arXiv subjects

Antonietta Mira

Publications and source records attributed to Antonietta Mira.

At least 37 records · Page 2Linked to original sources

arXiv2022

Regularized Zero-Variance Control Variates

Zero-variance control variates (ZV-CV) are a post-processing method to reduce the variance of Monte Carlo estimators of expectations using the derivatives of the log target. Once the derivatives are available, the only additional computational effort lies in solving a linear regression problem. Significant variance reductions have been achieved with this method in low dimensional examples, but the number of covariates in the regression rapidly increases with the dimension of the target. In this paper, we present compelling empirical evidence that the use of penalized regression techniques in the selection of high-dimensional control variates provides performance gains over the classical least squares method. Another type of regularization based on using subsets of derivatives, or a priori regularization as we refer to it in this paper, is also proposed to reduce computational and storage requirements. Several examples showing the utility and limitations of regularized ZV-CV for Bayesian inference are given. The methods proposed in this paper are accessible through the R package ZVCV.

stat.CO↗

arXiv2022

Learning Summary Statistics for Bayesian Inference with Autoencoders

For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory approximation of the posterior. Therefore, we propose to use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information on the noise that has been used to generate the training data. We validate the approach empirically on two types of stochastic models.

cs.LG↗

arXiv2022

A predictive model for planning emergency events rescue during COVID-19 in Lombardy, Italy

Italy, particularly the Lombardy region, was among the first countries outside of Asia to report cases of COVID-19. The emergency medical service called Regional Emergency Agency (AREU) coordinates the intra- and inter-regional non-hospital emergency network and the European emergency number service in Lombardy. AREU must deal with daily and seasonal variations of call volume. The number and type of emergency calls changed dramatically during the COVID-19 pandemic. A model to predict incoming calls and how many of these turn into events, i.e., dispatch of transport and equipment until the rescue is completed, was developed to address the emergency period. We used the generalized additive model with a negative binomial family to predict the number of events one, two, five, and seven days ahead. The over-dispersion of the data was tackled by using the negative binomial family and the nonlinear relationship between the number of events and covariates (e.g., seasonal effects) by smoothing splines. The model coefficients show the effect of variables, e.g., the day of the week, on the number of events and how these effects change during the pre-COVID-19 period. The proposed model returns reasonable mean absolute errors for most of the 2020-2021 period.

stat.AP↗

arXiv2022

On the intrinsic dimensionality of Covid-19 data: a global perspective

This paper aims to develop a global perspective of the complexity of the relationship between the standardised per-capita growth rate of Covid-19 cases, deaths, and the OxCGRT Covid-19 Stringency Index, a measure describing a country's stringency of lockdown policies. To achieve our goal, we use a heterogeneous intrinsic dimension estimator implemented as a Bayesian mixture model, called Hidalgo. We identify that the Covid-19 dataset may project onto two low-dimensional manifolds without significant information loss. The low dimensionality suggests strong dependency among the standardised growth rates of cases and deaths per capita and the OxCGRT Covid-19 Stringency Index for a country over 2020-2021. Given the low dimensional structure, it may be feasible to model observable Covid-19 dynamics with few parameters. Importantly, we identify spatial autocorrelation in the intrinsic dimension distribution worldwide. Moreover, we highlight that high-income countries are more likely to lie on low-dimensional manifolds, likely arising from aging populations, comorbidities, and increased per capita mortality burden from Covid-19. Finally, we temporally stratify the dataset to examine the intrinsic dimension at a more granular level throughout the Covid-19 pandemic.

stat.AP↗

arXiv2022

Personalized pathology test for Cardio-vascular disease: Approximate Bayesian computation with discriminative summary statistics learning

Cardio/cerebrovascular diseases (CVD) have become one of the major health issue in our societies. But recent studies show that the present pathology tests to detect CVD are ineffectual as they do not consider different stages of platelet activation or the molecular dynamics involved in platelet interactions and are incapable to consider inter-individual variability. Here we propose a stochastic platelet deposition model and an inferential scheme to estimate the biologically meaningful model parameters using approximate Bayesian computation with a summary statistic that maximally discriminates between different types of patients. Inferred parameters from data collected on healthy volunteers and different patient types help us to identify specific biological parameters and hence biological reasoning behind the dysfunction for each type of patients. This work opens up an unprecedented opportunity of personalized pathology test for CVD detection and medical treatment.

stat.ME↗

arXiv2021

ABCpy: A High-Performance Computing Perspective to Approximate Bayesian Computation

ABCpy is a highly modular scientific library for Approximate Bayesian Computation (ABC) written in Python. The main contribution of this paper is to document a software engineering effort that enables domain scientists to easily apply ABC to their research without being ABC experts; using ABCpy they can easily run large parallel simulations without much knowledge about parallelization. Further, ABCpy enables ABC experts to easily develop new inference schemes and evaluate them in a standardized environment and to extend the library with new algorithms. These benefits come mainly from the modularity of ABCpy. We give an overview of the design of ABCpy and provide a performance evaluation concentrating on parallelization. This points us towards the inherent imbalance in some of the ABC algorithms. We develop a dynamic scheduling MPI implementation to mitigate this issue and evaluate the various ABC algorithms according to their adaptability towards high-performance computing.

stat.CO↗

arXiv2021

A Bayesian Semiparametric Vector Multiplicative Error Model

Interactions among multiple time series of positive random variables are crucial in diverse financial applications, from spillover effects to volatility interdependence. A popular model in this setting is the vector Multiplicative Error Model (vMEM) which poses a linear iterative structure on the dynamics of the conditional mean, perturbed by a multiplicative innovation term. A main limitation of vMEM is however its restrictive assumption on the distribution of the random innovation term. A Bayesian semiparametric approach that models the innovation vector as an infinite location-scale mixture of multidimensional kernels with support on the positive orthant is used to address this major shortcoming of vMEM. Computational complications arising from the constraints to the positive orthant are avoided through the formulation of a slice sampler on the parameter-extended unconstrained version of the model. The method is applied to simulated and real data and a flexible specification is obtained that outperforms the classical ones in terms of fitting and predictive power.

stat.CO↗

arXiv2021

Revealing three-dimensional quantum criticality by Sr-substitution in Han Purple

Classical and quantum phase transitions (QPTs), with their accompanying concepts of criticality and universality, are a cornerstone of statistical thermodynamics. An exemplary controlled QPT is the field-induced magnetic ordering of a gapped quantum magnet. Although numerous "quasi-one-dimensional" coupled spin-chain and -ladder materials are known whose ordering transition is three-dimensional (3D), quasi-2D systems are special for several physical reasons. Motivated by the ancient pigment Han Purple (BaCuSi$_{2}$O$_{6}$), a quasi-2D material displaying anomalous critical properties, we present a complete analysis of Ba$_{0.9}$Sr$_{0.1}$CuSi$_{2}$O$_{6}$. We measure the zero-field magnetic excitations by neutron spectroscopy and deduce the magnetic Hamiltonian. We probe the field-induced transition by combining magnetization, specific-heat, torque and magnetocalorimetric measurements with low-temperature nuclear magnetic resonance studies near the QPT. By a Bayesian statistical analysis and large-scale Quantum Monte Carlo simulations, we demonstrate unambiguously that observable 3D quantum critical scaling is restored by the structural simplification arising from light Sr-substitution in Han Purple.

cond-mat.str-el↗

arXiv2021

Distributional Results for Model-Based Intrinsic Dimension Estimators

Modern datasets are characterized by a large number of features that may conceal complex dependency structures. To deal with this type of data, dimensionality reduction techniques are essential. Numerous dimensionality reduction methods rely on the concept of intrinsic dimension, a measure of the complexity of the dataset. In this article, we first review the TWO-NN model, a likelihood-based intrinsic dimension estimator recently introduced in the literature. The TWO-NN estimator is based on the statistical properties of the ratio of the distances between a point and its first two nearest neighbors, assuming that the points are a realization from an homogeneous Poisson point process. We extend the TWO-NN theoretical framework by providing novel distributional results of consecutive and generic ratios of distances. These distributional results are then employed to derive intrinsic dimension estimators, called Cride and Gride. These novel estimators are more robust to noisy measurements than the TWO-NN and allow the study of the evolution of the intrinsic dimension as a function of the scale used to analyze the dataset. We discuss the properties of the different estimators with the help of simulation scenarios.

stat.ME↗

arXiv2021

A Bayesian latent allocation model for clustering compositional data with application to the Great Barrier Reef

Relative abundance is a common metric to estimate the composition of species in ecological surveys reflecting patterns of commonness and rarity of biological assemblages. Measurements of coral reef compositions formed by four communities along Australia's Great Barrier Reef (GBR) gathered between 2012 and 2017 are the focus of this paper. We undertake the task of finding clusters of transect locations with similar community composition and investigate changes in clustering dynamics over time. During these years, an unprecedented sequence of extreme weather events (cyclones and coral bleaching) impacted the 58 surveyed locations. The dependence between constituent parts of a composition presents a challenge for existing multivariate clustering approaches. In this paper, we introduce a finite mixture of Dirichlet distributions with group-specific parameters, where cluster memberships are dictated by unobserved latent variables. The inference is carried in a Bayesian framework, where MCMC strategies are outlined to sample from the posterior model. Simulation studies are presented to illustrate the performance of the model in a controlled setting. The application of the model to the 2012 coral reef data reveals that clusters were spatially distributed in similar ways across reefs which indicates a potential influence of wave exposure at the origin of coral reef community composition. The number of clusters estimated by the model decreased from four in 2012 to two from 2014 until 2017. Posterior probabilities of transect allocations to the same cluster substantially increase through time showing a potential homogenization of community composition across the whole GBR. The Bayesian model highlights the diversity of coral reef community composition within a coral reef and rapid changes across large spatial scales that may contribute to undermining the future of the GBR's biodiversity.

stat.AP↗

arXiv2020

Scalable Approximate Bayesian Computation for Growing Network Models via Extrapolated and Sampled Summaries

Approximate Bayesian computation (ABC) is a simulation-based likelihood-free method applicable to both model selection and parameter estimation. ABC parameter estimation requires the ability to forward simulate datasets from a candidate model, but because the sizes of the observed and simulated datasets usually need to match, this can be computationally expensive. Additionally, since ABC inference is based on comparisons of summary statistics computed on the observed and simulated data, using computationally expensive summary statistics can lead to further losses in efficiency. ABC has recently been applied to the family of mechanistic network models, an area that has traditionally lacked tools for inference and model choice. Mechanistic models of network growth repeatedly add nodes to a network until it reaches the size of the observed network, which may be of the order of millions of nodes. With ABC, this process can quickly become computationally prohibitive due to the resource intensive nature of network simulations and evaluation of summary statistics. We propose two methodological developments to enable the use of ABC for inference in models for large growing networks. First, to save time needed for forward simulating model realizations, we propose a procedure to extrapolate (via both least squares and Gaussian processes) summary statistics from small to large networks. Second, to reduce computation time for evaluating summary statistics, we use sample-based rather than census-based summary statistics. We show that the ABC posterior obtained through this approach, which adds two additional layers of approximation to the standard ABC, is similar to a classic ABC posterior. Although we deal with growing network models, both extrapolated summaries and sampled summaries are expected to be relevant in other ABC settings where the data are generated incrementally.

stat.ME↗

arXiv2020

A Common Atom Model for the Bayesian Nonparametric Analysis of Nested Data

The use of high-dimensional data for targeted therapeutic interventions requires new ways to characterize the heterogeneity observed across subgroups of a specific population. In particular, models for partially exchangeable data are needed for inference on nested datasets, where the observations are assumed to be organized in different units and some sharing of information is required to learn distinctive features of the units. In this manuscript, we propose a nested Common Atoms Model (CAM) that is particularly suited for the analysis of nested datasets where the distributions of the units are expected to differ only over a small fraction of the observations sampled from each unit. The proposed CAM allows a two-layered clustering at the distributional and observational level and is amenable to scalable posterior inference through the use of a computationally efficient nested slice-sampler algorithm. We further discuss how to extend the proposed modeling framework to handle discrete measurements, and we conduct posterior inference on a real microbiome dataset from a diet swap study to investigate how the alterations in intestinal microbiota composition are associated with different eating habits. We further investigate the performance of our model in capturing true distributional structures in the population by means of a simulation study.

stat.ME↗

arXiv2020

Data segmentation based on the local intrinsic dimension

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data. Contrary to common intuition, there are cases where the ID varies within the same data set. This fact has been highlighted in technical discussions, but seldom exploited to analyze large data sets and obtain insight into their structure. Here we develop a robust approach to discriminate regions with different local IDs and segment the points accordingly. Our approach is computationally efficient and can be proficiently used even on large data sets. We find that many real-world data sets contain regions with widely heterogeneous dimensions. These regions host points differing in core properties: folded vs unfolded configurations in a protein molecular dynamics trajectory, active vs non-active regions in brain imaging data, and firms with different financial risk in company balance sheets. A simple topological feature, the local ID, is thus sufficient to achieve an unsupervised segmentation of high-dimensional data, complementary to the one given by clustering algorithms.

stat.ML↗

arXiv2020

Estimating a novel stochastic model for within-field disease dynamics of banana bunchy top virus via approximate Bayesian computation

The Banana Bunchy Top Virus (BBTV) is one of the most economically important vector-borne banana diseases throughout the Asia-Pacific Basin and presents a significant challenge to the agricultural sector. Current models of BBTV are largely deterministic, limited by an incomplete understanding of interactions in complex natural systems, and the appropriate identification of parameters. A stochastic network-based Susceptible-Infected model has been created which simulates the spread of BBTV across the subsections of a banana plantation, parameterising nodal recovery, neighbouring and distant infectivity across summer and winter. Findings from posterior results achieved through Markov Chain Monte Carlo approach to approximate Bayesian computation suggest seasonality in all parameters, which are influenced by correlated changes in inspection accuracy, temperatures and aphid activity. This paper demonstrates how the model may be used for monitoring and forecasting of various disease management strategies to support policy-level decision making.

stat.AP↗

arXiv2020

The role of intrinsic dimension in high-resolution player tracking data -- Insights in basketball

A new range of statistical analysis has emerged in sports after the introduction of the high-resolution player tracking technology, specifically in basketball. However, this high dimensional data is often challenging for statistical inference and decision making. In this article, we employ Hidalgo, a state-of-the-art Bayesian mixture model that allows the estimation of heterogeneous intrinsic dimensions (ID) within a dataset and propose some theoretical enhancements. ID results can be interpreted as indicators of variability and complexity of basketball plays and games. This technique allows classification and clustering of NBA basketball player's movement and shot charts data. Analyzing movement data, Hidalgo identifies key stages of offensive actions such as creating space for passing, preparation/shooting and following through. We found that the ID value spikes reaching a peak between 4 and 8 seconds in the offensive part of the court after which it declines. In shot charts, we obtained groups of shots that produce substantially higher and lower successes. Overall, game-winners tend to have a larger intrinsic dimension which is an indication of more unpredictability and unique shot placements. Similarly, we found higher ID values in plays when the score margin is small compared to large margin ones. These outcomes could be exploited by coaches to obtain better offensive/defensive results.

stat.AP↗

arXiv2019

Flexible model selection for mechanistic network models

Network models are applied across many domains where data can be represented as a network. Two prominent paradigms for modeling networks are statistical models (probabilistic models for the observed network) and mechanistic models (models for network growth and/or evolution). Mechanistic models are better suited for incorporating domain knowledge, to study effects of interventions (such as changes to specific mechanisms) and to forward simulate, but they typically have intractable likelihoods. As such, and in a stark contrast to statistical models, there is a relative dearth of research on model selection for such models despite the otherwise large body of extant work. In this paper, we propose a simulator-based procedure for mechanistic network model selection that borrows aspects from Approximate Bayesian Computation (ABC) along with a means to quantify the uncertainty in the selected model. To select the most suitable network model, we consider and assess the performance of several learning algorithms, most notably the so-called Super Learner, which makes our framework less sensitive to the choice of a particular learning algorithm. Our approach takes advantage of the ease to forward simulate from mechanistic network models to circumvent their intractable likelihoods. The overall process is flexible and widely applicable. Our simulation results demonstrate the approach's ability to accurately discriminate between competing mechanistic models. Finally, we showcase our approach with a protein-protein interaction network model from the literature for yeast (Saccharomyces cerevisiae).

stat.ME↗

arXiv2019

Conditionally Gaussian Random Sequences for an Integrated Variance Estimator with Correlation between Noise and Returns

Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the financial literature are not designed to explicitly handle such a dependence, or handle it only in special settings. We provide an integrated variance estimator that is robust to correlated noise and returns. For this purpose, a generalization of the Forward Filtering Backward Sampling algorithm is proposed, to provide a sampling technique for a latent conditionally Gaussian random sequence. We apply our methodology to intra-day Microsoft prices, and compare it in a simulation study with established alternatives, showing an advantage in terms of root mean square error and dispersion.

stat.CO↗

arXiv2019

Likelihood-free parameter estimation for dynamic queueing networks: case study of passenger flow in an international airport terminal

Dynamic queueing networks (DQN) model queueing systems where demand varies strongly with time, such as airport terminals. With rapidly rising global air passenger traffic placing increasing pressure on airport terminals, efficient allocation of resources is more important than ever. Parameter inference and quantification of uncertainty are key challenges for developing decision support tools. The DQN likelihood function is, in general, intractable and current approaches to simulation make likelihood-free parameter inference methods, such as approximate Bayesian computation (ABC), infeasible since simulating from these models is computationally expensive. By leveraging a recent advance in computationally efficient queueing simulation, we develop the first parameter inference approach for DQNs. We demonstrate our approach with data of passenger flows in a real airport terminal, and we show that our model accurately recreates the behaviour of the system and is useful for decision support. Special care must be taken in developing the distance for ABC since any useful output must vary with time. We use maximum mean discrepancy, a metric on probability measures, as the distance function for ABC. Prediction intervals of performance measures for decision support tools are easily constructed using draws from posterior samples, which we demonstrate with a scenario of a delayed flight.

stat.ME↗