Miracle-dz/UniFAR-FTUs huggingface dataset:
Equivalence classes of staged trees

In this paper we give a complete characterization of the statistical equivalence classes of CEGs and of staged trees. We are able to show that all graphical representations of the same model share a common polynomial description. Then, simple transformations on that polynomial enable us to traverse the corresponding class of graphs. We illustrate our results with a real analysis of the implicit dependence relationships within a previously studied dataset.
Selective inference with a randomized response

Inspired by sample splitting and the reusable holdout introduced in the field of differential privacy, we consider selective inference with a randomized response. We discuss two major advantages of using a randomized response for model selection. First, the selectively valid tests are more powerful after randomized selection. Second, it allows consistent estimation and weak convergence of selective inference procedures. Under independent sampling, we prove a selective (or privatized) central limit theorem that transfers procedures valid under asymptotic normality without selection to their corresponding selective counterparts. This allows selective inference in nonparametric settings. Finally, we propose a framework of inference after combining multiple randomized selection procedures. We focus on the classical asymptotic setting, leaving the interesting high-dimensional asymptotic questions for future work.
Generating correlated random vector by polynomial normal transformation

This paper develops a polynomial normal transformation model, whereby various non-normal probability distributions can be simulated by the standard normal distribution. Two methods are presented to determine the coefficients of polynomial model: (1) probability weighted moment (PWM) matching (2) percentile matching. Compared to the existing raw moment or L-moment matching, the proposed methods are more computationally convenient, and can be used to estimate the coefficients of polynomial model with a higher degree. Furthermore, for two correlated random variables, a polynomial equation is derived to estimate the equivalent correlation coefficient in standard normal space, and random vector with non-normal marginal distributions and prescribed correlation matrix can be generated. Finally, numerical examples are worked to demonstrate the proposed method.
Graphical models for studying museum networks: the Abbonamento Musei Torino Piemonte

Probabilistic graphical models are a powerful tool to represent real-word phenomena and to learn network structures starting from data. This paper applies graphical models in a new framework to study association rules driven by consumer choices in a network of museums. The network consists of the museums participating in the program of Abbonamento Musei Torino Piemonte, which is a yearly subscription managed by the Associazione Torino Citt\`a Capitale Europea. Consumers are card-holders, who are allowed to entry to all the museums in the network for one year. We employ graphical models to highlight associations among the museums driven by card-holder visiting behaviour. We use both undirected graphs to investigate the strength of the network and directed graphs to highlight asimmetry in the association rules.
Orthogonal symmetric non-negative matrix factorization under the stochastic block model

We present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks. While the exact factorization of a given order may not exist and is NP hard to compute, we obtain an approximate factorization by solving an optimization problem. We establish the connection of the factors obtained through the factorization to a non-negative basis of an invariant subspace of the estimated matrix, drawing parallel with the spectral clustering. Using such factorization for clustering in networks is motivated by analyzing a block-diagonal Laplacian matrix with the blocks representing the connected components of a graph. The method is shown to be consistent for community detection in graphs generated from the stochastic block model and the degree corrected stochastic block model. Simulation results and real data analysis show the effectiveness of these methods under a wide variety of situations, including sparse and highly heterogeneous graphs where the usual spectral clustering is known to fail. Our method also performs better than the state of the art in popular benchmark network datasets, e.g., the political web blogs and the karate club data.
Deep recurrent Gaussian process with variational Sparse Spectrum approximation

Modeling sequential data has become more and more important in practice. Some applications are autonomous driving, virtual sensors and weather forecasting. To model such systems so called recurrent models are used. In this article we introduce two new Deep Recurrent Gaussian Process (DRGP) models based on the Sparse Spectrum Gaussian Process (SSGP) and the improved variational version called Variational Sparse Spectrum Gaussian Process (VSSGP). We follow the recurrent structure given by an existing DRGP based on a specific sparse Nystrom approximation. Therefore, we also variationally integrate out the input-space and hence can propagate uncertainty through the layers. We can show that for the resulting lower bound an optimal variational distribution exists. Training is realized through optimizing the variational lower bound. Using Distributed Variational Inference (DVI), we can reduce the computational complexity. We improve over current state of the art methods in prediction accuracy for experimental data-sets used for their evaluation and introduce a new data-set for engine control, named Emission. Furthermore, our method can easily be adapted for unsupervised learning, e.g. the latent variable model and its deep version.
Statistical details of the default priors in the Bambi library

This is a companion paper to Yarkoni and Westfall (2017), which describes the Python package Bambi for estimating Bayesian generalized linear mixed models using a simple interface. Here I give the statistical details underlying the default, weakly informative priors used in all models when the user does not specify the priors. Our approach is to first deduce what the variances of the slopes would be if we were instead to have defined the priors on the partial correlation scale, and then to set independent Normal priors on the slopes with variances equal to these implied variances. Our approach is similar in spirit to that of Zellner's g-prior (Zellner 1986), in that it involves a multivariate normal prior on the regression slopes, with a tuning parameter to control the width or informativeness of the priors irrespective of the scales of the data and predictors. The primary differences are that here the tuning parameter is directly interpretable as the standard deviation of the distribution of plausible partial correlations, and that this tuning parameter can have different values for different coefficients. The default priors for the intercepts and random effects are ultimately based on the prior slope variances.
Tuning of MCMC with Langevin, Hamiltonian, and other stochastic autoregressive proposals

Proposals for Metropolis-Hastings MCMC derived by discretizing Langevin diffusion or Hamiltonian dynamics are examples of stochastic autoregressive proposals that form a natural wider class of proposals with equivalent computability. We analyze Metropolis-Hastings MCMC with stochastic autoregressive proposals applied to target distributions that are absolutely continuous with respect to some Gaussian distribution to derive expressions for expected acceptance probability and expected jump size, as well as measures of computational cost, in the limit of high dimension. Thus, we are able to unify existing analyzes for these classes of proposals, and to extend the theoretical results that provide useful guidelines for tuning the proposals for optimal computational efficiency. For the simplified Langevin algorithm we find that it is optimal to take at least three steps of the proposal before the Metropolis-Hastings accept-reject step, and for Hamiltonian/hybrid Monte Carlo we provide new guidelines for the optimal number of integration steps and criteria for choosing the optimal mass matrix.
Bayesian modelling of networks in complex business intelligence problems

Complex network data problems are increasingly common in many fields of application. Our motivation is drawn from strategic marketing studies monitoring customer choices of specific products, along with co‐subscription networks encoding multiple‐purchasing behaviour. Data are available for several agencies within the same insurance company, and our goal is to exploit co‐subscription networks efficiently to inform targeted advertising of cross‐sell strategies to currently monoproduct customers. We address this goal by developing a Bayesian hierarchical model, which clusters agencies according to common monoproduct customer choices and co‐subscription networks. Within each cluster, we efficiently model customer behaviour via a cluster‐dependent mixture of latent eigenmodels. This formulation provides key information on monoproduct customer choices and multiple‐purchasing behaviour within each cluster, informing targeted cross‐sell strategies. We develop simple algorithms for tractable inference and assess performance in simulations and an application to business intelligence.
Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression

ABSTRACT We propose an algorithm, semismooth Newton coordinate descent (SNCD), for the elastic-net penalized Huber loss regression and quantile regression in high dimensional settings. Unlike existing coordinate descent type algorithms, the SNCD updates a regression coefficient and its corresponding subgradient simultaneously in each iteration. It combines the strengths of the coordinate descent and the semismooth Newton algorithm, and effectively solves the computational challenges posed by dimensionality and nonsmoothness. We establish the convergence properties of the algorithm. In addition, we present an adaptive version of the “strong rule” for screening predictors to gain extra efficiency. Through numerical experiments, we demonstrate that the proposed algorithm is very efficient and scalable to ultrahigh dimensions. We illustrate the application via a real data example. Supplementary materials for this article are available online.
Well-Posed Bayesian Inverse Problems: Priors with Exponential Tails

We consider the well-posedness of Bayesian inverse problems when the prior measure has exponential tails. In particular, we consider the class of convex (log-concave) probability measures which include the Gaussian and Besov measures as well as certain classes of hierarchical priors. We identify appropriate conditions on the likelihood distribution and the prior measure which guarantee existence, uniqueness and stability of the posterior measure with respect to perturbations of the data. We also consider consistent approximations of the posterior such as discretization by projection. Finally, we present a general recipe for construction of convex priors on Banach spaces which will be of interest in practical applications where one often works with spaces such as $L^2$ or the continuous functions.
Towards reduction of autocorrelation in HMC by machine learning

In this paper we propose new algorithm to reduce autocorrelation in Markov chain Monte-Carlo algorithms for euclidean field theories on the lattice. Our proposing algorithm is the Hybrid Monte-Carlo algorithm (HMC) with restricted Boltzmann machine. We examine the validity of the algorithm by employing the phi-fourth theory in three dimension. We observe reduction of the autocorrelation both in symmetric and broken phase as well. Our proposing algorithm provides consistent central values of expectation values of the action density and one-point Green's function with ones from the original HMC in both the symmetric phase and broken phase within the statistical error. On the other hand, two-point Green's functions have slight difference between one calculated by the HMC and one by our proposing algorithm in the symmetric phase. Furthermore, near the criticality, the distribution of the one-point Green's function differs from the one from HMC. We discuss the origin of discrepancies and its improvement.
Parsimonious and Efficient Likelihood Composition by Gibbs Sampling

The traditional maximum likelihood estimator (MLE) is often of limited use in complex high-dimensional data due to the intractability of the underlying likelihood function. Maximum composite likelihood estimation (McLE) avoids full likelihood specification by combining a number of partial likelihood objects depending on small data subsets, thus enabling inference for complex data. A fundamental difficulty in making the McLE approach practicable is the selection from numerous candidate likelihood objects for constructing the composite likelihood function. In this article, we propose a flexible Gibbs sampling scheme for optimal selection of sub-likelihood components. The sampled composite likelihood functions are shown to converge to the one maximally informative on the unknown parameters in equilibrium, since sub-likelihood objects are chosen with probability depending on the variance of the corresponding McLE. A penalized version of our method generates sparse likelihoods with a relatively small number of components when the data complexity is intense. Our algorithms are illustrated through numerical examples on simulated data as well as real genotype single nucleotide polymorphism (SNP) data from a case–control study.
Clustering Nonstationary Circadian Rhythms using Locally Stationary Wavelet Representations

How does soil pollution affect a plant's circadian clock? Are there any differences between how the clock reacts when exposed to different concentrations of elements of the periodic table? If so, can we characterise these differences? We approach these questions by analysing and modelling circadian plant data, where the levels of expression of a luciferase reporter gene were measured at regular intervals over a number of days after exposure to different concentrations of lithium. A key aspect of circadian data analysis is to determine whether a time series (derived from experimental data) is `rhythmic' and, if so, to determine the underlying period. However, our dataset displays nonstationary traits such as changes in amplitude, gradual changes in period and phase-shifts. In this paper, we develop clustering methods using a wavelet transform. Wavelets are chosen as they are ideally suited to identifying discriminant local time and scale features. Furthermore, we propose treating the observed time series as realisations of locally stationary wavelet processes. This allows us to define and estimate the evolutionary wavelet spectrum. We can then compare, in a quantitative way, using a functional principal components analysis, the time-frequency patterns of the time series. Our approach uses a clustering algorithm to group the data according to their time-frequency patterns. We demonstrate the advantages of our methodology over alternative approaches and show that it successfully clusters our data.
Hierarchical Stochastic Model in Bayesian Inference: Theoretical Implications and Efficient Approximation

We classify two types of Hierarchical Bayesian Model found in the literature as Hierarchical Prior Model (HPM) and Hierarchical Stochastic Model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of polynomial functions, we show that the HSM is capable of separating different types of uncertainties in a system and quantifying uncertainty of reduced order models under the Bayesian model class selection framework. To tackle the huge computational cost for analyzing HSM, we propose an efficient approximation scheme based on Importance Sampling and Empirical Interpolation Method. We illustrate our method using two examples - a Molecular Dynamics simulation for Krypton and a pharmacokinetic/pharmacodynamic model for cancer drug.
Adaptation of the visibility graph algorithm to find the time lag between hydrogeological time series

Estimating the time lag between two hydrogeologic time series (e.g. precipitation and water levels in an aquifer) is of significance for a hydrogeologist-modeler. In this paper, we present a method to quantify such lags by adapting the visibility graph algorithm, which converts time series into a mathematical graph. We present simulation results to assess the performance of the method. We also illustrate the utility of our approach using a real world hydrogeologic dataset.
Elicitation, measuring bias, checking for prior-data conflict and inference with a Dirichlet prior

Methods are developed for eliciting a Dirichlet prior based upon bounds on the individual probabilities that hold with virtual certainty. This approach to selecting a prior is applied to a contingency table problem where it is demonstrated how to assess the bias in the prior as well as how to check for prior-data conflict. It is shown that the assessment of a hypothesis via relative belief can easily take into account what it means for the falsity of the hypothesis to correspond to a difference of practical importance and provide evidence in favor of a hypothesis.
Group-sparse block PCA and explained variance

The paper addresses the simultneous determination of goup-sparse loadings by block optimization, and the correlated problem of defining explained variance for a set of non orthogonal components. We give in both cases a comprehensive mathematical presentation of the problem, which leads to propose i) a new formulation/algorithm for group-sparse block PCA and ii) a framework for the definition of explained variance with the analysis of five definitions. The numerical results i) confirm the superiority of block optimization over deflation for the determination of group-sparse loadings, and the importance of group information when available, and ii) show that ranking of algorithms according to explained variance is essentially independant of the definition of explained variance. These results lead to propose a new optimal variance as the definition of choice for explained variance.
Proportional mean residual life model with censored survival data under case-cohort design

Proportional mean residual life model is studied for analysing survival data from the case-cohort design. To simultaneously estimate the regression parameters and the baseline mean residual life function, weighted estimating equations based on an inverse selection probability are proposed. The resulting regression coefficients estimates are shown to be consistent and asymptotic normal with easily estimated variance-covariance. Simulation studies show that the proposed estimators perform very well. An application to a real dataset from the South Welsh nickel refiners study is also given to illustrate the methodology.
Some exercises with the Lasso and its compatibility constant

We consider the Lasso for a noiseless experiment where one has observations $X \beta^0$ and uses the penalized version of basis pursuit. We compute for some special designs the compatibility constant, a quantity closely related to the restricted eigenvalue. We moreover show the dependence of the (penalized) prediction error on this compatibility constant. This exercise illustrates that compatibility is necessarily entering into the bounds for the (penalized) prediction error and that the bounds in the literature therefore are - up to constants - tight. We also give conditions that show that in the noisy case the dominating term for the prediction error is given by the prediction error of the noiseless case.
A convergence diagnostic for Bayesian clustering

In many applications of Bayesian clustering, posterior sampling on the discrete state space of cluster allocations is achieved via Markov chain Monte Carlo (MCMC) techniques. As it is typically challenging to design transition kernels to explore this state space efficiently, MCMC convergence diagnostics for clustering applications are especially important. Here we propose a diagnostic tool for discrete‐space MCMC, focusing on Bayesian clustering applications where the model parameters have been integrated out. We construct a Hotelling‐type statistic on the highest probability states, and use regenerative sampling theory to derive its equilibrium distribution. By leveraging information from the unnormalized posterior, our diagnostic offers added protection against seemingly convergent chains in which the relative frequency of visited states is incorrect. The methodology is illustrated with a Bayesian clustering analysis of genetic mutants of the flowering plant Arabidopsis thaliana.
Orthogonal series density estimation for complex surveys

ABSTRACT We propose an orthogonal series density estimator for complex surveys, where samples are neither independent nor identically distributed. The proposed estimator is proved to be design-unbiased and asymptotically design-consistent. The asymptotic normality is proved under both design and combined spaces. Two data driven estimators are proposed based on the proposed oracle estimator. We show the efficiency of the proposed estimators in simulation studies. A real survey data example is provided for an illustration.
Shape-constrained partial identification of a population mean under unknown probabilities of sample selection

A prevailing challenge in the biomedical and social sciences is to estimate a population mean from a sample obtained with unknown selection probabilities. Using a well-known ratio estimator, Aronow and Lee (2013) proposed a method for partial identification of the mean by allowing the unknown selection probabilities to vary arbitrarily between two fixed extreme values. In this paper, we show how to leverage auxiliary shape constraints on the population outcome distribution, such as symmetry or log-concavity, to obtain tighter bounds on the population mean. We use this method to estimate the performance of Aymara students---an ethnic minority in the north of Chile---in a national educational standardized test. We implement this method in the new statistical software package scbounds for R.
Reti bayesiane per lo studio del fenomeno degli incidenti stradali tra i giovani in Toscana

This paper aims to analyse adolescents' road accidents in Tuscany. The analysis is based on the Database Edit of Osservatorio di Epidemiologia della Toscana. Complexity and heterogeneity of Edit's data represet an interesting scope to apply Machine Learning methods. In particular, in this paper is proposed an analysis based on a Bayesian probabilistic network, used to discover relationships between adolescents' characteristics and behaviours that are more often associated with an audacious driving style. The probabilistic network developed by this study can be considered a useful starting point for follow up reasearches, aiming to develop a causal network, a tool to limit this phenomenon.
A New Spectral Method for Latent Variable Models

This paper presents an algorithm for the unsupervised learning of latent variable models from unlabeled sets of data. We base our technique on spectral decomposition, providing a technique that proves to be robust both in theory and in practice. We also describe how to use this algorithm to learn the parameters of two well known text mining models: single topic model and Latent Dirichlet Allocation, providing in both cases an efficient technique to retrieve the parameters to feed the algorithm. We compare the results of our algorithm with those of existing algorithms on synthetic data, and we provide examples of applications to real world text corpora for both single topic model and LDA, obtaining meaningful results.