Miracle-dz/UniFAR-FTUs huggingface dataset:
Bayesian Nonparametric Estimation of a Unimodal Density via two $\mathbf{S}$-paths

A Bayesian nonparametric method for unimodal densities on the real line is provided by considering a class of species sampling mixture models containing random densities that are unimodal and not necessarily symmetric. This class of densities generalize the model considered by Brunner (1992, Statist. Probab. Lett.), in which the Dirichlet process is replaced by a more general class of species sampling models. A novel and explicit characterization of the posterior distribution via a finite mixture of two dependent $\mathbf{S}$-paths is derived. This results in a closed-form and tractable Bayes estimator for any unimodal density in terms of a finite sum over two $\mathbf{S}$-paths. To approximate this class of estimates, we propose a sequential importance sampling algorithm that exploits the idea of the accelerated path sampler, an efficient path-sampling Markov chain Monte Carlo method. Numerical simulations are given to demonstrate the practicality and the effectiveness of our methodology.
Mitigating Included- and Omitted-Variable Bias in Estimates of Disparate Impact

Managers, employers, policymakers, and others often seek to understand whether decisions are biased against certain groups. One popular analytic strategy is to estimate disparities after adjusting for observed covariates, typically with a regression model. This approach, however, suffers from two key statistical challenges. First, omitted-variable bias can skew results if the model does not adjust for all relevant factors; second, and conversely, included-variable bias -- a lesser-known phenomenon -- can skew results if the set of covariates includes irrelevant factors. Here we introduce a new, three-step statistical method, which we call risk-adjusted regression, to address both concerns in settings where decision makers have clearly measurable objectives. In the first step, we use all available covariates to estimate the value, or inversely, the risk, of taking a certain action, such as approving a loan application or hiring a job candidate. Second, we measure disparities in decisions after adjusting for these risk estimates alone, mitigating the problem of included-variable bias. Finally, in the third step, we assess the sensitivity of results to potential mismeasurement of risk, addressing concerns about omitted-variable bias. To do so, we develop a novel, non-parametric sensitivity analysis that yields tight bounds on the true disparity in terms of the average gap between true and estimated risk -- a single interpretable parameter that facilitates credible estimates. We demonstrate this approach on a detailed dataset of 2.2 million police stops of pedestrians in New York City, and show that traditional statistical tests of discrimination can substantially underestimate the magnitude of disparities.
More Investment in Research and Development for Better Education in the Future?

The question in this paper is whether R&D efforts affect education performance in small classes. Merging two datasets collected from the PISA studies and the World Development Indicators and using Learning Bayesian Networks, we prove the existence of a statistical causal relationship between investment in R&D of a country and its education performance (PISA scores). We also prove that the effect of R\&D on Education is long term as a country has to invest at least 10 years before beginning to improve the level of young pupils.
Graphon estimation via nearest neighbor algorithm and 2D fused lasso denoising

We propose a class of methods for graphon estimation based on exploiting connections with nonparametric regression. The idea is to construct an ordering of the nodes in the network, similar in spirit to Chan and Airoldi (2014). However, rather than only considering orderings based on the empirical degree as in Chan and Airoldi (2014), we use the nearest neighbor algorithm which is an approximating solution to the traveling salesman problem. This in turn can handle general distances $\hat{d}$ between the nodes, something that allows us to incorporate rich information of the network. Once an ordering is constructed, we formulate a 2D grid graph denoising problem that we solve through fused lasso regularization. For particular choices of the metric $\hat{d}$, we show that the corresponding two-step estimator can attain competitive rates when the true model is the stochastic block model, and when the underlying graphon is piecewise H\"{o}lder or it has bounded variation.
An estimator for the tail-index of graphex processes

Graphex processes resolve some pathologies in traditional random graph models, notably, providing models that are both projective and allow sparsity. In a recent paper, Caron and Rousseau (2017) show that for a large class of graphex models, the sparsity behaviour is governed by a single parameter: the tail-index of the function (the graphon) that parameterizes the model. We propose an estimator for this parameter and quantify its risk. Our estimator is a simple, explicit function of the degrees of the observed graph. In many situations of practical interest, the risk decays polynomially in the size of the observed graph. We illustrate the importance of a good estimator for the tail-index through the graph analogue of the unseen species problem. We also derive the analogous results for the bipartite graphex processes.
End-of-Use Core Triage in Extreme Scenarios Based on a Threshold Approach

Remanufacturing is a significant factor in securing sustainability through a circular economy. Sorting plays a significant role in remanufacturing pre-processing inspections. Its significance can increase when remanufacturing facilities encounter extreme situations, such as abnormally huge core arrivals. Our main objective in this work is switching from less efficient to a more efficient model and to characterize extreme behavior of core arrival in remanufacturing and applying the developed model to triage cores. Central tendency core flow models are not sufficient to handle extreme situations, however, complementary Extreme Value (EV) approaches have shown to improve model efficiency. Extreme core flows to remanufacturing facilities are rare but still likely and can adversely affect remanufacturing business operations. In this investigation, extreme end-of-use core flow is modelled by a threshold approach using the Generalized Pareto Distribution (GPD). It is shown that GPD has better performance than its maxima-block GEV counterpart from practical and data efficiency perspectives. The model is validated by a synthesized big dataset, tested by sophisticated statistical Anderson Darling (AD) test, and is applied to a case of extreme flow to a valve shop in order to predict probability of over-capacity arrivals that is critical in remanufacturing business management. Finally, the GPD model combined with triage strategies is used to initiate investigations into the efficacy of different triage methods in remanufacturing operations.
Manifold valued data analysis of samples of networks, with applications in corpus linguistics

Networks can be used in many applications, such as in the analysis of text documents, social interactions and brain activity. We develop a general framework for extrinsic statistical analysis of samples of networks, motivated by networks representing text documents in corpus linguistics. We identify networks with their graph Laplacian matrices, for which we define metrics, embeddings, tangent spaces, and a projection from Euclidean space to the space of graph Laplacians. This framework provides a way of computing means, performing principal component analysis and regression, and carrying out hypothesis tests, such as for testing for equality of means between two samples of networks. We apply the methodology to the set of novels by Jane Austen and Charles Dickens.
Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle

We study field equations for a weak anisotropic model on the tangent Lorentz bundle TM of a spacetime manifold. A geometrical extension of general relativity (GR) is considered by introducing the concept of local anisotropy, i.e. a direct dependence of geometrical quantities on observer 4−velocity. In this approach, we consider a metric on TM as the sum of an h-Riemannian metric structure and a weak anisotropic perturbation, field equations with extra terms are obtained for this model. As well, extended Raychaudhuri equations are studied in the framework of Finsler-like extensions. Canonical momentum and mass-shell equation are also generalized in relation to their GR counterparts. Quantization of the mass-shell equation leads to a generalization of the Klein–Gordon equation and dispersion relation for a scalar field. In this model the accelerated expansion of the universe can be attributed to the geometry itself. A cosmological bounce is modeled with the introduction of an anisotropic scalar field. Also, the electromagnetic field equations are directly incorporated in this framework.
Temporal correlation between the optical and γ-ray flux variations in the blazar 3C 454.3

Blazars show optical and γ-ray flux variations that are generally correlated, although there are exceptions. Here we present anomalous behaviour seen in the blazar 3C 454.3 based on an analysis of quasi-simultaneous data at optical, ultraviolet, X-ray, and γ-ray energies, spanning about 9 yr from 2008 August to 2017 February. We have identified four time intervals (epochs), A, B, D, and E, when the source showed large-amplitude optical flares. In epochs A and B the optical and γ-ray flares are correlated, while in D and E corresponding flares in γ-rays are weak or absent. In epoch B the degree of optical polarization strongly correlates with changes in optical flux during a short-duration optical flare superimposed on one of long duration. In epoch E the optical flux and degree of polarization are anticorrelated during both the rising and declining phases of the optical flare. We carried out broad-band spectral energy distribution (SED) modelling of the source for the flaring epochs A,B, D, and E, and a quiescent epoch, C. Our SED modelling indicates that optical flares with absent or weak corresponding γ-ray flares in epochs D and E could arise from changes in a combination of parameters, such as the bulk Lorentz factor, magnetic field, and electron energy density, or be due to changes in the location of the γ-ray-emitting regions.
Switching Regression Models and Causal Inference in the Presence of Discrete Latent Variables

Given a response $Y$ and a vector $X = (X^1, \dots, X^d)$ of $d$ predictors, we investigate the problem of inferring direct causes of $Y$ among the vector $X$. Models for $Y$ that use all of its causal covariates as predictors enjoy the property of being invariant across different environments or interventional settings. Given data from such environments, this property has been exploited for causal discovery. Here, we extend this inference principle to situations in which some (discrete-valued) direct causes of $ Y $ are unobserved. Such cases naturally give rise to switching regression models. We provide sufficient conditions for the existence, consistency and asymptotic normality of the MLE in linear switching regression models with Gaussian noise, and construct a test for the equality of such models. These results allow us to prove that the proposed causal discovery method obtains asymptotic false discovery control under mild conditions. We provide an algorithm, make available code, and test our method on simulated data. It is robust against model violations and outperforms state-of-the-art approaches. We further apply our method to a real data set, where we show that it does not only output causal predictors, but also a process-based clustering of data points, which could be of additional interest to practitioners.
A Potential Outcomes Approach to Answer Reviewing in Multiple-Choice Exams

Does reviewing previous answers during multiple-choice exams help examinees increase their final score? This article formalizes the question using a rigorous causal framework, the potential outcomes framework. Viewing examinees' reviewing status as a treatment and their final score as an outcome, the article first explains the challenges of identifying the causal effect of answer reviewing in regular exam-taking settings. In addition to the incapability of randomizing the treatment selection (reviewing status) and the lack of other information to make this selection process ignorable, the treatment variable itself is not fully known to researchers. Looking at examinees' answer sheet data, it is unclear whether an examinee who did not change his or her answer on a specific item reviewed it but retained the initial answer (treatment condition) or chose not to review it (control condition). Despite such challenges, however, the article develops partial identification strategies and shows that the sign of the answer reviewing effect can be reasonably inferred. By analyzing a statewide math assessment data set, the article finds that reviewing initial answers is generally beneficial for examinees.
Cosmology with powerful radio-loud AGNs

Immensely bright quasars and radio-loud active galactic nuclei (AGNs) provide an enticing opportunity to construct standard candles detectable up to the very early universe. An analytic theory is proposed to measure the distance to powerful Fanaroff & Riley type-II (FR-II) radio sources based on their integrated flux density across a broad range of radio frequencies, and the angular size and axial ratio of their synchrotron-emitting lobes. This technique can be used at low redshift to construct absolute standard candles in conjunction with X-ray observations of the host cluster, or at high redshift to measure the relative distances of objects and constrain the curvature of our Universe. Distances calculated with this method are consistent for dissimilar objects at the same redshift; the two lobes of Cygnus A have flux densities, linear sizes, and spectral break frequencies varying between 15 and 35 per cent yet their fitted distances are the same to within 7 per cent. These distance estimates together yield a transverse comoving distance to Cygnus A of 261 +70 -55 Mpc corresponding to a Hubble constant of H0 = 64 +17 -13 km s−1 Mpc−1. Large samples of suitable FR-II sources could provide a measure of the Hubble constant independent of existing techniques such as the cosmic microwave background, baryon acoustic oscillations, and type 1a supernovae.
Minimax optimal sequential hypothesis tests for Markov processes

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses is revisited and it is shown that the partial derivatives of the corresponding cost function are closely related to the performance metrics of the underlying sequential test. Second, an implicit characterization of the least favorable distributions for a given testing policy is stated. By combining the results on optimal sequential tests and least favorable distributions, sufficient conditions for a sequential test to be minimax optimal under general distributional uncertainties are obtained. The cost function of the minimax optimal test is further identified as a generalized $f$-dissimilarity and the least favorable distributions as those that are most similar with respect to this dissimilarity. Numerical examples for minimax optimal sequential tests under different uncertainties illustrate the theoretical results.
Doubly robust inference when combining probability and non‐probability samples with high dimensional data

We consider integrating a non‐probability sample with a probability sample which provides high dimensional representative covariate information of the target population. We propose a two‐step approach for variable selection and finite population inference. In the first step, we use penalized estimating equations with folded concave penalties to select important variables and show selection consistency for general samples. In the second step, we focus on a doubly robust estimator of the finite population mean and re‐estimate the nuisance model parameters by minimizing the asymptotic squared bias of the doubly robust estimator. This estimating strategy mitigates the possible first‐step selection error and renders the doubly robust estimator root n consistent if either the sampling probability or the outcome model is correctly specified.
Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models

Penalization of the likelihood by Jeffreys’ invariant prior, or a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial generalized linear models. The class of models includes logistic regression, where the Jeffreys-prior penalty is known additionally to reduce the asymptotic bias of the maximum likelihood estimator, and models with other commonly used link functions, such as probit and log-log. Shrinkage towards equiprobability across observations, relative to the maximum likelihood estimator, is established theoretically and studied through illustrative examples. Some implications of finiteness and shrinkage for inference are discussed, particularly when inference is based on Wald-type procedures. A widely applicable procedure is developed for computation of maximum penalized likelihood estimates, by using repeated maximum likelihood fits with iteratively adjusted binomial responses and totals. These theoretical results and methods underpin the increasingly widespread use of reduced-bias and similarly penalized binomial regression models in many applied fields.
PAC-BAYESIAN SUPERVISED CLASSIFICATION: The Thermodynamics of Statistical Learning

This monograph deals with adaptive supervised classification, using tools borrowed from statistical mechanics and information theory, stemming from the PACBayesian approach pioneered by David McAllester and applied to a conception of statistical learning theory forged by Vladimir Vapnik. Using convex analysis on the set of posterior probability measures, we show how to get local measures of the complexity of the classification model involving the relative entropy of posterior distributions with respect to Gibbs posterior measures. We then discuss relative bounds, comparing the generalization error of two classification rules, showing how the margin assumption of Mammen and Tsybakov can be replaced with some empirical measure of the covariance structure of the classification model.We show how to associate to any posterior distribution an effective temperature relating it to the Gibbs prior distribution with the same level of expected error rate, and how to estimate this effective temperature from data, resulting in an estimator whose expected error rate converges according to the best possible power of the sample size adaptively under any margin and parametric complexity assumptions. We describe and study an alternative selection scheme based on relative bounds between estimators, and present a two step localization technique which can handle the selection of a parametric model from a family of those. We show how to extend systematically all the results obtained in the inductive setting to transductive learning, and use this to improve Vapnik's generalization bounds, extending them to the case when the sample is made of independent non-identically distributed pairs of patterns and labels. Finally we review briefly the construction of Support Vector Machines and show how to derive generalization bounds for them, measuring the complexity either through the number of support vectors or through the value of the transductive or inductive margin.
M-estimation with the Trimmed ` 1 Penalty

We study high-dimensional estimators with the trimmed `1 penalty, which leaves the h largest parameter entries penalty-free. While optimization techniques for this nonconvex penalty have been studied, the statistical properties have not yet been analyzed. We present the first statistical analyses for M -estimation, and characterize support recovery, `∞ and `2 error of the trimmed `1 estimates as a function of the trimming parameter h. Our results show different regimes based on how h compares to the true support size. Our second contribution is a new algorithm for the trimmed regularization problem, which has the same theoretical convergence rate as difference of convex (DC) algorithms, but in practice is faster and finds lower objective values. Empirical evaluation of `1 trimming for sparse linear regression and graphical model estimation indicate that trimmed `1 can outperform vanilla `1 and non-convex alternatives. Our last contribution is to show that the trimmed penalty is beneficial beyond M -estimation, and yields promising results for two deep learning tasks: input structures recovery and network sparsification.
Gravity, Magnetic Field, and Turbulence: Relative Importance and Impact on Fragmentation in the Infrared Dark Cloud G34.43+00.24

We investigate the interplay between magnetic (B) field, gravity, and turbulence in the fragmentation process of cores within the filamentary infrared dark cloud G34.43+00.24. We observe the magnetic field morphology across G34.43, traced with thermal dust polarization at 350 μm with an angular resolution of 10″ (0.18 pc), and compare with the kinematics obtained from N2H+ across the filament. We derive local velocity gradients from N2H+, tracing motion in the plane of sky, and compare with the observed local B field orientations in the plane of sky. The B field orientations are found to be perpendicular to the long axis of the filament toward the MM1 and MM2 ridge, suggesting that the B field can guide material toward the filament. Toward MM3, the B field orientations appear more parallel to the filament and aligned with the elongated core of MM3, indicating a different role of the B field. In addition to a large-scale east–west velocity gradient, we find a close alignment between local B field orientations and local velocity gradients toward the MM1/MM2 ridge. This local correlation in alignment suggests that gas motions are influenced by the B field morphology or vice versa. Additionally, this alignment seems to become even closer with increasing integrated emission in N2H+, possibly indicating that a growing gravitational pull alignes the B field and gas motion more and more. We analyze and quantify B field, gravity, turbulence, and their relative importance toward the MM1, MM2, and MM3 regions with various techniques over two scales, a larger clump area at 2 pc scale and the smaller core area at 0.6 pc scale. While gravitational energy, B field, and turbulent pressure all grow systematically from large to small scale, the ratios among the three constituents clearly develop differently over scale. We propose that this varying relative importance between B field, gravity, and turbulence over scale drives and explains the different fragmentation types seen at subparsec scale (no fragmentation in MM1; aligned fragmentation in MM2; clustered fragmentation in MM3). We discuss uncertainties, subtleties, and the robustness of our conclusion, and we stress that a multiscale joint analysis is required to understand the dynamics in these systems.