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Antonio Canale

Publications and source records attributed to Antonio Canale.

At least 37 records · Page 2Linked to original sources
arXiv2022

Bayesian nonparametric analysis for the detection of spikes in noisy calcium imaging data

Recent advancements in miniaturized fluorescence microscopy have made it possible to investigate neuronal responses to external stimuli in awake behaving animals through the analysis of intra-cellular calcium signals. An on-going challenge is deconvolving the temporal signals to extract the spike trains from the noisy calcium signals' time-series. In this manuscript, we propose a nested Bayesian finite mixture specification that allows the estimation of spiking activity and, simultaneously, reconstructing the distributions of the calcium transient spikes' amplitudes under different experimental conditions. The proposed model leverages two nested layers of random discrete mixture priors to borrow information between experiments and discover similarities in the distributional patterns of neuronal responses to different stimuli. Furthermore, the spikes' intensity values are also clustered within and between experimental conditions to determine the existence of common (recurring) response amplitudes. Simulation studies and the analysis of a data set from the Allen Brain Observatory show the effectiveness of the method in clustering and detecting neuronal activities.

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arXiv2021

Importance conditional sampling for Pitman-Yor mixtures

Nonparametric mixture models based on the Pitman-Yor process represent a flexible tool for density estimation and clustering. Natural generalization of the popular class of Dirichlet process mixture models, they allow for more robust inference on the number of components characterizing the distribution of the data. We propose a new sampling strategy for such models, named importance conditional sampling (ICS), which combines appealing properties of existing methods, including easy interpretability and a within-iteration parallelizable structure. An extensive simulation study highlights the efficiency of the proposed method which, unlike other conditional samplers, shows stable performances for different specifications of the parameters characterizing the Pitman-Yor process. We further show that the ICS approach can be naturally extended to other classes of computationally demanding models, such as nonparametric mixture models for partially exchangeable data.

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arXiv2021

Generalized infinite factorization models

Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to infer the relative impact of the different components as well as the number of components. A popular idea is to include infinitely many components having impact decreasing with the component index. This article is motivated by two limitations of existing methods: (1) lack of careful consideration of the within component sparsity structure; and (2) no accommodation for grouped variables and other non-exchangeable structures. We propose a general class of infinite factorization models that address these limitations. Theoretical support is provided, practical gains are shown in simulation studies, and an ecology application focusing on modelling bird species occurrence is discussed.

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arXiv2021

Locally Sparse Function on function Regression

In functional data analysis, functional linear regression has attracted significant attention recently. Herein, we consider the case where both the response and covariates are functions. There are two available approaches for addressing such a situation: concurrent and nonconcurrent functional models. In the former, the value of the functional response at a given domain point depends only on the value of the functional regressors evaluated at the same domain point, whereas, in the latter, the functional covariates evaluated at each point of their domain have a non-null effect on the response at any point of its domain. To balance these two extremes, we propose a locally sparse functional regression model in which the functional regression coefficient is allowed (but not forced) to be exactly zero for a subset of its domain. This is achieved using a suitable basis representation of the functional regression coefficient and exploiting an overlapping group-Lasso penalty for its estimation. We introduce efficient computational strategies based on majorization-minimization algorithms and discuss appealing theoretical properties regarding the model support and consistency of the proposed estimator. We further illustrate the empirical performance of the method through simulations and two applications related to human mortality and bidding the energy market.

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arXiv2021

Inner spike and slab Bayesian nonparametric models

Discrete Bayesian nonparametric models whose expectation is a convex linear combination of a point mass at some point of the support and a diffuse probability distribution allow to incorporate strong prior information, while still being extremely flexible. Recent contributions in the statistical literature have successfully implemented such a modelling strategy in a variety of applications, including density estimation, nonparametric regression and model-based clustering. We provide a thorough study of a large class of nonparametric models we call inner spike and slab hNRMI models, which are obtained by considering homogeneous normalized random measures with independent increments (hNRMI) with base measure given by a convex linear combination of a point mass and a diffuse probability distribution. In this paper we investigate the distributional properties of these models and our results include: i) the exchangeable partition probability function they induce, ii) the distribution of the number of distinct values in an exchangeable sample, iii) the posterior predictive distribution, and iv) the distribution of the number of elements that coincide with the only point of the support with positive probability. Our findings are the main building block for an actual implementation of Bayesian inner spike and slab hNRMI models by means of a generalized Pólya urn scheme.

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arXiv2020

Bayesian non-asymptotic extreme value models for environmental data

Motivated by the analysis of extreme rainfall data, we introduce a general Bayesian hierarchical model for estimating the probability distribution of extreme values of intermittent random sequences, a common problem in geophysical and environmental science settings. The approach presented here relaxes the asymptotic assumption typical of the traditional extreme value (EV) theory, and accounts for the possible underlying variability in the distribution of event magnitudes and occurrences, which are described through a latent temporal process. Focusing on daily rainfall extremes, the structure of the proposed model lends itself to incorporating prior geo-physical understanding of the rainfall process. By means of an extensive simulation study, we show that this methodology can significantly reduce estimation uncertainty with respect to Bayesian formulations of traditional asymptotic EV methods, particularly in the case of relatively small samples. The benefits of the approach are further illustrated with an application to a large data set of 479 long daily rainfall historical records from across the continental United States. By comparing measures of in-sample and out-of-sample predictive accuracy, we find that the model structure developed here, combined with the use of all available observations for inference, significantly improves robustness with respect to overfitting to the specific sample.

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arXiv2020

Multiscale stick-breaking mixture models

We introduce a family of multiscale stick-breaking mixture models for Bayesian nonparametric density estimation. The Bayesian nonparametric literature is dominated by single scale methods, exception made for Pòlya trees and allied approaches. Our proposal is based on a mixture specification exploiting an infinitely-deep binary tree of random weights that grows according to a multiscale generalization of a large class of stick-breaking processes; this multiscale stick-breaking is paired with specific stochastic processes generating sequences of parameters that induce stochastically ordered kernel functions. Properties of this family of multiscale stick-breaking mixtures are described. Focusing on a Gaussian specification, a Markov Chain Montecarlo algorithm for posterior computation is introduced. The performance of the method is illustrated analyzing both synthetic and real data sets. The method is well-suited for data living in $\mathbb{R}$ and is able to detect densities with varying degree of smoothness and local features.

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arXiv2019

Simultaneous Transformation and Rounding (STAR) Models for Integer-Valued Data

We propose a simple yet powerful framework for modeling integer-valued data, such as counts, scores, and rounded data. The data-generating process is defined by Simultaneously Transforming and Rounding (STAR) a continuous-valued process, which produces a flexible family of integer-valued distributions capable of modeling zero-inflation, bounded or censored data, and over- or underdispersion. The transformation is modeled as unknown for greater distributional flexibility, while the rounding operation ensures a coherent integer-valued data-generating process. An efficient MCMC algorithm is developed for posterior inference and provides a mechanism for adaptation of successful Bayesian models and algorithms for continuous data to the integer-valued data setting. Using the STAR framework, we design a new Bayesian Additive Regression Tree (BART) model for integer-valued data, which demonstrates impressive predictive distribution accuracy for both synthetic data and a large healthcare utilization dataset. For interpretable regression-based inference, we develop a STAR additive model, which offers greater flexibility and scalability than existing integer-valued models. The STAR additive model is applied to study the recent decline in Amazon river dolphins.

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arXiv2019

Pairwise likelihood inference for the multivariate ordered probit model

This paper provides a closed form expression for the pairwise score vector for the multivariate ordered probit model. This result has several implications in likelihood-based inference. It is indeed used both to speed-up gradient based optimization routines for point estimation, and to provide a building block to compute standard errors and confidence intervals by means of the Godambe matrix.

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arXiv2018

Convex Mixture Regression for Quantitative Risk Assessment

There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health outcome. A main focus in these studies is inference on dose levels associated with a given increase in risk relative to a baseline. Popular methods either dichotomize the continuous response or focus on modeling changes with the dose in the expectation of the outcome. Such choices may lead to information loss and provide inaccurate inference on dose-response relationships. We instead propose a Bayesian convex mixture regression model that allows the entire distribution of the health outcome to be unknown and changing with the dose. To balance flexibility and parsimony, we rely on a mixture model for the density at the extreme doses, and express the conditional density at each intermediate dose via a convex combination of these extremal densities. This representation generalizes classical dose-response models for quantitative outcomes, and provides a more parsimonious, but still powerful, formulation compared to nonparametric methods, thereby improving interpretability and efficiency in inference on risk functions. A Markov chain Monte Carlo algorithm for posterior inference is developed, and the benefits of our methods are outlined in simulations, along with a study on the impact of DDT exposure on gestational age.

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arXiv2017

Model based approach for household clustering with mixed scale variables

The Ministry of Social Development in Mexico is in charge of creating and assigning social programmes targeting specific needs in the population for the improvement of quality of life. To better target the social programmes, the Ministry is aimed to find clusters of households with the same needs based on demographic characteristics as well as poverty conditions of the household. Available data consists of continuous, ordinal, and nominal variables and the observations are not iid but come from a survey sample based on a complex design. We propose a Bayesian nonparametric mixture model that jointly models this mixed scale data and accommodates for the different sampling probabilities. The performance of the model is assessed via simulated data. A full analysis of socio-economic conditions in households in the State of Mexico is presented.

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arXiv2016

Bayesian nonparametric forecasting of monotonic functional time series

We propose a Bayesian nonparametric approach to modelling and predicting a class of functional time series with application to energy markets, based on fully observed, noise-free functional data. Traders in such contexts conceive profitable strategies if they can anticipate the impact of their bidding actions on the aggregate demand and supply curves, which in turn need to be predicted reliably. Here we propose a simple Bayesian nonparametric method for predicting such curves, which take the form of monotonic bounded step functions. We borrow ideas from population genetics by defining a class of interacting particle systems to model the functional trajectory, and develop an implementation strategy which uses ideas from Markov chain Monte Carlo and approximate Bayesian computation techniques and allows to circumvent the intractability of the likelihood. Our approach shows great adaptation to the degree of smoothness of the curves and the volatility of the functional series, proves to be robust to an increase of the forecast horizon and yields an uncertainty quantification for the functional forecasts. We illustrate the model and discuss its performance with simulated datasets and on real data relative to the Italian natural gas market.

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arXiv2015

Posterior asymptotics of nonparametric location-scale mixtures for multivariate density estimation

Density estimation represents one of the most successful applications of Bayesian nonparametrics. In particular, Dirichlet process mixtures of normals are the gold standard for density estimation and their asymptotic properties have been studied extensively, especially in the univariate case. However a gap between practitioners and the current theoretical literature is present. So far, posterior asymptotic results in the multivariate case are available only for location mixtures of Gaussian kernels with independent prior on the common covariance matrix, while in practice as well as from a conceptual point of view a location-scale mixture is often preferable. In this paper we address posterior consistency for such general mixture models by adapting a convergence rate result which combines the usual low-entropy, high-mass sieve approach with a suitable summability condition. Specifically, we establish consistency for Dirichlet process mixtures of Gaussian kernels with various prior specifications on the covariance matrix. Posterior convergence rates are also discussed.

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arXiv2014

Scalable multiscale density estimation

Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of dimensionality, it is necessary to assume the data are concentrated near a lower-dimensional subspace. However, Bayesian methods for learning this subspace along with the density of the data scale poorly computationally. To solve this problem, we propose an empirical Bayes approach, which estimates a multiscale dictionary using geometric multiresolution analysis in a first stage. We use this dictionary within a multiscale mixture model, which allows uncertainty in component allocation, mixture weights and scaling factors over a binary tree. A computational algorithm is proposed, which scales efficiently to massive dimensional problems. We provide some theoretical support for this geometric density estimation (GEODE) method, and illustrate the performance through simulated and real data examples.

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arXiv2014

Multiscale Bernstein polynomials for densities

Our focus is on constructing a multiscale nonparametric prior for densities. The Bayes density estimation literature is dominated by single scale methods, with the exception of Polya trees, which favor overly-spiky densities even when the truth is smooth. We propose a multiscale Bernstein polynomial family of priors, which produce smooth realizations that do not rely on hard partitioning of the support. At each level in an infinitely-deep binary tree, we place a beta dictionary density; within a scale the densities are equivalent to Bernstein polynomials. Using a stick-breaking characterization, stochastically decreasing weights are allocated to the finer scale dictionary elements. A slice sampler is used for posterior computation, and properties are described. The method characterizes densities with locally-varying smoothness, and can produce a sequence of coarse to fine density estimates. An extension for Bayesian testing of group differences is introduced and applied to DNA methylation array data.

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arXiv2014

Bayesian multivariate mixed-scale density estimation

Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to jointly model continuous, count and categorical variables under a nonparametric prior, which is induced through rounding latent variables having an unknown density with respect to Lebesgue measure. For the proposed class of priors, we provide sufficient conditions for large support, strong consistency and rates of posterior contraction. These conditions allow one to convert sufficient conditions obtained in the setting of multivariate continuous density estimation to the mixed scale case. To illustrate the procedure a rounded multivariate nonparametric mixture of Gaussians is introduced and applied to a crime and communities dataset.

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arXiv2013

Bayesian nonparametric location-scale-shape mixtures

Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location-scale mixture of Gaussian kernels is the golden standard, both having nice theoretical properties and computational tractability. In this paper we explore the use of the skew-normal kernel, which can naturally accommodate several degrees of skewness by the use of a third parameter. The choice of this kernel function allows us to formulate nonparametric location-scale-shape mixture prior with large support and good performance in different applications. Asymptotically, we show that this modelling framework is consistent in frequentist sense. Efficient Gibbs sampling algorithms are also discussed and the performance of the methods are tested through simulations and applications to galaxy velocity and fertility data. Extensions to accommodate discrete data are also discussed.

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