Miracle-dz/UniFAR-FTUs huggingface dataset:
Variational inference for count response semiparametric regression

Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e. a non-negative integer. We treat both the Poisson and Negative Binomial families as models for the response variable. Our approach utilizes recently developed methodology known as non-conjugate variational message passing. For concreteness, we focus on generalized additive mixed models, although our variational approximation approach extends to a wide class of semiparametric regression models such as those containing interactions and elaborate random effect structure.
Group bound: confidence intervals for groups of variables in sparse high dimensional regression without assumptions on the design

It is in general challenging to provide confidence intervals for individual variables in high dimensional regression without making strict or unverifiable assumptions on the design matrix. We show here that a ‘group bound’ confidence interval can be derived without making any assumptions on the design matrix. The lower bound for the regression coefficient of individual variables can be derived via linear programming. The idea also generalizes naturally to groups of variables, where we can derive a one‐sided confidence interval for the joint effect of a group. Although the confidence intervals of individual variables are by the nature of the problem often very wide, it is shown to be possible to detect the contribution of groups of highly correlated predictor variables even when no variable individually shows a significant effect. The assumptions that are necessary to detect the effect of groups of variables are shown to be weaker than the weakest known assumptions that are necessary to detect the effect of individual variables.
Estimation and Inference for Linear Panel Data Models Under Misspecification When Both n and T are Large

This article considers fixed effects (FE) estimation for linear panel data models under possible model misspecification when both the number of individuals, n, and the number of time periods, T, are large. We first clarify the probability limit of the FE estimator and argue that this probability limit can be regarded as a pseudo-true parameter. We then establish the asymptotic distributional properties of the FE estimator around the pseudo-true parameter when n and T jointly go to infinity. Notably, we show that the FE estimator suffers from the incidental parameters bias of which the top order is O(T− 1), and even after the incidental parameters bias is completely removed, the rate of convergence of the FE estimator depends on the degree of model misspecification and is either (nT)− 1/2 or n− 1/2. Second, we establish asymptotically valid inference on the (pseudo-true) parameter. Specifically, we derive the asymptotic properties of the clustered covariance matrix (CCM) estimator and the cross-section bootstrap, and show that they are robust to model misspecification. This establishes a rigorous theoretical ground for the use of the CCM estimator and the cross-section bootstrap when model misspecification and the incidental parameters bias (in the coefficient estimate) are present. We conduct Monte Carlo simulations to evaluate the finite sample performance of the estimators and inference methods, together with a simple application to the unemployment dynamics in the U.S.
Finding the basic neighborhood in variable range Markov random fields: application in SNP association studies

The SNPs (Single Nucleotide Polymorphisms) genotyping platforms are of great value for gene mapping of complex diseases. Nowadays, the high-density of these molecular markers enables studies of dependence patterns between loci over the genome, allowing a simultaneous inference of dependence structure and disease association. In this paper we propose a method based on the theory of variable range Markov random fields to estimate the extent of dependence among SNPs allowing variable windows along the genome. The advantage of this method is that it allows the simultaneous prediction of dependence and independence regions among SNPs, without restricting a priori the range of dependence. We introduce an estimator based on the idea of penalized maximum likelihood to find the conditional dependence neighborhood of each SNP in the sample and we prove its consistency. We apply our method to autosomal SNPs genotypic data with unknown phase in the context of case-control association studies. By examining rheumatoid arthritis data from the Genetic Analysis Workshop 16 (GAW16), we show the utility of the Markov model under variable range dependence.
The SWELLS survey – VI. Hierarchical inference of the initial mass functions of bulges and discs

The long-standing assumption that the stellar initial mass function (IMF) is universal has recently been challenged by a number of observations. Several studies have shown that a \heavy" IMF (e.g., with a Salpeter-like abundance of low mass stars and thus normalisation) is preferred for massive early-type galaxies, while this IMF is inconsistent with the properties of less massive, later-type galaxies. These discoveries motivate the hypothesis that the IMF may vary (possibly very slightly) across galaxies and across components of individual galaxies (e.g. bulges vs discs). In this paper we use a sample of 19 late-type strong gravitational lenses from the SWELLS survey to investigate the IMFs of the bulges and discs in late-type galaxies. We perform a joint analysis of the galaxies’ total masses (constrained by strong gravitational lensing) and stellar masses (constrained by optical and near-infrared colors in the context of a stellar population synthesis [SPS] model, up to an IMF normalisation parameter). Using minimal assumptions apart from the physical constraint that the total stellar mass m within any aperture must be less than the total mass mtot within the aperture, we nd that the bulges of the galaxies cannot have IMFs heavier (i.e. implying high mass per unit luminosity) than Salpeter, while the disc IMFs are not well constrained by this data set. We also discuss the necessity for hierarchical modelling when combining incomplete information about multiple astronomical objects. This modelling approach allows us to place upper limits on the size of any departures from universality. More data, including spatially resolved kinematics (as in paper V) and stellar population diagnostics over a range of bulge and disc masses, are needed to robustly quantify how the IMF varies within galaxies.
Kinetic Energy Plus Penalty Functions for Sparse Estimation

In this paper we propose and study a family of sparsity-inducing penalty functions. Since the penalty functions are related to the kinetic energy in special relativity, we call them \emph{kinetic energy plus} (KEP) functions. We construct the KEP function by using the concave conjugate of a $\chi^2$-distance function and present several novel insights into the KEP function with $q=1$. In particular, we derive a thresholding operator based on the KEP function, and prove its mathematical properties and asymptotic properties in sparsity modeling. Moreover, we show that a coordinate descent algorithm is especially appropriate for the KEP function. Additionally, we discuss the relationship of KEP with the penalty functions $\ell_{1/2}$ and MCP. The theoretical and empirical analysis validates that the KEP function is effective and efficient in high-dimensional data modeling.
Aggregated functional data model for near-infrared spectroscopy calibration and prediction

Calibration and prediction for NIR spectroscopy data are performed based on a functional interpretation of the Beer–Lambert formula. Considering that, for each chemical sample, the resulting spectrum is a continuous curve obtained as the summation of overlapped absorption spectra from each analyte plus a Gaussian error, we assume that each individual spectrum can be expanded as a linear combination of B-splines basis. Calibration is then performed using two procedures for estimating the individual analytes’ curves: basis smoothing and smoothing splines. Prediction is done by minimizing the square error of prediction. To assess the variance of the predicted values, we use a leave-one-out jackknife technique. Departures from the standard error models are discussed through a simulation study, in particular, how correlated errors impact on the calibration step and consequently on the analytes’ concentration prediction. Finally, the performance of our methodology is demonstrated through the analysis of two publicly available datasets.
When Does More Regularization Imply Fewer Degrees of Freedom? Sufficient Conditions and Counter Examples from Lasso and Ridge Regression

Regularization aims to improve prediction performance of a given statistical modeling approach by moving to a second approach which achieves worse training error but is expected to have fewer degrees of freedom, i.e., better agreement between training and prediction error. We show here, however, that this expected behavior does not hold in general. In fact, counter examples are given that show regularization can increase the degrees of freedom in simple situations, including lasso and ridge regression, which are the most common regularization approaches in use. In such situations, the regularization increases both training error and degrees of freedom, and is thus inherently without merit. On the other hand, two important regularization scenarios are described where the expected reduction in degrees of freedom is indeed guaranteed: (a) all symmetric linear smoothers, and (b) linear regression versus convex constrained linear regression (as in the constrained variant of ridge regression and lasso).
Omnibus CLTs for Fr\'echet means and nonparametric inference on non-Euclidean spaces

Two central limit theorems for sample Fr\'echet means are derived, both significant for nonparametric inference on non-Euclidean spaces. The first one, Theorem 2.2, encompasses and improves upon most earlier CLTs on Fr\'echet means and broadens the scope of the methodology beyond manifolds to diverse new non-Euclidean data including those on certain stratified spaces which are important in the study of phylogenetic trees. It does not require that the underlying distribution $Q$ have a density, and applies to both intrinsic and extrinsic analysis. The second theorem, Theorem 3.3, focuses on intrinsic means on Riemannian manifolds of dimensions $d>2$ and breaks new ground by providing a broad CLT without any of the earlier restrictive support assumptions. It makes the statistically reasonable assumption of a somewhat smooth density of $Q$. The excluded case of dimension $d=2$ proves to be an enigma, although the first theorem does provide a CLT in this case as well under a support restriction. Theorem 3.3 immediately applies to spheres $S^d$, $d>2$, which are also of considerable importance in applications to axial spaces and to landmarks based image analysis, as these spaces are quotients of spheres under a Lie group $\mathcal G $ of isometries of $S^d$.
Rate optimality of Random walk Metropolis algorithm in high-dimension with heavy-tailed target distribution

High-dimensional asymptotics of the random walk Metropolis-Hastings (RWM) algorithm is well understood for a class of light-tailed target distributions. We develop a study for heavy-tailed target distributions, such as the Student $t$-distribution or the stable distribution. The performance of the RWM algorithms heavily depends on the tail property of the target distribution. The expected squared jumping distance (ESJD) is a common measure of efficiency for light-tail case but it does not work for heavy-tail case since the ESJD is unbounded. For this reason, we use the rate of weak consistency as a measure of efficiency. When the number of dimension is $d$, we show that the rate for the RWM algorithm is $d^2$ for the heavy-tail case where it is $d$ for the light-tail case. Also, we show that the Gaussian RWM algorithm attains the optimal rate among all RWM algorithms. Thus no heavy-tail proposal distribution can improve the rate.
Nonstationary, Nonparametric, Nonseparable Bayesian Spatio-Temporal Modeling using Kernel Convolution of Order Based Dependent Dirichlet Process

In this article, using kernel convolution of order based dependent Dirichlet process (Griffin and Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as we show, satisfies desirable properties, and includes the stationary, separable, parametric processes as special cases. We also investigate the smoothness properties of our proposed model. Since our model entails an infinite random series, for Bayesian model fitting purpose we must either truncate the series or more appropriately consider a random number of summands, which renders the model dimension a random variable. We attack the variable dimensionality problem using Transdimensional Transformation based Markov Chain Monte Carlo introduced by Das and Bhattacharya (2019b), which can update all the variables and also change dimensions in a single block using essentially a single random variable drawn from some arbitrary density defined on a relevant support. For the sake of completeness we also address the problem of truncating the infinite series by providing a uniform bound on the error incurred by truncating the infinite series. We illustrate the effectiveness of our model and methodologies on a simulated data set and demonstrate that our approach significantly outperforms that of Fuentes and Reich (2013) which is based on principles somewhat similar to ours. We also fit two real, spatial and spatio-temporal datasets with our approach and obtain quite encouraging results in both the cases.
Generalized information criterion for model selection in penalized graphical models

This paper introduces an estimator of the relative directed distance between an estimated model and the true model, based on the Kulback-Leibler divergence and is motivated by the generalized information criterion proposed by Konishi and Kitagawa. This estimator can be used to select model in penalized Gaussian copula graphical models. The use of this estimator is not feasible for high-dimensional cases. However, we derive an efficient way to compute this estimator which is feasible for the latter class of problems. Moreover, this estimator is, generally, appropriate for several penalties such as lasso, adaptive lasso and smoothly clipped absolute deviation penalty. Simulations show that the method performs similarly to KL oracle estimator and it also improves BIC performance in terms of support recovery of the graph. Specifically, we compare our method with Akaike information criterion, Bayesian information criterion and cross validation for band, sparse and dense network structures.
A new three-parameter lifetime distribution and associated inference

In this paper, a new three-parameter lifetime distribution is introduced and many of its standard properties are discussed. These include shape of the probability density function, hazard rate function and its shape, quantile function, limiting distributions of order statistics, and the moments. The unknown parameters are estimated by the maximum likelihood estimation procedure. We develop an EM algorithm to find the maximum likelihood estimates of the parameters, because they are not available in closed form. The Fisher information matrix is also obtained and it can be used for constructing the asymptotic confidence intervals. Finally, a real-data application is given to demonstrate the performance of the new distribution.
Bayesian inference of cosmic density fields from non-linear, scale-dependent, and stochastic biased tracers

We present a Bayesian reconstruction algorithm to generate unbiased samples of the underlying dark matter field from galaxy redshift data. Our new con tribution consists of implementing a non-Poisson likelihood including a deterministic non-linear and scale-dependent bias. In particular we present the Hamiltonian equations of motions for the negative binomial (NB) probability distribution function. This permits us to efficiently sample the posterior distribution function of density fields given a sample of galaxi es using the Hamiltonian Monte Carlo technique implemented in the ARGO code. We have tested our algorithm with the Bolshoi N -body simulation, inferring the underlying dark matter density field from a subsample of the halo catalogue. Our method shows that we can draw closely unbiased samples (compatible within 1-σ) from the posterior distribution up to scales of about k �1 h Mpc 1 in terms of power-spectra and cell-to-cell correlations. We fi nd that a Poisson likelihood yields reconstructions with power spectra deviating more than 10% at k = 0.2 h Mpc 1 . Our reconstruction algorithm is especially suited for emission l ine galaxy data for which a complex non-linear stochastic biasing treatment beyond Poissonity becomes indispensable.
Learning rates for the risk of kernel-based quantile regression estimators in additive models

Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel-based methods for additive models. These learning rates compare favorably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel-based quantile regression using the Gaussian radial basis function kernel, provided the assumption of an additive model is valid. Additionally, a concrete example is presented to show that a Gaussian function depending only on one variable lies in a reproducing kernel Hilbert space generated by an additive Gaussian kernel, but does not belong to the reproducing kernel Hilbert space generated by the multivariate Gaussian kernel of the same variance.
Sparse high-dimensional varying coefficient model: Nonasymptotic minimax study

The objective of the present paper is to develop a minimax theory for the varying coefficient model in a non-asymptotic setting. We consider a high- dimensional sparse varying coefficient model where only few of the covariates are present and only some of those covariates are time dependent. Our analysis allows the time dependent covariates to have different degrees of smoothness and to be spatially inhomogeneous. We develop the minimax lower bounds for the quadratic risk and construct an adaptive estimator which attains those lower bounds within a constant (if all time-dependent covariates are spatially homogeneous) or logarithmic factor of the number of observations.
Laplace deconvolution on the basis of time domain data and its application to dynamic contrast‐enhanced imaging

We consider the problem of Laplace deconvolution with noisy discrete non‐equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over a Laguerre functions basis (which acts as a surrogate eigenfunction basis of the Laplace convolution operator) using a regression setting. The expansion results in a small system of linear equations with the matrix of the system being triangular and Toeplitz. Because of this triangular structure, there is a common number m of terms in the function expansions to control, which is realized via a complexity penalty. The advantage of this methodology is that it leads to very fast computations, produces no boundary effects due to extension at zero and cut‐off at T and provides an estimator with the risk within a logarithmic factor of m of the oracle risk. We emphasize that we consider the true observational model with possibly non‐equispaced observations which are available on a finite interval of length T which appears in many different contexts, and we account for the bias associated with this model (which is not present in the case T→∞). The study is motivated by perfusion imaging using a short injection of contrast agent, a procedure which is applied for medical assessment of microcirculation within tissues such as cancerous tumours. The presence of a tuning parameter a allows the choice of the most advantageous time units, so that both the kernel and the unknown right‐hand side of the equation are well represented for the deconvolution. The methodology is illustrated by an extensive simulation study and a real data example which confirms that the technique proposed is fast, efficient, accurate, usable from a practical point of view and very competitive.
A General Stochastic Algorithmic Framework for Minimizing Expensive Black Box Objective Functions Based on Surrogate Models and Sensitivity Analysis

We are focusing on bound constrained global optimization problems, whose objective functions are computationally expensive black-box functions and have multiple local minima. The recently popular Metric Stochastic Response Surface (MSRS) algorithm proposed by \cite{Regis2007SRBF} based on adaptive or sequential learning based on response surfaces is revisited and further extended for better performance in case of higher dimensional problems. Specifically, we propose a new way to generate the candidate points which the next function evaluation point is picked from according to the metric criteria, based on a new definition of distance, and prove the global convergence of the corresponding. Correspondingly, a more adaptive implementation of MSRS, named "SO-SA", is presented. "SO-SA" is is more likely to perturb those most sensitive coordinates when generating the candidate points, instead of perturbing all coordinates simultaneously. Numerical experiments on both synthetic problems and real problems demonstrate the advantages of our new algorithm, compared with many state of the art alternatives. }
Extracting the Italian output gap: a Bayesian approach

During the last decades particular eort has been directed towards understanding and predicting the relevant state of the business cycle with the objective of decomposing permanent shocks from those having only a transitory impact on real output. This trend{cycle decomposition has a relevant impact on several economic and scal variables and constitutes by itself an important indicator for policy purposes. This paper deals with trend{cycle decomposition for the Italian economy having some interesting peculiarities which makes it attractive to analyse from both a statistic and an historical perspective. We propose an univariate model for the quarterly real GDP, subsequently extended to include the price dynamics through a Phillips curve. This study considers a series of the Italian quarterly real GDP recently released by OECD which includes both the 1960s and the recent global nancial crisis of 2007{2008. Parameters estimate as well as the signal extraction are performed within the Bayesian paradigm which eectively handles complex models where the parameters enter the log{likelihood function in a strongly nonlinear way. A new Adaptive Independent Metropolis{within{Gibbs sampler is then developed to eciently simulate the parameters of the unobserved cycle. Our results suggest that ination inuences the Output Gap estimate, making the extracted Italian OG an important indicator of ination pressures on the real side of the economy, as stated by the Phillips theory. Moreover, our estimate of the sequence of peaks and troughs of the Output Gap is in line with the OECD ocial dating of the Italian business cycle.