arXiv subjects

Fernando A. Quintana

Publications and source records attributed to Fernando A. Quintana.

12 recordsLinked to original sources

arXiv2026

Bayesian Mixture Models for Histograms: with Applications to Large Datasets

In many real-world scenarios, especially those involving privacy constraints or data summarization, data are available only in aggregated forms, such as histograms or frequency tables. This work introduces a novel Bayesian method for inferring the underlying population distribution by fitting a mixture model to binned data. While we focus on mixtures of normal distributions, the framework is flexible and can be extended to other distributional families. We place a prior distribution on the number of mixture components, accommodating both finite and countably infinite mixtures, and perform inference using reversible jump MCMC. The proposed approach demonstrates strong performance on large-scale data, showcasing the potential of nonparametric Bayesian modeling in practical applications. Furthermore, we extend the method to model multiple histograms simultaneously and cluster them using the Dirichlet process. This enables information sharing across populations and provides a principled posterior probability to assess homogeneity between groups. Some theoretical results supporting the performance of our proposed methodology are also discussed.

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arXiv2022

Bayesian Nonparametric Vector Autoregressive Models via a Logit Stick-breaking Prior: an Application to Child Obesity

Overweight and obesity in adults are known to be associated with risks of metabolic and cardiovascular diseases. Because obesity is an epidemic, increasingly affecting children, it is important to understand if this condition persists from early life to childhood and if different patterns of obesity growth can be detected. Our motivation starts from a study of obesity over time in children from South Eastern Asia. Our main focus is on clustering obesity patterns after adjusting for the effect of baseline information. Specifically, we consider a joint model for height and weight patterns taken every 6 months from birth. We propose a novel model that facilitates clustering by combining a vector autoregressive sampling model with a dependent logit stick-breaking prior. Simulation studies show the superiority of the model to capture patterns, compared to other alternatives. We apply the model to the motivating dataset, and discuss the main features of the detected clusters. We also compare alternative models with ours in terms of predictive performances.

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arXiv2021

Dependent Modeling of Temporal Sequences of Random Partitions

We consider the task of modeling a dependent sequence of random partitions. It is well-known that a random measure in Bayesian nonparametrics induces a distribution over random partitions. The community has therefore assumed that the best approach to obtain a dependent sequence of random partitions is through modeling dependent random measures. We argue that this approach is problematic and show that the random partition model induced by dependent Bayesian nonparametric priors exhibit counter-intuitive dependence among partitions even though the dependence for the sequence of random probability measures is intuitive. Because of this, we advocate instead to model the sequence of random partitions directly when clustering is of principal interest. To this end, we develop a class of dependent random partition models that explicitly models dependence in a sequence of partitions. We derive conditional and marginal properties of the joint partition model and devise computational strategies when employing the method in Bayesian modeling. In the case of temporal dependence, we demonstrate through simulation how the methodology produces partitions that evolve gently and naturally over time. We further illustrate the utility of the method by applying it to an environmental data set that exhibits spatio-temporal dependence.

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arXiv2021

The semi-hierarchical Dirichlet Process and its application to clustering homogeneous distributions

Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the semi-hierarchical Dirichlet process, a novel hierarchical prior that extends the hierarchical Dirichlet process of Teh et al. (2006) and that avoids the degeneracy issues of nested processes recently described by Camerlenghi et al. (2019a). We go beyond the simple yes/no answer to the homogeneity question and embed the proposed prior in a random partition model; this procedure allows us to give a more comprehensive response to the above question and in fact find groups of populations that are internally homogeneous when I greater or equal than 2 such populations are considered. We study theoretical properties of the semi-hierarchical Dirichlet process and of the Bayes factor for the homogeneity test when I = 2. Extensive simulation studies and applications to educational data are also discussed.

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arXiv2020

Discovering Interactions Using Covariate Informed Random Partition Models

Combination chemotherapy treatment regimens created for patients diagnosed with childhood acute lymphoblastic leukemia have had great success in improving cure rates. Unfortunately, patients prescribed these types of treatment regimens have displayed susceptibility to the onset of osteonecrosis. Some have suggested that this is due to pharmacokinetic interaction between two agents in the treatment regimen (asparaginase and dexamethasone) and other physiological variables. Determining which physiological variables to consider when searching for interactions in scenarios like these, minus a priori guidance, has proved to be a challenging problem, particularly if interactions influence the response distribution in ways beyond shifts in expectation or dispersion only. In this paper we propose an exploratory technique that is able to discover associations between covariates and responses in a very general way. The procedure connects covariates to responses very flexibly through dependent random partition prior distributions, and then employs machine learning techniques to highlight potential associations found in each cluster. We provide a simulation study to show utility and apply the method to data produced from a study dedicated to learning which physiological predictors influence severity of osteonecrosis multiplicatively.

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arXiv2020

Clustering and Prediction with Variable Dimension Covariates

In many applied fields incomplete covariate vectors are commonly encountered. It is well known that this can be problematic when making inference on model parameters, but its impact on prediction performance is less understood. We develop a method based on covariate dependent partition models that seamlessly handles missing covariates while completely avoiding any type of imputation. The method we develop allows in-sample predictions as well as out-of-sample prediction, even if the missing pattern in the new subjects' incomplete covariate vector was not seen in the training data. Any data type, including categorical or continuous covariates are permitted. In simulation studies the proposed method compares favorably. We illustrate the method in two application examples.

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arXiv2017

Determinantal point process mixtures via spectral density approach

We consider mixture models where location parameters are a priori encouraged to be well separated. We explore a class of determinantal point process (DPP) mixture models, which provide the desired notion of separation or repulsion. Instead of using the rather restrictive case where analytical results are available, we adopt a spectral representation from which approximations to the DPP intensity functions can be readily computed. For the sake of concreteness the presentation focuses on a power exponential spectral density, but the proposed approach is in fact quite general. We later extend our model to incorporate covariate information in the likelihood and also in the assignment to mixture components, yielding a trade-off between repulsiveness of locations in the mixtures and attraction among subjects with similar covariates. We develop full Bayesian inference, and explore model properties and posterior behavior using several simulation scenarios and data illustrations.

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arXiv2015

Predictions Based on the Clustering of Heterogeneous Functions via Shape and Subject-Specific Covariates

We consider a study of players employed by teams who are members of the National Basketball Association where units of observation are functional curves that are realizations of production measurements taken through the course of one's career. The observed functional output displays large amounts of between player heterogeneity in the sense that some individuals produce curves that are fairly smooth while others are (much) more erratic. We argue that this variability in curve shape is a feature that can be exploited to guide decision making, learn about processes under study and improve prediction. In this paper we develop a methodology that takes advantage of this feature when clustering functional curves. Individual curves are flexibly modeled using Bayesian penalized B-splines while a hierarchical structure allows the clustering to be guided by the smoothness of individual curves. In a sense, the hierarchical structure balances the desire to fit individual curves well while still producing meaningful clusters that are used to guide prediction. We seamlessly incorporate available covariate information to guide the clustering of curves non-parametrically through the use of a product partition model prior for a random partition of individuals. Clustering based on curve smoothness and subject-specific covariate information is particularly important in carrying out the two types of predictions that are of interest, those that complete a partially observed curve from an active player, and those that predict the entire career curve for a player yet to play in the National Basketball Association.

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arXiv2015

Spatial Product Partition Models

When modeling geostatistical or areal data, spatial structure is commonly accommodated via a covariance function for the former and a neighborhood structure for the latter. In both cases the resulting spatial structure is a consequence of implicit spatial grouping in that observations near in space are assumed to behave similarly. It would be desirable to develop spatial methods that explicitly model the partitioning of spatial locations providing more control over resulting spatial structures and being able to better balance global vs local spatial dependence. To this end, we extend product partition models to a spatial setting so that the partitioning of locations into spatially dependent clusters is explicitly modeled. We explore the spatial structures that result from employing a spatial product partition model and demonstrate its flexibility in accommodating many types of spatial dependencies. We illustrate the method's utility through simulation studies and an education application.

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arXiv2013

Defining Predictive Probability Functions for Species Sampling Models

We review the class of species sampling models (SSM). In particular, we investigate the relation between the exchangeable partition probability function (EPPF) and the predictive probability function (PPF). It is straightforward to define a PPF from an EPPF, but the converse is not necessarily true. In this paper we introduce the notion of putative PPFs and show novel conditions for a putative PPF to define an EPPF. We show that all possible PPFs in a certain class have to define (unnormalized) probabilities for cluster membership that are linear in cluster size. We give a new necessary and sufficient condition for arbitrary putative PPFs to define an EPPF. Finally, we show posterior inference for a large class of SSMs with a PPF that is not linear in cluster size and discuss a numerical method to derive its PPF.

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arXiv2012

Multivariate Bayesian semiparametric models for authentication of food and beverages

Food and beverage authentication is the process by which foods or beverages are verified as complying with its label description, for example, verifying if the denomination of origin of an olive oil bottle is correct or if the variety of a certain bottle of wine matches its label description. The common way to deal with an authentication process is to measure a number of attributes on samples of food and then use these as input for a classification problem. Our motivation stems from data consisting of measurements of nine chemical compounds denominated Anthocyanins, obtained from samples of Chilean red wines of grape varieties Cabernet Sauvignon, Merlot and Carménère. We consider a model-based approach to authentication through a semiparametric multivariate hierarchical linear mixed model for the mean responses, and covariance matrices that are specific to the classification categories. Specifically, we propose a model of the ANOVA-DDP type, which takes advantage of the fact that the available covariates are discrete in nature. The results suggest that the model performs well compared to other parametric alternatives. This is also corroborated by application to simulated data.

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arXiv2007

Random-set methods identify distinct aspects of the enrichment signal in gene-set analysis

A prespecified set of genes may be enriched, to varying degrees, for genes that have altered expression levels relative to two or more states of a cell. Knowing the enrichment of gene sets defined by functional categories, such as gene ontology (GO) annotations, is valuable for analyzing the biological signals in microarray expression data. A common approach to measuring enrichment is by cross-classifying genes according to membership in a functional category and membership on a selected list of significantly altered genes. A small Fisher's exact test $p$-value, for example, in this $2\times2$ table is indicative of enrichment. Other category analysis methods retain the quantitative gene-level scores and measure significance by referring a category-level statistic to a permutation distribution associated with the original differential expression problem. We describe a class of random-set scoring methods that measure distinct components of the enrichment signal. The class includes Fisher's test based on selected genes and also tests that average gene-level evidence across the category. Averaging and selection methods are compared empirically using Affymetrix data on expression in nasopharyngeal cancer tissue, and theoretically using a location model of differential expression. We find that each method has a domain of superiority in the state space of enrichment problems, and that both methods have benefits in practice. Our analysis also addresses two problems related to multiple-category inference, namely, that equally enriched categories are not detected with equal probability if they are of different sizes, and also that there is dependence among category statistics owing to shared genes. Random-set enrichment calculations do not require Monte Carlo for implementation. They are made available in the R package allez.

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