arXiv subjects

L. Martino

Publications and source records attributed to L. Martino.

At least 19 recordsLinked to original sources

arXiv2026

A note on the area under the likelihood and the fake evidence for model selection

Improper priors are not allowed for the computation of the Bayesian evidence $Z=p({\bf y})$ (a.k.a., marginal likelihood), since in this case $Z$ is not completely specified due to an arbitrary constant involved in the computation. However, in this work, we remark that they can be employed in a specific type of model selection problem: when we have several (possibly infinite) models belonging to the same parametric family (i.e., for tuning parameters of a parametric model). However, the quantities involved in this type of selection cannot be considered as Bayesian evidences: we suggest to use the name ``fake evidences'' (or ``areas under the likelihood'' in the case of uniform improper priors). We also show that, in this model selection scenario, using a diffuse prior and increasing its scale parameter asymptotically to infinity, we cannot recover the value of the area under the likelihood, obtained with a uniform improper prior. We first discuss it from a general point of view. Then we provide, as an applicative example, all the details for Bayesian regression models with nonlinear bases, considering two cases: the use of a uniform improper prior and the use of a Gaussian prior, respectively. A numerical experiment is also provided confirming and checking all the previous statements.

stat.ME↗

arXiv2026

Effective sample size approximations as entropy measures

In this work, we analyze alternative effective sample size (ESS) metrics for importance sampling algorithms, and discuss a possible extended range of applications. We show the relationship between the ESS expressions used in the literature and two entropy families, the Rényi and Tsallis entropy. The Rényi entropy is connected to the Huggins-Roy's ESS family introduced in \cite{Huggins15}. We prove that that all the ESS functions included in the Huggins-Roy's family fulfill all the desirable theoretical conditions. We analyzed and remark the connections with several other fields, such as the Hill numbers introduced in ecology, the Gini inequality coefficient employed in economics, and the Gini impurity index used mainly in machine learning, to name a few. Finally, by numerical simulations, we study the performance of different ESS expressions contained in the previous ESS families in terms of approximation of the theoretical ESS definition, and show the application of ESS formulas in a variable selection problem.

math.ST↗

arXiv2026

An automatic counting algorithm for the quantification and uncertainty analysis of the number of microglial cells trainable in small and heterogeneous datasets

Counting immunopositive cells on biological tissues generally requires either manual annotation or (when available) automatic rough systems, for scanning signal surface and intensity in whole slide imaging. In this work, we tackle the problem of counting microglial cells in lumbar spinal cord cross-sections of rats by omitting cell detection and focusing only on the counting task. Manual cell counting is, however, a time-consuming task and additionally entails extensive personnel training. The classic automatic color-based methods roughly inform about the total labeled area and intensity (protein quantification) but do not specifically provide information on cell number. Since the images to be analyzed have a high resolution but a huge amount of pixels contain just noise or artifacts, we first perform a pre-processing generating several filtered images {(providing a tailored, efficient feature extraction)}. Then, we design an automatic kernel counter that is a non-parametric and non-linear method. The proposed scheme can be easily trained in small datasets since, in its basic version, it relies only on one hyper-parameter. However, being non-parametric and non-linear, the proposed algorithm is flexible enough to express all the information contained in rich and heterogeneous datasets as well (providing the maximum overfit if required). Furthermore, the proposed kernel counter also provides uncertainty estimation of the given prediction, and can directly tackle the case of receiving several expert opinions over the same image. Different numerical experiments with artificial and real datasets show very promising results. Related Matlab code is also provided.

cs.CE↗

arXiv2025

A recurrent 70-100 minute quasi-periodic pulsation in the intermediate-aged mid-M dwarf GJ 3512

We report the discovery of a {recurrent} quasi-periodic pulsation (QPP) in the late-M dwarf GJ 3512 (M5.5V) using multiple TESS datasets. A strong signal with a period of 70-100 minutes was detected in wavelet analyses of the two-minute cadence light curve from Sector 20. This signal was detected also in observations from Sectors 47 and 60. The QPP persisted for weeks in sector 20 and spanned nearly three years of TESS coverage. There was no significant damping between major flares. This behavior contrasts with that of previously reported stellar QPPs, which are confined to individual flares and decay on timescales of minutes to hours. The oscillation amplitude is at the milli-magnitude level. A pulsation origin is discarded since theoretical instability strips for 100-minute pulsations are restricted to pre-main sequence stars, while GJ 3512 is an intermediate age (2-8 Gyr) main-sequence dwarf. The persistence across independent TESS sectors discards an instrumental artifact origin and points to a likely coronal origin instead, such as oscillatory reconnection or thermal non-equilibrium cycles in large active regions. This represents the first detection of a likely sustained QPP with these characteristics in a late-type star, highlighting the need for further investigation into physical mechanisms behind such variability.

astro-ph.SR↗

arXiv2025

Target-aware Bayesian inference via generalized thermodynamic integration

In Bayesian inference, we are usually interested in the numerical approximation of integrals that are posterior expectations or marginal likelihoods (a.k.a., Bayesian evidence). In this paper, we focus on the computation of the posterior expectation of a function $f(\x)$. We consider a \emph{target-aware} scenario where $f(\x)$ is known in advance and can be exploited in order to improve the estimation of the posterior expectation. In this scenario, this task can be reduced to perform several independent marginal likelihood estimation tasks. The idea of using a path of tempered posterior distributions has been widely applied in the literature for the computation of marginal likelihoods. Thermodynamic integration, path sampling and annealing importance sampling are well-known examples of algorithms belonging to this family of methods. In this work, we introduce a generalized thermodynamic integration (GTI) scheme which is able to perform a target-aware Bayesian inference, i.e., GTI can approximate the posterior expectation of a given function. Several scenarios of application of GTI are discussed and different numerical simulations are provided.

stat.CO↗

arXiv2025

Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals

In this paper we address the problem of performing Bayesian inference for the parameters of a nonlinear multi-output model and the covariance matrix of the different output signals. We propose an adaptive importance sampling (AIS) scheme for multivariate Bayesian inversion problems, which is based in two main ideas: the variables of interest are split in two blocks and the inference takes advantage of known analytical optimization formulas. We estimate both the unknown parameters of the multivariate non-linear model and the covariance matrix of the noise. In the first part of the proposed inference scheme, a novel AIS technique called adaptive target adaptive importance sampling (ATAIS) is designed, which alternates iteratively between an IS technique over the parameters of the non-linear model and a frequentist approach for the covariance matrix of the noise. In the second part of the proposed inference scheme, a prior density over the covariance matrix is considered and the cloud of samples obtained by ATAIS are recycled and re-weighted to obtain a complete Bayesian study over the model parameters and covariance matrix. ATAIS is the main contribution of the work. Additionally, the inverted layered importance sampling (ILIS) is presented as a possible compelling algorithm (but based on a conceptually simpler idea). Different numerical examples show the benefits of the proposed approaches

stat.CO↗

arXiv2025

A survey of Monte Carlo methods for noisy and costly densities with application to reinforcement learning and ABC

This survey gives an overview of Monte Carlo methodologies using surrogate models, for dealing with densities which are intractable, costly, and/or noisy. This type of problem can be found in numerous real-world scenarios, including stochastic optimization and reinforcement learning, where each evaluation of a density function may incur some computationally-expensive or even physical (real-world activity) cost, likely to give different results each time. The surrogate model does not incur this cost, but there are important trade-offs and considerations involved in the choice and design of such methodologies. We classify the different methodologies into three main classes and describe specific instances of algorithms under a unified notation. A modular scheme which encompasses the considered methods is also presented. A range of application scenarios is discussed, with special attention to the likelihood-free setting and reinforcement learning. Several numerical comparisons are also provided.

cs.LG↗

arXiv2023

Universal and Automatic Elbow Detection for Learning the Effective Number of Components in Model Selection Problems

We design a Universal Automatic Elbow Detector (UAED) for deciding the effective number of components in model selection problems. The relationship with the information criteria widely employed in the literature is also discussed. The proposed UAED does not require the knowledge of a likelihood function and can be easily applied in diverse applications, such as regression and classification, feature and/or order selection, clustering, and dimension reduction. Several experiments involving synthetic and real data show the advantages of the proposed scheme with benchmark techniques in the literature.

cs.CE↗

arXiv2023

Spectral information criterion for automatic elbow detection

We introduce a generalized information criterion that contains other well-known information criteria, such as Bayesian information Criterion (BIC) and Akaike information criterion (AIC), as special cases. Furthermore, the proposed spectral information criterion (SIC) is also more general than the other information criteria, e.g., since the knowledge of a likelihood function is not strictly required. SIC extracts geometric features of the error curve and, as a consequence, it can be considered an automatic elbow detector. SIC provides a subset of all possible models, with a cardinality that often is much smaller than the total number of possible models. The elements of this subset are elbows of the error curve. A practical rule for selecting a unique model within the sets of elbows is suggested as well. Theoretical invariance properties of SIC are analyzed. Moreover, we test SIC in ideal scenarios where provides always the optimal expected results. We also test SIC in several numerical experiments: some involving synthetic data, and two experiments involving real datasets. They are all real-world applications such as clustering, variable selection, or polynomial order selection, to name a few. The results show the benefits of the proposed scheme. Matlab code related to the experiments is also provided. Possible future research lines are finally discussed.

stat.ME↗

arXiv2022

An exhaustive variable selection study for linear models of soundscape emotions: rankings and Gibbs analysis

In the last decade, soundscapes have become one of the most active topics in Acoustics, providing a holistic approach to the acoustic environment, which involves human perception and context. Soundscapes-elicited emotions are central and substantially subtle and unnoticed (compared to speech or music). Currently, soundscape emotion recognition is a very active topic in the literature. We provide an exhaustive variable selection study (i.e., a selection of the soundscapes indicators) to a well-known dataset (emo-soundscapes). We consider linear soundscape emotion models for two soundscapes descriptors: arousal and valence. Several ranking schemes and procedures for selecting the number of variables are applied. We have also performed an alternating optimization scheme for obtaining the best sequences keeping fixed a certain number of features. Furthermore, we have designed a novel technique based on Gibbs sampling, which provides a more complete and clear view of the relevance of each variable. Finally, we have also compared our results with the analysis obtained by the classical methods based on p-values. As a result of our study, we suggest two simple and parsimonious linear models of only 7 and 16 variables (within the 122 possible features) for the two outputs (arousal and valence), respectively. The suggested linear models provide very good and competitive performance, with $R^2>0.86$ and $R^2>0.63$ (values obtained after a cross-validation procedure), respectively.

cs.SD↗

arXiv2022

On the safe use of prior densities for Bayesian model selection

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal likelihoods depends on the prior choice. For model selection, even diffuse priors can be actually very informative, unlike for the parameter estimation problem. Furthermore, when the prior is improper, the marginal likelihood of the corresponding model is undetermined. In this work, we discuss the issue of prior sensitivity of the marginal likelihood and its role in model selection. We also comment on the use of uninformative priors, which are very common choices in practice. Several practical suggestions are discussed and many possible solutions, proposed in the literature, to design objective priors for model selection are described. Some of them also allow the use of improper priors. The connection between the marginal likelihood approach and the well-known information criteria is also presented. We describe the main issues and possible solutions by illustrative numerical examples, providing also some related code. One of them involving a real-world application on exoplanet detection.

stat.ME↗

arXiv2022

MCMC-driven importance samplers

Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on the class of Layered Adaptive Importance Sampling (LAIS) scheme, which is a family of adaptive importance samplers where Markov chain Monte Carlo algorithms are employed to drive an underlying multiple importance sampling scheme. The modular nature of LAIS allows for different possible implementations, yielding a variety of different performance and computational costs. In this work, we propose different enhancements of the classical LAIS setting in order to increase the efficiency and reduce the computational cost, of both upper and lower layers. The different variants address computational challenges arising in real-world applications, for instance with highly concentrated posterior distributions. Furthermore, we introduce different strategies for designing cheaper schemes, for instance, recycling samples generated in the upper layer and using them in the final estimators in the lower layer. Different numerical experiments, considering several challenging scenarios, show the benefits of the proposed schemes comparing with benchmark methods presented in the literature.

stat.CO↗

arXiv2021

A Bayesian inference and model selection algorithm with an optimisation scheme to infer the model noise power

Model fitting is possibly the most extended problem in science. Classical approaches include the use of least-squares fitting procedures and maximum likelihood methods to estimate the value of the parameters in the model. However, in recent years, Bayesian inference tools have gained traction. Usually, Markov chain Monte Carlo methods are applied to inference problems, but they present some disadvantages, particularly when comparing different models fitted to the same dataset. Other Bayesian methods can deal with this issue in a natural and effective way. We have implemented an importance sampling algorithm adapted to Bayesian inference problems in which the power of the noise in the observations is not known a priori. The main advantage of importance sampling is that the model evidence can be derived directly from the so-called importance weights -- while MCMC methods demand considerable postprocessing. The use of our adaptive target, adaptive importance sampling (ATAIS) method is shown by inferring, on the one hand, the parameters of a simulated flaring event which includes a damped oscillation {and, on the other hand, real data from the Kepler mission. ATAIS includes a novel automatic adaptation of the target distribution. It automatically estimates the variance of the noise in the model. ATAIS admits parallelisation, which decreases the computational run-times notably. We compare our method against a nested sampling method within a model selection problem.

astro-ph.IM↗

arXiv2021

A Survey of Monte Carlo Methods for Parameter Estimation

Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the maximum likelihood (ML) or maximum a posteriori (MAP) estimators, or by performing a multi-dimensional integration, as in the minimum mean squared error (MMSE) estimators. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and the Monte Carlo (MC) methodology is one feasible approach. MC methods proceed by drawing random samples, either from the desired distribution or from a simpler one, and using them to compute consistent estimators. The most important families of MC algorithms are Markov chain MC (MCMC) and importance sampling (IS). On the one hand, MCMC methods draw samples from a proposal density, building then an ergodic Markov chain whose stationary distribution is the desired distribution by accepting or rejecting those candidate samples as the new state of the chain. On the other hand, IS techniques draw samples from a simple proposal density, and then assign them suitable weights that measure their quality in some appropriate way. In this paper, we perform a thorough review of MC methods for the estimation of static parameters in signal processing applications. A historical note on the development of MC schemes is also provided, followed by the basic MC method and a brief description of the rejection sampling (RS) algorithm, as well as three sections describing many of the most relevant MCMC and IS algorithms, and their combined use.

stat.CO↗

arXiv2021

Automatic tempered posterior distributions for Bayesian inversion problems

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the variables of interest (i.e., the parameters of the model to invert), whereas we employ a maximum likelihood approach for the estimation of the noise power. The whole technique is implemented by means of an iterative procedure, alternating sampling and optimization steps. Moreover, the noise power is also used as a tempered parameter for the posterior distribution of the the variables of interest. Therefore, a sequence of tempered posterior densities is generated, where the tempered parameter is automatically selected according to the actual estimation of the noise power. A complete Bayesian study over the model parameters and the scale parameter can be also performed. Numerical experiments show the benefits of the proposed approach.

stat.CO↗

arXiv2021

Deep Importance Sampling based on Regression for Model Inversion and Emulation

Understanding systems by forward and inverse modeling is a recurrent topic of research in many domains of science and engineering. In this context, Monte Carlo methods have been widely used as powerful tools for numerical inference and optimization. They require the choice of a suitable proposal density that is crucial for their performance. For this reason, several adaptive importance sampling (AIS) schemes have been proposed in the literature. We here present an AIS framework called Regression-based Adaptive Deep Importance Sampling (RADIS). In RADIS, the key idea is the adaptive construction via regression of a non-parametric proposal density (i.e., an emulator), which mimics the posterior distribution and hence minimizes the mismatch between proposal and target densities. RADIS is based on a deep architecture of two (or more) nested IS schemes, in order to draw samples from the constructed emulator. The algorithm is highly efficient since employs the posterior approximation as proposal density, which can be improved adding more support points. As a consequence, RADIS asymptotically converges to an exact sampler under mild conditions. Additionally, the emulator produced by RADIS can be in turn used as a cheap surrogate model for further studies. We introduce two specific RADIS implementations that use Gaussian Processes (GPs) and Nearest Neighbors (NN) for constructing the emulator. Several numerical experiments and comparisons show the benefits of the proposed schemes. A real-world application in remote sensing model inversion and emulation confirms the validity of the approach.

stat.CO↗

arXiv2021

Adaptive quadrature schemes for Bayesian inference via active learning

Numerical integration and emulation are fundamental topics across scientific fields. We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate posterior density, combining it with Monte Carlo sampling methods and other quadrature rules. The nodes of the quadrature are sequentially chosen by maximizing a suitable acquisition function, which takes into account the current approximation of the posterior and the positions of the nodes. This maximization does not require additional evaluations of the true posterior. We introduce two specific schemes based on Gaussian and Nearest Neighbors (NN) bases. For the Gaussian case, we also provide a novel procedure for fitting the bandwidth parameter, in order to build a suitable emulator of a density function. With both techniques, we always obtain a positive estimation of the marginal likelihood (a.k.a., Bayesian evidence). An equivalent importance sampling interpretation is also described, which allows the design of extended schemes. Several theoretical results are provided and discussed. Numerical results show the advantage of the proposed approach, including a challenging inference problem in an astronomic dynamical model, with the goal of revealing the number of planets orbiting a star.

stat.CO↗

arXiv2020

A likely magnetic activity cycle for the exoplanet host M dwarf GJ 3512

Current radial velocity data from specialized instruments contain a large amount of information that may pass unnoticed if their analysis is not accurate. The joint use of Bayesian inference tools and frequency analysis has been shown effective to reveal exoplanets but they have been used less frequently to investigate stellar activity. We intend to use radial velocity data of the exoplanet host star GJ 3512 to investigate its magnetic activity. Our study includes the analysis of the photometric data available. The main objectives of our work are to constrain the orbital parameters of the exoplanets in the system, to determine the current level of activity of the star and to derive an activity cycle length for it. An adaptive importance sampling method was used to determine the parameters of the exoplanets orbit. Generalized Lomb-Scargle periodograms were constructed with both radial velocity curve and photometric data. A careful analysis of the harmonic frequencies was conducted in each periodogram. Our fit to multiple Keplerian orbits constrained the orbital parameters of two giant gas planets orbiting the star GJ 3512. The host star showed an increase of its magnetic activity during the last observing campaign. The accurate fit of the radial velocity curve data to the multi-Keplerian orbit permitted to reveal the star rotation in the residuals of the best fit and estimate an activity cycle length of ~ 14 years.

astro-ph.EP↗