Miracle-dz/UniFAR-FTUs huggingface dataset:
The semiparametric Bernstein-von Mises theorem

In a smooth semiparametric estimation problem, the marginal posterior for the parameter of interest is expected to be asymptotically normal and satisfy frequentist criteria of optimality if the model is endowed with a suitable prior. It is shown that, under certain straightforward and interpretable conditions, the assertion of Le Cam’s acclaimed, but strictly parametric, Bernstein-von Mises theorem [Univ. California Publ. Statist. 1 (1953) 277-329] holds in the semiparametric situation as well. As a consequence, Bayesian point-estimators achieve efficiency, for example, in the sense of Hajek’s convolution theorem [Z. Wahrsch. Verw. Gebiete 14 (1970) 323-330]. The model is required to satisfy differentiability and metric entropy conditions, while the nuisance prior must assign nonzero mass to certain Kullback-Leibler neighborhoods [Ghosal, Ghosh and van der Vaart Ann. Statist. 28 (2000) 500-531]. In addition, the marginal posterior is required to converge at parametric rate, which appears to be the most stringent condition in examples. The results are applied to estimation of the linear coefficient in partial linear regression, with a Gaussian prior on a smoothness class for the nuisance.
CroP: Color Constancy Benchmark Dataset Generator

Implementing color constancy as a pre-processing step in contemporary digital cameras is of significant importance as it removes the influence of scene illumination on object colors. Several benchmark color constancy datasets have been created for the purpose of developing and testing new color constancy methods. However, they all have numerous drawbacks including a small number of images, erroneously extracted ground-truth illuminations, long histories of misuses, violations of their stated assumptions, etc. To overcome such and similar problems, in this paper a color constancy benchmark dataset generator is proposed. For a given camera sensor it enables generation of any number of realistic raw images taken in a subset of the real world, namely images of printed photographs. Datasets with such images share many positive features with other existing real-world datasets, while some of the negative features are completely eliminated. The generated images can be successfully used to train methods that afterward achieve high accuracy on real-world datasets. This opens the way for creating large enough datasets for advanced deep learning techniques. Experimental results are presented and discussed. The source code is available at http://www.fer. unizg.hr/ipg/resources/colorconstancy/.
Predicting Inflation: Professional Experts Versus No-Change Forecasts

We compare forecasts of United States inflation from the Survey of Professional Forecasters (SPF) to predictions made by simple statistical techniques. In nowcasting, economic expertise is persuasive. When projecting beyond the current quarter, novel yet simplistic probabilistic no-change forecasts are equally competitive. We further interpret surveys as ensembles of forecasts, and show that they can be used similarly to the ways in which ensemble prediction systems have transformed weather forecasting. Then we borrow another idea from weather forecasting, in that we apply statistical techniques to postprocess the SPF forecast, based on experience from the recent past. The foregoing conclusions remain unchanged after survey postprocessing.
The Slope Heuristics in Heteroscedastic Regression

We consider the estimation of a regression function with random design and heteroscedastic noise in a non-parametric setting. More precisely, we address the problem of characterizing the optimal penalty when the regression function is estimated by using a penalized least-squares model selection method. In this context, we show the existence of a minimal penalty, de ned to be the maximum level of penalization under which the model selection procedure totally misbehaves. Moreover, the optimal penalty is shown to be twice the minimal one and to satisfy a nonasymptotic pathwise oracle inequality with leading constant almost one. When the shape of the optimal penalty is known, this allows to apply the so-called slope heuristics initially proposed by Birge and Massart (2007), which further provides with a data-driven calibration of penalty procedure. Finally, the use of the results obtained in [30], considering the least-squares estimation of a regression function on a xed nite-dimensional linear model, allows us to go beyond the case of histogram models, which is already treated by Arlot and Massart in [6].
Looking for continuous local martingales with the crossing tree (Working Paper)

We present statistical tests for the continuous martingale hypothesis. That is, whether an observed process is a continuous local martingale, or equivalently a continuous time-changed Brownian motion. Our technique is based on the concept of the crossing tree. Simulation experiments are used to assess the power of the tests, which is generally higher than recently proposed tests using the estimated quadratic variation (i.e., realised volatility). In particular, the crossing tree shows significantly more power with shorter datasets. We then show results from applying the methodology to high frequency currency exchange rate data. We show that in 2003, for the AUD-USD, GBP-USD, JPY-USD and EUR-USD rates, at small timescales (less than 15 minutes or so) the continuous martingale hypothesis is rejected, but not so at larger timescales. For 2003 EUR-GBP data, the hypothesis is rejected at small timescales and some moderate timescales, but not all.
A pseudo-likelihood approach for multivariate meta-analysis of test accuracy studies with multiple thresholds

Multivariate meta-analysis of test accuracy studies when tests are evaluated in terms of sensitivity and specificity at more than one threshold represents an effective way to synthesize results by fully exploiting the data, if compared to univariate meta-analyses performed at each threshold independently. The approximation of logit transformations of sensitivities and specificities at different thresholds through a normal multivariate random-effects model is a recent proposal that straightforwardly extends the bivariate models well recommended for the one threshold case. However, drawbacks of the approach, such as poor estimation of the within-study correlations between sensitivities and between specificities, and severe computational issues can make it unappealing. We propose an alternative method for inference on common diagnostic measures using a pseudo-likelihood constructed under a working independence assumption between sensitivities and between specificities at different thresholds in the same study. The method does not require within-study correlations, overcomes the convergence issues and can be effortlessly implemented. Simulation studies highlight a satisfactory performance of the method, remarkably improving the results from the multivariate normal counterpart under different scenarios. The pseudo-likelihood approach is illustrated in the evaluation of a test used for diagnosis of preeclampsia as a cause of maternal and perinatal morbidity and mortality.
A self‐normalized approach to confidence interval construction in time series

Summary. We propose a new method to construct confidence intervals for quantities that are associated with a stationary time series, which avoids direct estimation of the asymptotic variances. Unlike the existing tuning‐parameter‐dependent approaches, our method has the attractive convenience of being free of any user‐chosen number or smoothing parameter. The interval is constructed on the basis of an asymptotically distribution‐free self‐normalized statistic, in which the normalizing matrix is computed by using recursive estimates. Under mild conditions, we establish the theoretical validity of our method for a broad class of statistics that are functionals of the empirical distribution of fixed or growing dimension. From a practical point of view, our method is conceptually simple, easy to implement and can be readily used by the practitioner. Monte Carlo simulations are conducted to compare the finite sample performance of the new method with those delivered by the normal approximation and the block bootstrap approach.
Inference Trees: Adaptive Inference with Exploration

We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with exploitation, ensures consistency, and alleviates pathologies in existing adaptive methods. ITs adaptively sample from hierarchical partitions of the parameter space, while simultaneously learning these partitions in an online manner. This enables ITs to not only identify regions of high posterior mass, but also maintain uncertainty estimates to track regions where significant posterior mass may have been missed. ITs can be based on any inference method that provides a consistent estimate of the marginal likelihood. They are particularly effective when combined with sequential Monte Carlo, where they capture long-range dependencies and yield improvements beyond proposal adaptation alone.
Piecewise deterministic Markov processes and their invariant measures

Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which implies quantitative bounds on the total variation between the marginal distributions of the two processes. Finally two results are established regarding the invariant measures of PDMPs. A practical condition to show that a probability measure is invariant for the associated PDMP semi-group is presented. In a second time, a bound on the invariant probability measures in V-norm of two PDMPs following the same differential flow is established. This last result is then applied to study the asymptotic bias of some non-exact PDMP MCMC methods.
Improving the Johnson-Lindenstrauss Lemma

The Johnson-Lindenstrauss Lemma allows for the projection of $n$ points in $p-$dimensional Euclidean space onto a $k-$dimensional Euclidean space, with $k \ge \frac{24\ln \emph{n}}{3\epsilon^2-2\epsilon^3}$, so that the pairwise distances are preserved within a factor of $1\pm\epsilon$. Here, working directly with the distributions of the random distances rather than resorting to the moment generating function technique, an improvement on the lower bound for $k$ is obtained. The additional reduction in dimension when compared to bounds found in the literature, is at least $13\%$, and, in some cases, up to $30\%$ additional reduction is achieved. Using the moment generating function technique, we further provide a lower bound for $k$ using pairwise $L_2$ distances in the space of points to be projected and pairwise $L_1$ distances in the space of the projected points. Comparison with the results obtained in the literature shows that the bound presented here provides an additional $36-40\%$ reduction.
A Rejoinder to Mackintosh and some Remarks on the Concept of General Intelligence

In 2000 Nicholas J. Mackintosh (2000) published an article in "Nature" referring to the concept of general intelligence ("g") claiming that there is clear empirical evidence for the existence of the g factor and psychologists are "united in their support of g". Surprisingly, his view remained yet unchallenged although this issue is by no means as clear-cut as Mackintosh argues. Let us therefore attempt to clarify some common but unfortunately major misconceptions about g, which Mackintosh, following Jensen's (1998) precedent, recounted in his "Nature" article. The bottom line is that Spearman's g does not exist, that this has been known and acknowledged by leading scholars (Guttman, 1992; Thurstone, 1947) of factor analysis for decades so that the task of objectively defining human intelligence remains unfinished.
Fast Learning Rate of lp-MKL and its Minimax Optimality

In this paper, we give a new sharp generalization bound of lp-MKL which is a generalized framework of multiple kernel learning (MKL) and imposes lp-mixed-norm regularization instead of l1-mixed-norm regularization. We utilize localization techniques to obtain the sharp learning rate. The bound is characterized by the decay rate of the eigenvalues of the associated kernels. A larger decay rate gives a faster convergence rate. Furthermore, we give the minimax learning rate on the ball characterized by lp-mixed-norm in the product space. Then we show that our derived learning rate of lp-MKL achieves the minimax optimal rate on the lp-mixed-norm ball.
Sparsity-accuracy trade-off in MKL

We empirically investigate the best trade-off between sparse and uniformly-weighted multiple kernel learning (MKL) using the elastic-net regularization on real and simulated datasets. We find that the best trade-off parameter depends not only on the sparsity of the true kernel-weight spectrum but also on the linear dependence among kernels and the number of samples.
Divergence of sample quantiles

We show that the left (right) sample quantile tends to the left (right) distribution quantile at p in [0,1], if the left and right quantiles are identical at p. We show that the sample quantiles diverge almost surely otherwise. The latter can be considered as a generalization of the well-known result that the sum of a random sample of a fair coin with 1 denoting heads and -1 denoting tails is 0 infinitely often. In the case that the sample quantiles do not converge we show that the limsup is the right quantile and the liminf is the left quantile.
A nonparametric urn-based approach to interacting failing systems with an application to credit risk modeling

In this paper we propose a new nonparametric approach to interacting failing systems (FS), that is systems whose probability of failure is not negligible in a fixed time horizon, a typical example being firms and financial bonds. The main purpose when studying a FS is to calculate the probability of default and the distribution of the number of failures that may occur during the observation period. A model used to study a failing system is defined default model. In particular, we present a general recursive model constructed by the means of inter- acting urns. After introducing the theoretical model and its properties we show a first application to credit risk modeling, showing how to assess the idiosyncratic probability of default of an obligor and the joint probability of failure of a set of obligors in a portfolio of risks, that are divided into reliability classes.
Boulevard: Regularized Stochastic Gradient Boosted Trees and Their Limiting Distribution

This paper examines a novel gradient boosting framework for regression. We regularize gradient boosted trees by introducing subsampling and employ a modified shrinkage algorithm so that at every boosting stage the estimate is given by an average of trees. The resulting algorithm, titled Boulevard, is shown to converge as the number of trees grows. We also demonstrate a central limit theorem for this limit, allowing a characterization of uncertainty for predictions. A simulation study and real world examples provide support for both the predictive accuracy of the model and its limiting behavior.
Optically Faint Massive Balmer Break Galaxies at z > 3 in the CANDELS/GOODS Fields

We present a sample of 33 Balmer break galaxies (BBGs) selected as Hubble Space Telescope/F160W dropouts in the deepest CANDELS/GOODS fields (H ≳ 27.3 mag) but relatively bright in Spitzer/IRAC ([3.6], [4.5] < 24.5 mag), implying red colors (median and quartiles: ). Half of these BBGs are newly identified sources. Our BBGs are massive ( ), high-redshift ( ), dusty ( ) galaxies. The spectral energy distributions (SEDs) of half of our sample indicate that they are star-forming galaxies with typical specific star formation rates (SFRs) of 0.5–1.0 Gyr−1, qualifying them as main-sequence (MS) galaxies at 3 < z < 6. One-third of these SEDs indicate the presence of prominent emission lines (Hβ + [O iii], Hα + [N ii]) boosting the IRAC fluxes and red colors. Approximately 20% of the BBGs are very dusty (A(V) ∼ 2.5 mag) starbursts with strong mid-to-far-infrared detections and extreme SFRs (SFR > 103 M☉ yr−1) that place them above the MS. The rest, 30%, are post-starbursts or quiescent galaxies located >2σ below the MS with mass-weighted ages older than 700 Myr. Only two of the 33 galaxies are X-ray-detected active galactic nuclei (AGNs) with optical/near-infrared SEDs dominated by stellar emission, but the presence of obscured AGNs in the rest of the sources cannot be discarded. Our sample accounts for 8% of the total number density of galaxies at z > 3, but it is a significant contributor (30%) to the general population of red galaxies at 4 < z < 6. Finally, our results point out that one of every 30 massive galaxies in the local universe was assembled in the first 1.5 Gyr after the big bang, a fraction that is not reproduced by state-of-the-art galaxy formation simulations.
TESTING AFFILIATION IN PRIVATE-VALUES MODELS OF FIRST-PRICE AUCTIONS USING GRID DISTRIBUTIONS

Within the private-values paradigm, we construct a tractable empirical model of equilibrium behaviour at first-price auctions when bidders' valuations are potentially dependent, but not necessarily affiliated. We develop a test of affiliation and apply our framework to data from low-price, sealed-bid auctions held by the Department of Transportation in the State ofMichigan to procure road-resurfacing services: we do not reject the hypothesis of affiliation in cost signals.
Two novel costs for determining the tuning parameters of the Kalman Filter

The Kalman filter (KF) and the extended Kalman filter (EKF) are well established techniques for state estimation. However, the choice of the filter tuning parameters still poses a major challenge for the engineers [1]. In the present work, two new costs have been proposed for determining the filter tuning parameters on the basis of the innovation covariance. This provides a cost function based method for the selection of suitable combination(s) of filter tuning parameters in order to ensure the design of a KF or an EKF having an optimally balanced RMSE performance. Index Terms-Kalman filter, tuning parameters, innovation covariance, cost function
The Bayes oracle and asymptotic optimality of multiple testing procedures under sparsity

Within a Bayesian decision theoretic framework we investigate some asymptotic optimality properties of a large class of multiple testing rules. A parametric setup is considered, in which observations come from a normal scale mixture model and the total loss is assumed to be the sum of losses for individual tests. Our model can be used for testing point null hypotheses, as well as to distinguish large signals from a multitude of very small effects. A rule is defined to be asymptotically Bayes optimal under sparsity (ABOS), if within our chosen asymptotic framework the ratio of its Bayes risk and that of the Bayes oracle (a rule which minimizes the Bayes risk) converges to one. Our main interest is in the asymptotic scheme where the proportion p of "true" alternatives converges to zero. We fully characterize the class of fixed threshold multiple testing rules which are ABOS, and hence derive conditions for the asymptotic optimality of rules controlling the Bayesian False Discovery Rate (BFDR). We finally provide conditions under which the popular Benjamini-Hochberg (BH) and Bonferroni procedures are ABOS and show that for a wide class of sparsity levels, the threshold of the former can be approximated by a nonrandom threshold.
Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC)

We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We apply this novel methodology to five population growth models, including models with strong and weak Allee effects, and test if it can efficiently sample from the complex likelihood surface that is often associated with these models. Utilising real and also synthetically generated data sets we examine the extent to which observation noise and process error may frustrate efforts to choose between these models. Our novel algorithm involves an Adaptive Metropolis proposal combined with an SIR Particle MCMC algorithm (AdPMCMC). We show that the AdPMCMC algorithm samples complex, high-dimensional spaces efficiently, and is therefore superior to standard Gibbs or Metropolis Hastings algorithms that are known to converge very slowly when applied to the non-linear state space ecological models considered in this paper. Additionally, we show how the AdPMCMC algorithm can be used to recursively estimate the Bayesian Cram\'er-Rao Lower Bound of Tichavsk\'y (1998). We derive expressions for these Cram\'er-Rao Bounds and estimate them for the models considered. Our results demonstrate a number of important features of common population growth models, most notably their multi-modal posterior surfaces and dependence between the static and dynamic parameters. We conclude by sampling from the posterior distribution of each of the models, and use Bayes factors to highlight how observation noise significantly diminishes our ability to select among some of the models, particularly those that are designed to reproduce an Allee effect.
Constructing Summary Statistics for Approximate Bayesian Computation: Semi-automatic ABC

Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for such models. It replaces calculation of the likelihood by a step which involves simulating artificial data for different parameter values, and comparing summary statistics of the simulated data to summary statistics of the observed data. Here we show how to construct appropriate summary statistics for ABC in a semi-automatic manner. We aim for summary statistics which will enable inference about certain parameters of interest to be as accurate as possible. Theoretical results show that optimal summary statistics are the posterior means of the parameters. While these cannot be calculated analytically, we use an extra stage of simulation to estimate how the posterior means vary as a function of the data; and then use these estimates of our summary statistics within ABC. Empirical results show that our approach is a robust method for choosing summary statistics, that can result in substantially more accurate ABC analyses than the ad-hoc choices of summary statistics proposed in the literature. We also demonstrate advantages over two alternative methods of simulation-based inference.
Group Lasso for high dimensional sparse quantile regression models

This paper studies the statistical properties of the group Lasso estimator for high dimensional sparse quantile regression models where the number of explanatory variables (or the number of groups of explanatory variables) is possibly much larger than the sample size while the number of variables in "active" groups is sufficiently small. We establish a non-asymptotic bound on the $\ell_{2}$-estimation error of the estimator. This bound explains situations under which the group Lasso estimator is potentially superior/inferior to the $\ell_{1}$-penalized quantile regression estimator in terms of the estimation error. We also propose a data-dependent choice of the tuning parameter to make the method more practical, by extending the original proposal of Belloni and Chernozhukov (2011) for the $\ell_{1}$-penalized quantile regression estimator. As an application, we analyze high dimensional additive quantile regression models. We show that under a set of suitable regularity conditions, the group Lasso estimator can attain the convergence rate arbitrarily close to the oracle rate. Finally, we conduct simulations experiments to examine our theoretical results.