arXiv subjects

Tabea Rebafka

Publications and source records attributed to Tabea Rebafka.

14 recordsLinked to original sources

arXiv2026

Beyond Degree: Rooted Motif Signatures for Latent Position Identifiability in Graphon Models

Graphon estimation requires structural assumptions to address its intrinsic non-identifiability. A standard approach is degree-based identifiability, where the degree function is assumed to be strictly monotonic. This assumption is rather restrictive and fails for graphons with constant or non-injective degree function, even when distinct latent positions have different connectivity profiles. In this paper, we introduce \emph{rooted motif signatures} as higher-order node-level representations for graphons. They extend the degree function by recording, at each latent position, the densities of rooted motifs such as triangles, cycles, paths, and other local subgraph patterns. We study the extent to which these signatures can distinguish latent positions beyond degree information. For generic finite-rank graphons, we prove that suitable rooted motif signatures determine the connectivity profiles of latent positions. We also explain why such a property cannot hold for arbitrary graphons without additional assumptions, since different latent positions may have identical rooted motif signatures. On the statistical side, we define empirical rooted motif signatures from a single observed graph and prove uniform concentration bounds for these estimators. Simulation experiments illustrate that rooted motif signatures can reveal latent structure in settings where degree-based representations are uninformative, including graphons with constant or non-injective degree functions and stochastic block models with equal block degrees.

math.ST↗

arXiv2026

A Bayesian framework with adaptive elastic nets for the inference of Gaussian graphical models

Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior accounts for degree heterogeneity edge sparsity, and graph topology the graph. The resulting posterior distribution is incorporated into a multiple testing procedure for graph inference with false discovery rate control. Computation is carried out through a combination of adaptive elastic nets and a variational expectation--maximization algorithm. In simulations, the method achieves reliable false discovery rate control while maintaining strong power, especially in heterogeneous networks such as graphs with hubs, and remains competitive under structural misspecification. Applications to breast cancer gene expression data and financial return networks show that the method yields sparse and interpretable conditional dependence graphs while retaining the most stable interactions detected by competing approaches.

stat.ME↗

arXiv2026

Low-Complexity and Consistent Graphon Estimation from Multiple Networks

Recovering the random graph model from an observed collection of networks is known to present significant challenges in the setting, where the networks do not share a common node set and have different sizes. More specifically, the goal is the estimation of the graphon function that parametrizes the nonparametric exchangeable random graph model. Existing methods typically suffer from either limited accuracy or high computational complexity. We introduce a new histogram-based estimator with low algorithmic complexity that achieves high accuracy by jointly aligning the nodes of all graphs, in contrast to most conventional methods that order nodes graph by graph. Consistency results of the proposed graphon estimator are established. A numerical study shows that the proposed estimator outperforms existing methods in terms of accuracy, especially when the dataset comprises only small and variable-size networks. Moreover, the computing time of the new method is considerably shorter than that of other consistent methodologies. Additionally, when applied to a graph neural network classification task, the proposed estimator enables more effective data augmentation, yielding improved performance across diverse real-world datasets.

stat.ME↗

arXiv2024

Enhancing the Power of Gaussian Graphical Model Inference by Modeling the Graph Structure

For the problem of inferring a Gaussian graphical model (GGM), this work explores the application of a recent approach from the multiple testing literature for graph inference. The main idea of the method by Rebafka et al. (2022) is to model the data by a latent variable model, the so-called noisy stochastic block model (NSBM), and then use the associated ${\ell}$-values to infer the graph. The inferred graph controls the false discovery rate, that means that the proportion of falsely declared edges does not exceed a user-defined nominal level. Here it is shown that any test statistic from the GGM literature can be used as input for the NSBM approach to perform GGM inference. To make the approach feasible in practice, a new, computationally efficient inference algorithm for the NSBM is developed relying on a greedy approach to maximize the integrated complete-data likelihood. Then an extensive numerical study illustrates that the NSBM approach outperforms the state of the art for any of the here considered GGM-test statistics. In particular in sparse settings and on real datasets a significant gain in power is observed.

stat.ME↗

arXiv2023

Model-based clustering of multiple networks with a hierarchical algorithm

The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of stochastic block models is proposed. A clustering is obtained by maximizing the integrated classification likelihood criterion. This is done by a hierarchical agglomerative algorithm, that starts from singleton clusters and successively merges clusters of networks. As such, a sequence of nested clusterings is computed that can be represented by a dendrogram providing valuable insights on the collection of networks. Using a Bayesian framework, model selection is performed in an automated way since the algorithm stops when the best number of clusters is attained. The algorithm is computationally efficient, when carefully implemented. The aggregation of clusters requires a means to overcome the label-switching problem of the stochastic block model and to match the block labels of the networks. To address this problem, a new tool is proposed based on a comparison of the graphons of the associated stochastic block models. The clustering approach is assessed on synthetic data. An application to a set of ecological networks illustrates the interpretability of the obtained results.

math.ST↗

arXiv2023

False membership rate control in mixture models

The clustering task consists in partitioning elements of a sample into homogeneous groups. Most datasets contain individuals that are ambiguous and intrinsically difficult to attribute to one or another cluster. However, in practical applications, misclassifying individuals is potentially disastrous and should be avoided. To keep the misclassification rate small, one can decide to classify only a part of the sample. In the supervised setting, this approach is well known and referred to as classification with an abstention option. In this paper the approach is revisited in an unsupervised mixture model framework and the purpose is to develop a method that comes with the guarantee that the false membership rate (FMR) does not exceed a pre-defined nominal level $α$. A plug-in procedure is proposed, for which a theoretical analysis is provided, by quantifying the FMR deviation with respect to the target level $α$ with explicit remainder terms. Bootstrap versions of the procedure are shown to improve the performance in numerical experiments.

math.ST↗

arXiv2023

Data-Driven Score-Based Models for Generating Stable Structures with Adaptive Crystal Cells

The discovery of new functional and stable materials is a big challenge due to its complexity. This work aims at the generation of new crystal structures with desired properties, such as chemical stability and specified chemical composition, by using machine learning generative models. Compared to the generation of molecules, crystal structures pose new difficulties arising from the periodic nature of the crystal and from the specific symmetry constraints related to the space group. In this work, score-based probabilistic models based on annealed Langevin dynamics, which have shown excellent performance in various applications, are adapted to the task of crystal generation. The novelty of the presented approach resides in the fact that the lattice of the crystal cell is not fixed. During the training of the model, the lattice is learned from the available data, whereas during the sampling of a new chemical structure, two denoising processes are used in parallel to generate the lattice along the generation of the atomic positions. A multigraph crystal representation is introduced that respects symmetry constraints, yielding computational advantages and a better quality of the sampled structures. We show that our model is capable of generating new candidate structures in any chosen chemical system and crystal group without any additional training. To illustrate the functionality of the proposed method, a comparison of our model to other recent generative models, based on descriptor-based metrics, is provided.

physics.comp-ph↗

arXiv2023

Self-Organizing Maps for Exploration of Partially Observed Data and Imputation of Missing Values

The self-organizing map is an unsupervised neural network which is widely used for data visualisation and clustering in the field of chemometrics. The classical Kohonen algorithm that computes self-organizing maps is suitable only for complete data without any missing values. However, in many applications, partially observed data are the norm. In this paper, we propose an extension of self-organizing maps to incomplete data via a new criterion that also defines estimators of the missing values. In addition, an adaptation of the Kohonen algorithm, named missSOM, is provided to compute these self-organizing maps and impute missing values. An efficient implementation is provided. Numerical experiments on simulated data and a chemical dataset illustrate the short computing time of missSOM and assess its performance regarding various criteria and in comparison to the state of the art.

stat.ME↗

arXiv2020

Properties of the Stochastic Approximation EM Algorithm with Mini-batch Sampling

To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown to be convergent under classicalconditions as the number of iterations increases. Numerical experiments illustrate the performance of the mini-batch algorithm in various models.In particular, we highlight that mini-batch sampling results in an important speed-up of the convergence of the sequence of estimators generated by the algorithm. Moreover, insights on the effect of the mini-batch size on the limit distribution are presented. Finally, we illustrate how to use mini-batch sampling in practice to improve results when a constraint on the computing time is given.

stat.CO↗

arXiv2019

Graph inference with clustering and false discovery rate control

In this paper, a noisy version of the stochastic block model (NSBM) is introduced and we investigate the three following statistical inferences in this model: estimation of the model parameters, clustering of the nodes and identification of the underlying graph. While the two first inferences are done by using a variational expectation-maximization (VEM) algorithm, the graph inference is done by controlling the false discovery rate (FDR), that is, the average proportion of errors among the edges declared significant, and by maximizing the true discovery rate (TDR), that is, the average proportion of edges declared significant among the true edges. Provided that the VEM algorithm provides reliable parameter estimates and clustering, we theoretically show that our procedure does control the FDR while satisfying an optimal TDR property, up to remainder terms that become small when the size of the graph grows. Numerical experiments show that our method outperforms the classical FDR controlling methods that ignore the underlying SBM topology. In addition, these simulations demonstrate that the FDR/TDR properties of our method are robust to model mis-specification, that is, are essentially maintained outside our model.

math.ST↗

arXiv2017

A semiparametric extension of the stochastic block model for longitudinal networks

To model recurrent interaction events in continuous time, an extension of the stochastic block model is proposed where every individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous Poisson process with intensity driven by the individuals' latent groups. The model is shown to be identifiable and its estimation is based on a semiparametric variational expectation-maximization algorithm. Two versions of the method are developed, using either a nonparametric histogram approach (with an adaptive choice of the partition size) or kernel intensity estimators. The number of latent groups can be selected by an integrated classification likelihood criterion. Finally, we demonstrate the performance of our procedure on synthetic experiments, analyse two datasets to illustrate the utility of our approach and comment on competing methods.

stat.ME↗

arXiv2015

Nonparametric estimation of the mixing density using polynomials

We consider the problem of estimating the mixing density $f$ from $n$ i.i.d. observations distributed according to a mixture density with unknown mixing distribution. In contrast with finite mixtures models, here the distribution of the hidden variable is not bounded to a finite set but is spread out over a given interval. We propose an approach to construct an orthogonal series estimator of the mixing density $f$ involving Legendre polynomials. The construction of the orthonormal sequence varies from one mixture model to another. Minimax upper and lower bounds of the mean integrated squared error are provided which apply in various contexts. In the specific case of exponential mixtures, it is shown that the estimator is adaptive over a collection of specific smoothness classes, more precisely, there exists a constant $A\textgreater{}0$ such that, when the order $m$ of the projection estimator verifies $m\sim A \log(n)$, the estimator achieves the minimax rate over this collection. Other cases are investigated such as Gamma shape mixtures and scale mixtures of compactly supported densities including Beta mixtures. Finally, a consistent estimator of the support of the mixing density $f$ is provided.

math.ST↗

arXiv2011

OMP-type Algorithm with Structured Sparsity Patterns for Multipath Radar Signals

A transmitted, unknown radar signal is observed at the receiver through more than one path in additive noise. The aim is to recover the waveform of the intercepted signal and to simultaneously estimate the direction of arrival (DOA). We propose an approach exploiting the parsimonious time-frequency representation of the signal by applying a new OMP-type algorithm for structured sparsity patterns. An important issue is the scalability of the proposed algorithm since high-dimensional models shall be used for radar signals. Monte-Carlo simulations for modulated signals illustrate the good performance of the method even for low signal-to-noise ratios and a gain of 20 dB for the DOA estimation compared to some elementary method.

math.ST↗

arXiv2010

Adaptive Density Estimation in the Pile-up Model Involving Measurement Errors

Motivated by fluorescence lifetime measurements this paper considers the problem of nonparametric density estimation in the pile-up model. Adaptive nonparametric estimators are proposed for the pile-up model in its simple form as well as in the case of additional measurement errors. Furthermore, oracle type risk bounds for the mean integrated squared error (MISE) are provided. Finally, the estimation methods are assessed by a simulation study and the application to real fluorescence lifetime data.

stat.AP↗