed, our approach is an extension of Dirichlet invariant process for the symmetric distributions on the real line to a bivariate spherically symmetric distribution where the underlying distribution is invariant under a finite group of rotations. Moreover, we obtain the Dirichlet invariant process posterior for the infinite transformation group and we prove that it approaches to Dirichlet process.
Putative spin-nematic phase in 
BaCdVO(PO4)2

We report neutron scattering and AC magnetic susceptibility measurements of the 2D spin-1/2 frustrated magnet BaCdVO(PO$_{4}$)$_{2}$. At temperatures well below $T_{\sf N}\approx 1K$, we show that only 34 % of the spin moment orders in an up-up-down-down strip structure. Dominant magnetic diffuse scattering and comparison to published $\mu$sr measurements indicates that the remaining 66 % is fluctuating. This demonstrates the presence of strong frustration, associated with competing ferromagnetic and antiferromagnetic interactions, and points to a subtle ordering mechanism driven by magnon interactions. On applying magnetic field, we find that at $T=0.1$ K the magnetic order vanishes at 3.8 T, whereas magnetic saturation is reached only above 4.5 T. We argue that the putative high-field phase is a realization of the long-sought bond-spin-nematic state.
Sparse Regression: Scalable Algorithms and Empirical Performance

In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance to practitioners. We demonstrate empirically how noise and correlation impact both the accuracy - the number of correct features selected - and the false detection - the number of incorrect features selected - for five methods: the cardinality-constrained formulation, its Boolean relaxation, $\ell_1$ regularization and two methods with non-convex penalties. A cogent feature selection method is expected to exhibit a two-fold convergence, namely the accuracy and false detection rate should converge to $1$ and $0$ respectively, as the sample size increases. As a result, proper method should recover all and nothing but true features. Empirically, the integer optimization formulation and its Boolean relaxation are the closest to exhibit this two properties consistently in various regimes of noise and correlation. In addition, apart from the discrete optimization approach which requires a substantial, yet often affordable, computational time, all methods terminate in times comparable with the \verb|glmnet| package for Lasso. We released code for methods that were not publicly implemented. Jointly considered, accuracy, false detection and computational time provide a comprehensive assessment of each feature selection method and shed light on alternatives to the Lasso-regularization which are not as popular in practice yet.
Skew Adjustment Factors for Fragilities of California Box-Girder Bridges Subjected to near-Fault and Far-Field Ground Motions

Past reconnaissance studies revealed that bridges close to active faults are more susceptible to damage and more than 60% of the bridges in California are skewed. To assess the combined effect of near-fault ground motions and skewness, this paper evaluates the seismic vulnerability of skewed concrete box-girder bridges in California subjected to near-fault and far-field ground motions. The relative risk of skewness and fault-location on the bridges is evaluated by developing fragility curves of bridge components and system accounting for the material, geometric, and structural uncertainties. It is noted that the skewness and bridge site close to active faults make bridges more vulnerable, and the existing modification factor in HAZUS cannot capture the variation in the median value of the fragilities appropriately. A new set of fragility adjustment factors for skewness coupled with the effect of fault location is suggested in this paper.
A descriptive study of variable discretization and cost-sensitive logistic regression on imbalanced credit data

ABSTRACT Training classification models on imbalanced data tends to result in bias towards the majority class. In this paper, we demonstrate how variable discretization and cost-sensitive logistic regression help mitigate this bias on an imbalanced credit scoring dataset, and further show the application of the variable discretization technique on the data from other domains, demonstrating its potential as a generic technique for classifying imbalanced data beyond credit socring. The performance measurements include ROC curves, Area under ROC Curve (AUC), Type I Error, Type II Error, accuracy, and F1 score. The results show that proper variable discretization and cost-sensitive logistic regression with the best class weights can reduce the model bias and/or variance. From the perspective of the algorithm, cost-sensitive logistic regression is beneficial for increasing the value of predictors even if they are not in their optimized forms while maintaining monotonicity. From the perspective of predictors, the variable discretization performs better than cost-sensitive logistic regression, provides more reasonable coefficient estimates for predictors which have nonlinear relationships against their empirical logit, and is robust to penalty weights on misclassifications of events and non-events determined by their apriori proportions.
Synth-Validation: Selecting the Best Causal Inference Method for a Given Dataset

Many decisions in healthcare, business, and other policy domains are made without the support of rigorous evidence due to the cost and complexity of performing randomized experiments. Using observational data to answer causal questions is risky: subjects who receive different treatments also differ in other ways that affect outcomes. Many causal inference methods have been developed to mitigate these biases. However, there is no way to know which method might produce the best estimate of a treatment effect in a given study. In analogy to cross-validation, which estimates the prediction error of predictive models applied to a given dataset, we propose synth-validation, a procedure that estimates the estimation error of causal inference methods applied to a given dataset. In synth-validation, we use the observed data to estimate generative distributions with known treatment effects. We apply each causal inference method to datasets sampled from these distributions and compare the effect estimates with the known effects to estimate error. Using simulations, we show that using synth-validation to select a causal inference method for each study lowers the expected estimation error relative to consistently using any single method.