Miracle-dz/UniFAR-FTUs huggingface dataset:
Comparative Study of Differentially Private Data Synthesis Methods

When sharing data among researchers or releasing data for public use, there is a risk of exposing sensitive information of individuals in the data set. Data synthesis (DS) is a statistical disclosure limitation technique for releasing synthetic data sets with pseudo individual records. Traditional DS techniques often rely on strong assumptions of a data intruder's behaviors and background knowledge to assess disclosure risk. Differential privacy (DP) formulates a theoretical approach for a strong and robust privacy guarantee in data release without having to model intruders' behaviors. Efforts have been made aiming to incorporate the DP concept in the DS process. In this paper, we examine current DIfferentially Private Data Synthesis (DIPS) techniques for releasing individual-level surrogate data for the original data, compare the techniques conceptually, and evaluate the statistical utility and inferential properties of the synthetic data via each DIPS technique through extensive simulation studies. Our work sheds light on the practical feasibility and utility of the various DIPS approaches, and suggests future research directions for DIPS.
Dynamic shrinkage processes

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on a global–local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular global–local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modelling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólya–gamma scale mixture representation of the process proposed. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than do competing methods, and we apply the model for irregular curve fitting of minute‐by‐minute Twitter central processor unit usage data. In addition, we develop an adaptive time varying parameter regression model to assess the efficacy of the Fama–French five‐factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that, with the exception of the market risk, no other risk factors are significant except for brief periods.
Manifold Learning Using Kernel Density Estimation and Local Principal Components Analysis

We consider the problem of recovering a $d-$dimensional manifold $\mathcal{M} \subset \mathbb{R}^n$ when provided with noiseless samples from $\mathcal{M}$. There are many algorithms (e.g., Isomap) that are used in practice to fit manifolds and thus reduce the dimensionality of a given data set. Ideally, the estimate $\mathcal{M}_\mathrm{put}$ of $\mathcal{M}$ should be an actual manifold of a certain smoothness; furthermore, $\mathcal{M}_\mathrm{put}$ should be arbitrarily close to $\mathcal{M}$ in Hausdorff distance given a large enough sample. Generally speaking, existing manifold learning algorithms do not meet these criteria. Fefferman, Mitter, and Narayanan (2016) have developed an algorithm whose output is provably a manifold. The key idea is to define an approximate squared-distance function (asdf) to $\mathcal{M}$. Then, $\mathcal{M}_\mathrm{put}$ is given by the set of points where the gradient of the asdf is orthogonal to the subspace spanned by the largest $n - d$ eigenvectors of the Hessian of the asdf. As long as the asdf meets certain regularity conditions, $\mathcal{M}_\mathrm{put}$ is a manifold that is arbitrarily close in Hausdorff distance to $\mathcal{M}$. In this paper, we define two asdfs that can be calculated from the data and show that they meet the required regularity conditions. The first asdf is based on kernel density estimation, and the second is based on estimation of tangent spaces using local principal components analysis.
Correlated Random Measures

ABSTRACT We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric models are usually built from completely random measures, a Poisson-process-based construction in which the atom weights are independent. Completely random measures imply strong independence assumptions in the corresponding hierarchical model, and these assumptions are often misplaced in real-world settings. Correlated random measures address this limitation. They model correlation within the measure by using a Gaussian process in concert with the Poisson process. With correlated random measures, for example, we can develop a latent feature model for which we can infer both the properties of the latent features and their dependency pattern. We develop several other examples as well. We study a correlated random measure model of pairwise count data. We derive an efficient variational inference algorithm and show improved predictive performance on large datasets of documents, web clicks, and electronic health records. Supplementary materials for this article are available online.
Community Detection by $L_0$-penalized Graph Laplacian

Community detection in network analysis aims at partitioning nodes in a network into $K$ disjoint communities. Most currently available algorithms assume that $K$ is known, but choosing a correct $K$ is generally very difficult for real networks. In addition, many real networks contain outlier nodes not belonging to any community, but currently very few algorithm can handle networks with outliers. In this paper, we propose a novel model free tightness criterion and an efficient algorithm to maximize this criterion for community detection. This tightness criterion is closely related with the graph Laplacian with $L_0$ penalty. Unlike most community detection methods, our method does not require a known $K$ and can properly detect communities in networks with outliers. Both theoretical and numerical properties of the method are analyzed. The theoretical result guarantees that, under the degree corrected stochastic block model, even for networks with outliers, the maximizer of the tightness criterion can extract communities with small misclassification rates even when the number of communities grows to infinity as the network size grows. Simulation study shows that the proposed method can recover true communities more accurately than other methods. Applications to a college football data and a yeast protein-protein interaction data also reveal that the proposed method performs significantly better.
Connecting pairwise spheres by depth: DCOPS

We extend the classical notion of the spherical depth in \mathbb{R}^k, to the important setup of data on a Riemannian manifold. We show that this notion of depth satisfies a set of desirable properties. For the empirical version of this depth function both uniform consistency and the asymptotic distribution are studied. Consistency is also shown for functional data. The behaviour of the depth is illustrated through several examples for Riemannian manifold data.
On finite sample properties of nonparametric discrete asymmetric kernel estimators

ABSTRACT The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their resulting non-consistent estimators, but this theoretical drawback of the estimators is balanced by some interesting features in small/medium samples. The role of modal probability and variance of discrete asymmetric kernels is highlighted to help better understand the performance of these kernels, in particular how the binomial kernel outperforms other asymmetric kernels. The performance of discrete asymmetric kernel estimators of probability mass functions is illustrated using simulations, in addition to applications to real data sets.
On the validity of parametric block correlation matrices with constant within and between group correlations

We consider the set Bp of parametric block correlation matrices with p blocks of various (and possibly different) sizes, whose diagonal blocks are compound symmetry (CS) correlation matrices and off-diagonal blocks are constant matrices. Such matrices appear in probabilistic models on categorical data, when the levels are partitioned in p groups, assuming a constant correlation within a group and a constant correlation for each pair of groups. We obtain two necessary and sufficient conditions for positive definiteness of elements of Bp. Firstly we consider the block average map φ, consisting in replacing a block by its mean value. We prove that for any A ∈ Bp , A is positive definite if and only if φ(A) is positive definite. Hence it is equivalent to check the validity of the covariance matrix of group means, which only depends on the number of groups and not on their sizes. This theorem can be extended to a wider set of block matrices. Secondly, we consider the subset of Bp for which the between group correlation is the same for all pairs of groups. Positive definiteness then comes down to find the positive definite interval of a matrix pencil on Sp. We obtain a simple characterization by localizing the roots of the determinant with within group correlation values.
The utility of a Bayesian analysis of complex models and the study of archeological ${}^{14}$C data

The paper presents a critical introduction to the complex statistical models used in ${}^{14}$C dating. The emphasis is on the estimation of the transit time between a sequence of archeological layers. Although a frequentist estimation of the parameters is relatively simple, confidence intervals constructions are not standard as the models are not regular. I argue that that the Bayesian paradigm is a natural approach to these models. It is simple, and gives immediate solutions to credible sets, with natural interpretation and simple construction. Indeed it is the standard tool of ${}^{14}$C analysis. However and necessarily, the Bayesian approach is based on technical assumptions that may dominate the scientific conclusion in a hard to predict way. I exemplify the discussion in two ways. Firstly, I simulate toy models. Secondly, I analyze a particular data set from the Iron Age period in Tel Rehov. These data are important to the debate on the absolute time of the Iron Age I/IIA transition in the Levant, and in particular to the feasibility of the Bible story about the United Monarchy of David and Solomon. Our conclusion is that the data in question cannot resolve this debate.
Analysis of Langevin Monte Carlo via Convex Optimization

In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order $2$. Using this interpretation and techniques borrowed from convex optimization, we give a non-asymptotic analysis of this method to sample from logconcave smooth target distribution on $\mathbb{R}^d$. Our proofs are then easily extended to the Stochastic Gradient Langevin Dynamics, which is a popular extension of the Unadjusted Langevin Algorithm. Finally, this interpretation leads to a new methodology to sample from a non-smooth target distribution, for which a similar study is done.
Representation for the Gauss-Laplace Transmutation

Under certain conditions, a symmetric unimodal continuous random variable $\xi$ can be represented as a scale mixture of the standard Normal distribution $Z$, i.e., $\xi = \sqrt{W} Z$, where the mixing distribution $W$ is independent of $Z. $ It is well known that if the mixing distribution is inverse Gamma, then $\xi$ is student's $t$ distribution. However, it is less well known that if the mixing distribution is Gamma, then $\xi$ is a Laplace distribution. Several existing proofs of the latter result rely on complex calculus and change of variables in integrals. We offer two simple and intuitive proofs based on representation and moment generating functions.
A Double Parametric Bootstrap Test for Topic Models

Non-negative matrix factorization (NMF) is a technique for finding latent representations of data. The method has been applied to corpora to construct topic models. However, NMF has likelihood assumptions which are often violated by real document corpora. We present a double parametric bootstrap test for evaluating the fit of an NMF-based topic model based on the duality of the KL divergence and Poisson maximum likelihood estimation. The test correctly identifies whether a topic model based on an NMF approach yields reliable results in simulated and real data.
Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss and Simpson’s Paradox

Statistical learning using imprecise probabilities is gaining more attention because it presents an alternative strategy for reducing irreplicable findings by freeing the user from the task of making up unwarranted high-resolution assumptions. However, model updating as a mathematical operation is inherently exact, hence updating imprecise models requires the user's judgment in choosing among competing updating rules. These rules often lead to incompatible inferences, and can exhibit unsettling phenomena like dilation, contraction and sure loss, which cannot occur with the Bayes rule and precise probabilities. We revisit a number of famous "paradoxes", including the three prisoners/Monty Hall problem, revealing that a logical fallacy arises from a set of marginally plausible yet jointly incommensurable assumptions when updating the underlying imprecise model. We establish an equivalence between Simpson's paradox and an implicit adoption of a pair of aggregation rules that induce sure loss. We also explore behavioral discrepancies between the generalized Bayes rule, Dempster's rule and the Geometric rule as alternative posterior updating rules for Choquet capacities of order 2. We show that both the generalized Bayes rule and Geometric rule are incapable of updating without prior information regardless of how strong the information in our data is, and that Dempster's rule and the Geometric rule can mathematically contradict each other with respect to dilation and contraction. Our findings show that unsettling updates reflect a collision between the rules' assumptions and the inexactness allowed by the model itself, highlighting the invaluable role of judicious judgment in handling low-resolution information, and the care we must take when applying learning rules to update imprecise probabilities.
Neyman-Pearson classification: parametrics and power enhancement

The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error under some user-specified level. This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people have clear priorities over the two error types. Despite recent advances in NP classification, the NP oracle inequalities, a core theoretical criterion to evaluate classifiers under the NP paradigm, were established only for classifiers based on nonparametric assumptions with bounded feature support. In this work, we conquer the challenges arisen from unbounded feature support in parametric settings and develop NP classification theory and methodology under these settings. Concretely, we propose a new parametric NP classifier NP-sLDA which satisfies the NP oracle inequalities. Furthermore, we construct an adaptive sample splitting scheme that can be applied universally to existing NP classifiers and this adaptive strategy greatly enhances the power of these classifiers. Through extensive numerical experiments and real data studies, we demonstrate the competence of NP-sLDA and the new sample splitting scheme.
Selective inference for the problem of regions via multiscale bootstrap

Selective inference procedures are considered for computing approximately unbiased $p$-values of hypothesis testing using nonparametric bootstrap resampling without direct access to the parameter space nor the null distribution. A typical example is to assess the uncertainty of hierarchical clustering, where we can easily compute a frequentist confidence level of each cluster by counting how many times it appears in bootstrap replicates. This is implemented in "pvclust" package of R, and we are going to extend it for selective inference. $P$-values are computed only for the obtained clusters for testing the null hypothesis that the cluster is not true. This is formulated as the "problem of regions" where hypotheses are represented as arbitrary shaped regions in a parameter space. Geometric quantities, namely, signed distance and mean curvature, determine the frequentist confidence level. Our idea is to estimate these geometric quantities by the multiscale bootstrap in which we change the sample size of bootstrap replicates. Our method is second-order accurate in the large sample theory of smooth boundary surfaces of regions, and it is also justified for nonsmooth surfaces. Our $p$-values are asymptotically equivalent to those of more computationally intensive iterated bootstrap.
Higgs Decays to $ZZ$ and $Z\gamma$ in the SMEFT: an NLO analysis

We calculate the complete one-loop electroweak corrections to the inclusive H → ZZ and H → Zγ decays in the dimension-6 extension of the Standard Model Eﬀective Field Theory (SMEFT). The corrections to H → ZZ are computed for on-shell Z bosons and are a precursor to the physical H → Zff calculation. We present compact numerical formulas for our results and demonstrate that the logarithmic contributions that result from the renormalization group evolution of the SMEFT coeﬃcients are larger than the ﬁnite NLO contributions to the decay widths. As a by-product of our calculation, we obtain the ﬁrst complete result for the ﬁnite corrections to G µ in the SMEFT.
A rate optimal procedure for sparse signal recovery under dependence

The paper considers the problem of identifying the sparse different components between two high dimensional means of column-wise dependent random vectors. We show that the dependence can be utilized to lower the identification boundary for signal recovery. Moreover, an optimal convergence rate for the marginal false non-discovery rate (mFNR) is established under the dependence. The convergence rate is faster than the optimal rate without dependence. To recover the sparse signal bearing dimensions, we propose a Dependence-Assisted Thresholding and Excising (DATE) procedure, which is shown to be rate optimal for the mFNR with the marginal false discovery rate (mFDR) controlled at a pre-specified level. Simulation studies and case study are given to demonstrate the performance of the proposed signal identification procedure.
Monotone Matrix Estimation via Robust Deconvolution

The goal of deconvolution is in estimating the distribution of a random variable based on its noisy observations. The goal of matrix estimation is in estimating the entries of a large matrix from observed entries, which are noisy versions of entries in a small fraction of the entire matrix. We study the rate of convergence for estimation of matrices with a certain monotonicity property. It turns out to be equivalent to solving a robust version of the deconvolution problem. As the main result of this paper, we provide a simple, intuitive algorithm for matrix estimation which extends the works by Fan (1991) and Delaigle et al. (2008). We show that our computationally efficient method achieves near optimal minimax rate for the matrix estimation as well as robust deconvolution. This rate is within a constant factor to the rate achieved by the kernel deconvolution estimator in the classical setup.
Robust semiparametric inference with missing data

Classical semiparametric inference with missing outcome data is not robust to contamination of the observed data and a single observation can have arbitrarily large influence on estimation of a parameter of interest. This sensitivity is exacerbated when inverse probability weighting methods are used, which may overweight contaminated observations. We introduce inverse probability weighted, double robust and outcome regression estimators of location and scale parameters, which are robust to contamination in the sense that their influence function is bounded. We give asymptotic properties and study finite sample behaviour. Our simulated experiments show that contamination can be more serious a threat to the quality of inference than model misspecification. An interesting aspect of our results is that the auxiliary outcome model used to adjust for ignorable missingness by some of the estimators, is also useful to protect against contamination. We also illustrate through a case study how both adjustment to ignorable missingness and protection against contamination are achieved through weighting schemes, which can be contrasted to gain further insights.
Mean Field Dynamics of Graphs II: Assessing the Risk for the Development of Phase Transitions in Empirical Data

Psychological disorders like major depressive disorder can be seen as complex dynamical systems. By looking at symptom activation patterns, we can investigate the dynamic behaviour of individuals to see whether or not they are at risk for sudden changes (phase transitions). Here, we show how a mean field approximation is used to reduce a dynamic multidimensional system to one-dimensional system to analyse the dynamics. Using maximum likelihood estimation, we can estimate the parameter of interest which, in combination with a bifurcation diagram, reflects the risk that someone has for experiencing a transition. After validating the proposed method with simulated data, we apply this method to three empirical examples, where we validate our method using data that contains a transition, and where we show its use in a clinical and general sample. Results show an increased risk for a transition when the transition actually occurred, and that members of both the clinical and general sample were not susceptible to transitions from a healthy to a depressed mood, or vice versa. We conclude that the mean field approximation is valid to assess the risk for a transition, and could in the future aid clinical therapists in the treatment of depressed patient.
Empirical Bayes approaches to PageRank type algorithms for rating scientific journals

Following criticisms against the journal Impact Factor, new journal influence scores have been developed such as the Eigenfactor or the Prestige Scimago Journal Rank. They are based on PageR-ank type algorithms on the cross-citations transition matrix of the citing-cited network. The PageR-ank algorithm performs a smoothing of the transition matrix combining a random walk on the data network and a teleportation to all possible nodes with fixed probabilities (the damping factor being α = 0.85). We reinterpret this smoothing matrix as the mean of a posterior distribution of a Dirichlet-multinomial model in an empirical Bayes perspective. We suggest a simple yet efficient way to make a clear distinction between structural and sampling zeroes. This allows us to contrast cases with self-citations are included or excluded to avoid overvalued journal bias. We estimate the model parameters by maximizing the marginal likelihood with a Majorize-Minimize algorithm. The procedure ends up with a score similar to the PageRank ones but with a damping factor depending on the journal at hand. The procedures are illustrated with an example about cross-citations among 47 statistical journals studied by Varin et al. (2016).