arXiv subjects

Antonietta Mira

Publications and source records attributed to Antonietta Mira.

48 records · Page 3Linked to original sources

arXiv2018

Marginal models with individual-specific effects for the analysis of longitudinal bipartite networks

A new modeling framework for bipartite social networks arising from a sequence of partially time-ordered relational events is proposed. We directly model the joint distribution of the binary variables indicating if each single actor is involved or not in an event. The adopted parametrization is based on first- and second-order effects, formulated as in marginal models for categorical data and free higher order effects. In particular, second-order effects are log-odds ratios with meaningful interpretation from the social perspective in terms of tendency to cooperate, in contrast to first-order effects interpreted in terms of tendency of each single actor to participate in an event. These effects are parametrized on the basis of the event times, so that suitable latent trajectories of individual behaviors may be represented. Inference is based on a composite likelihood function, maximized by an algorithm with numerical complexity proportional to the square of the number of units in the network. A classification composite likelihood is used to cluster the actors, simplifying the interpretation of the data structure. The proposed approach is illustrated on a dataset of scientific articles published in four top statistical journals from 2003 to 2012.

stat.ME↗

arXiv2018

Bayesian Calibration of Force-fields from Experimental Data: TIP4P Water

Molecular dynamics (MD) simulations give access to equilibrium structures and dynamic properties given an ergodic sampling and an accurate force-field. The force-field parameters are calibrated to reproduce properties measured by experiments or simulations. The main contribution of this paper is an approximate Bayesian framework for the calibration and uncertainty quantification of the force-field parameters, without assuming parameter uncertainty to be Gaussian. To this aim, since the likelihood function of the MD simulation models are intractable in absence of Gaussianity assumption, we use a likelihood-free inference scheme known as approximate Bayesian computation (ABC) and propose an adaptive population Monte Carlo ABC algorithm, which is illustrated to converge faster and scales better than previously used ABCsubsim algorithm for calibration of force-field of a helium system. The second contribution is the adaptation of ABC algorithms for High Performance Computing to MD simulation within the Python ecosystem ABCpy. We illustrate the performance of the developed methodology to learn posterior distribution and Bayesian estimates of Lennard-Jones force-field parameters of helium and TIP4P system of water implemented both for simulated and experimental datasets collected using Neutron and X-ray diffraction. For simulated data, the Bayesian estimate is in close agreement with the true parameter value used to generate the dataset. For experimental as well as for simulated data, the Bayesian posterior distribution shows a strong correlation pattern between the force-field parameters. Providing an estimate of the entire posterior distribution, our methodology also allows us to perform uncertainty quantification of model prediction. This research opens up the possibility to rigorously calibrate force-fields from available experimental datasets of any structural and dynamic property.

stat.AP↗

arXiv2018

Fast Maximum Likelihood estimation via Equilibrium Expectation for Large Network Data

A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach becomes increasingly problematic as network size increases. In the context of current research on efficient estimation of models for large network data sets, we propose a fast algorithm for maximum likelihood estimation (MLE) that afords a signifcant increase in the size of networks amenable to direct empirical analysis. The algorithm we propose in this paper relies on properties of Markov chains at equilibrium, and for this reason it is called equilibrium expectation (EE). We demonstrate the performance of the EE algorithm in the context of exponential random graphmodels (ERGMs) a family of statistical models commonly used in empirical research based on network data observed at a single period in time. Thus far, the lack of efcient computational strategies has limited the empirical scope of ERGMs to relatively small networks with a few thousand nodes. The approach we propose allows a dramatic increase in the size of networks that may be analyzed using ERGMs. This is illustrated in an analysis of several biological networks and one social network with 104,103 nodes

stat.ME↗

arXiv2018

Adaptive Incremental Mixture Markov chain Monte Carlo

We propose Adaptive Incremental Mixture Markov chain Monte Carlo (AIMM), a novel approach to sample from challenging probability distributions defined on a general state-space. While adaptive MCMC methods usually update a parametric proposal kernel with a global rule, AIMM locally adapts a semiparametric kernel. AIMM is based on an independent Metropolis-Hastings proposal distribution which takes the form of a finite mixture of Gaussian distributions. Central to this approach is the idea that the proposal distribution adapts to the target by locally adding a mixture component when the discrepancy between the proposal mixture and the target is deemed to be too large. As a result, the number of components in the mixture proposal is not fixed in advance. Theoretically, we prove that there exists a process that can be made arbitrarily close to AIMM and that converges to the correct target distribution. We also illustrate that it performs well in practice in a variety of challenging situations, including high-dimensional and multimodal target distributions.

stat.ME↗

arXiv2018

Parameter estimation of platelets deposition: Approximate Bayesian computation with high performance computing

Recent studies show the existing clinical tests to detect Cardio/cerebrovascular diseases (CVD) are ineffectual as they do not consider different stages of platelet activation or the molecular dynamics involved in platelet interactions. Further they are also incapable to consider inter-individual variability. A physical description of platelets deposition was introduced recently in Chopard et. al. [2017], by integrating fundamental understandings of how platelets interact in a numerical model, parameterized by five parameters. These parameters specify the deposition process and are relevant for a biomedical understanding of the phenomena. One of the main intuition is that these parameters are precisely the information needed for a pathological test identifying CVD captured and that they capture the inter-individual variability. Following this intuition, here we devise a Bayesian inferential scheme for estimation of these parameters. As the likelihood function of the numerical model is intractable due to the complex stochastic nature of the model, we use a likelihood-free inference scheme approximate Bayesian computation (ABC) to calibrate the parameters in a data-driven manner. As ABC requires the generation of many pseudo-data by expensive simulation runs, we use a high performance computing (HPC) framework for ABC to make the inference possible for this model. We illustrate that our mean posterior prediction of platelet deposition pattern matches the experimental dataset closely with a tight posterior prediction error margin for a collective dataset of 7 volunteers. The present approach can be used to build a new generation of personalized platelet functionality tests for CVD detection, using numerical modeling of platelet deposition, Bayesian uncertainty quantification and High performance computing.

stat.AP↗

arXiv2018

Bayesian Inference of Spreading Processes on Networks

Infectious diseases are studied to understand their spreading mechanisms, to evaluate control strategies and to predict the risk and course of future outbreaks. Because people only interact with a small number of individuals, and because the structure of these interactions matters for spreading processes, the pairwise relationships between individuals in a population can be usefully represented by a network. Although the underlying processes of transmission are different, the network approach can be used to study the spread of pathogens in a contact network or the spread of rumors in an online social network. We study simulated simple and complex epidemics on synthetic networks and on two empirical networks, a social / contact network in an Indian village and an online social network in the U.S. Our goal is to learn simultaneously about the spreading process parameters and the source node (first infected node) of the epidemic, given a fixed and known network structure, and observations about state of nodes at several points in time. Our inference scheme is based on approximate Bayesian computation (ABC), an inference technique for complex models with likelihood functions that are either expensive to evaluate or analytically intractable. ABC enables us to adopt a Bayesian approach to the problem despite the posterior distribution being very complex. Our method is agnostic about the topology of the network and the nature of the spreading process. It generally performs well and, somewhat counter-intuitively, the inference problem appears to be easier on more heterogeneous network topologies, which enhances its future applicability to real-world settings where few networks have homogeneous topologies.

stat.AP↗

arXiv2016

International Trade: a Reinforced Urn Network Model

We propose a unified modelling framework that theoretically justifies the main empirical regularities characterizing the international trade network. Each country is associated to a Polya urn whose composition controls the propensity of the country to trade with other countries. The urn composition is updated through the walk of the Reinforced Urn Process of Muliere et al. (2000). The model implies a local preferential attachment scheme and a power law right tail behaviour of bilateral trade flows. Different assumptions on the urns' reinforcement parameters account for local clustering, path-shortening and sparsity. Likelihood-based estimation approaches are facilitated by feasible likelihood analytical derivation in various network settings. A simulated example and the empirical results on the international trade network are discussed.

physics.soc-ph↗

arXiv2015

Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods

Many popular statistical models for complex phenomena are intractable, in the sense that the likelihood function cannot easily be evaluated. Bayesian estimation in this setting remains challenging, with a lack of computational methodology to fully exploit modern processing capabilities. In this paper we introduce novel control variates for intractable likelihoods that can dramatically reduce the Monte Carlo variance of Bayesian estimators. We prove that our control variates are well-defined and provide a positive variance reduction. Furthermore we show how to optimise these control variates for variance reduction. The methodology is highly parallel and offers a route to exploit multi-core processing architectures that complements recent research in this direction. Indeed, our work shows that it may not be necessary to parallelise the sampling process itself in order to harness the potential of massively multi-core architectures. Simulation results presented on the Ising model, exponential random graph models and non-linear stochastic differential equation models support our theoretical findings.

stat.CO↗

arXiv2014

Efficient computational strategies for doubly intractable problems with applications to Bayesian social networks

Powerful ideas recently appeared in the literature are adjusted and combined to design improved samplers for Bayesian exponential random graph models. Different forms of adaptive Metropolis-Hastings proposals (vertical, horizontal and rectangular) are tested and combined with the Delayed rejection (DR) strategy with the aim of reducing the variance of the resulting Markov chain Monte Carlo estimators for a given computational time. In the examples treated in this paper the best combination, namely horizontal adaptation with delayed rejection, leads to a variance reduction that varies between 92% and 144% relative to the adaptive direction sampling approximate exchange algorithm of Caimo and Friel (2011). These results correspond to an increased performance which varies from 10% to 94% if we take simulation time into account. The highest improvements are obtained when highly correlated posterior distributions are considered.

stat.CO↗

arXiv2012

Zero Variance Markov Chain Monte Carlo for Bayesian Estimators

Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the expected value of a function with respect to a, possibly unnormalized, probability distribution. A general purpose variance reduction technique for the MCMC estimator, based on the zero-variance principle introduced in the physics literature, is proposed. Conditions for asymptotic unbiasedness of the zero-variance estimator are derived. A central limit theorem is also proved under regularity conditions. The potential of the idea is illustrated with real applications to probit, logit and GARCH Bayesian models. For all these models, a central limit theorem and unbiasedness for the zero-variance estimator are proved (see the supplementary material available on-line).

stat.CO↗

arXiv2011

Adaptive Multiple Importance Sampling

The Adaptive Multiple Importance Sampling (AMIS) algorithm is aimed at an optimal recycling of past simulations in an iterated importance sampling scheme. The difference with earlier adaptive importance sampling implementations like Population Monte Carlo is that the importance weights of all simulated values, past as well as present, are recomputed at each iteration, following the technique of the deterministic multiple mixture estimator of Owen and Zhou (2000). Although the convergence properties of the algorithm cannot be fully investigated, we demonstrate through a challenging banana shape target distribution and a population genetics example that the improvement brought by this technique is substantial.

stat.CO↗

arXiv2004

Delayed Rejection Variational Monte Carlo

A new acceleration algorithm to address the problem of multiple time scales in variational Monte Carlo simulations is presented. After a first attempted move has been rejected, the delayed rejection algorithm attempts a second move with a smaller time step, so that even moves of the core electrons can be accepted. Results on Be and Ne atoms as test cases are presented. Correlation time and both average accepted displacement and acceptance ratio as a function of the distance from the nucleus evidence the efficiency of the proposed algorithm in dealing with the multiple time scales problem.

cond-mat.other↗