arXiv subjects

Luis Carvalho

Publications and source records attributed to Luis Carvalho.

At least 19 recordsLinked to original sources

arXiv2026

Linearly Constrained Generalized Linear Models with Applications in Origin-Destination Estimation

We show that data censored by linear constraints can be fit within the generalized linear model (GLM) framework, recovering the expected latent counts together with their uncertainty in a single Fisher-scoring procedure. Our motivating application is origin-destination (OD) estimation in transportation studies, where the latent data are the OD trip demands and constraints are either origin and destination marginal counts per zone, as in OD matrix estimation, or observed link counts, as in network tomography. Casting the problem as a linearly constrained GLM lets us treat, within one model, three features that arise routinely in practice: unmatched constraints, trip predictors such as costs, and prior information such as diagonal dominance and seed counts. We demonstrate the methodology in synthetic and small scale studies and in a larger case study based on simulated data from the BO4Mob study.

stat.ME↗

arXiv2026

Spatially orthogonal factor models for spatial transcriptomics and remote sensing data

Principal component analyses are often applied to spatial data towards inference on latent modes of spatial variation. These analyses are widespread across domains including spatial transcriptomics and environmental sciences, where the modes of spatial variation are represented by corresponding factors of gene expression or remotely sensed time series measurements. Many methods have been proposed for incorporating spatial information into a probabilistic PCA framework; however, there are three main drawbacks to currently available approaches. First, the loadings matrices are not orthogonal, and subsequent orthogonalization of those loadings corrupts the original prior spatial information. Furthermore, currently proposed methods assume stationarity in their spatial prior. Finally, current methods typically do not achieve linear-time computational complexity with respect to the number of spatial locations. To resolve these problems, we first parameterize the model directly with orthogonal loadings. For the prior distribution, we derive the sampling distribution of an SVD transformation with $k$ unique and $m-k$ repeated singular values. We then show under this model that the maximum a posteriori estimator for the orthogonal loadings is the eigendecomposition of $S + \frac{1}{n}\Sigma$, where $S$ is the empirical covariance matrix and $\Sigma$ is the prior spatial covariance. We develop a minorization-maximization-within-EM algorithm that is linear in computational complexity with respect to the number of spatial locations. We further extend our MM-EM algorithm to handle held-out locations and develop a validation strategy for optimizing the nonstationary prior covariance. Our methodology is used to infer the spatial distribution of direction-specific length scales in a human brain spatial transcriptomics case study, as well as a continental-scale phenology case study in sub-Saharan Africa.

stat.ME↗

arXiv2025

Bernstein Polynomial Processes for Continuous Time Change Detection

There is a lack of methodological results for continuous time change detection due to the challenges of noninformative prior specification and efficient posterior inference in this setting. Most methodologies to date assume data are collected according to uniformly spaced time intervals. This assumption incurs bias in the continuous time setting where, a priori, two consecutive observations measured closely in time are less likely to change than two consecutive observations that are far apart in time. Models proposed in this setting have required MCMC sampling which is not ideal. To address these issues, we derive the heterogeneous continuous time Markov chain that models change point transition probabilities noninformatively. By construction, change points under this model can be inferred efficiently using the forward backward algorithm and do not require MCMC sampling. We then develop a novel loss function for the continuous time setting, derive its Bayes estimator, and demonstrate its performance on synthetic data. A case study using time series of remotely sensed observations is then carried out on three change detection applications. To reduce falsely detected changes in this setting, we develop a semiparametric mean function that captures interannual variability due to weather in addition to trend and seasonal components.

stat.ME↗

arXiv2024

Multiclass ROC

Model evaluation is of crucial importance in modern statistics application. The construction of ROC and calculation of AUC have been widely used for binary classification evaluation. Recent research generalizing the ROC/AUC analysis to multi-class classification has problems in at least one of the four areas: 1. failure to provide sensible plots 2. being sensitive to imbalanced data 3. unable to specify mis-classification cost and 4. unable to provide evaluation uncertainty quantification. Borrowing from a binomial matrix factorization model, we provide an evaluation metric summarizing the pair-wise multi-class True Positive Rate (TPR) and False Positive Rate (FPR) with one-dimensional vector representation. Visualization on the representation vector measures the relative speed of increment between TPR and FPR across all the classes pairs, which in turns provides a ROC plot for the multi-class counterpart. An integration over those factorized vector provides a binary AUC-equivalent summary on the classifier performance. Mis-clasification weights specification and bootstrapped confidence interval are also enabled to accommodate a variety of of evaluation criteria. To support our findings, we conducted extensive simulation studies and compared our method to the pair-wise averaged AUC statistics on benchmark datasets.

stat.ML↗

arXiv2024

Computational Approaches for Exponential-Family Factor Analysis

We study a general factor analysis framework where the $n$-by-$p$ data matrix is assumed to follow a general exponential family distribution entry-wise. While this model framework has been proposed before, we here further relax its distributional assumption by using a quasi-likelihood setup. By parameterizing the mean-variance relationship on data entries, we additionally introduce a dispersion parameter and entry-wise weights to model large variations and missing values. The resulting model is thus not only robust to distribution misspecification but also more flexible and able to capture mean-dependent covariance structures of the data matrix. Our main focus is on efficient computational approaches to perform the factor analysis. Previous modeling frameworks rely on simulated maximum likelihood (SML) to find the factorization solution, but this method was shown to lead to asymptotic bias when the simulated sample size grows slower than the square root of the sample size $n$, eliminating its practical application for data matrices with large $n$. Borrowing from expectation-maximization (EM) and stochastic gradient descent (SGD), we investigate three estimation procedures based on iterative factorization updates. Our proposed solution does not show asymptotic biases, and scales even better for large matrix factorizations with error $O(1/p)$. To support our findings, we conduct simulation experiments and discuss its application in four case studies.

stat.ME↗

arXiv2023

Passage Summarization with Recurrent Models for Audio-Sheet Music Retrieval

Many applications of cross-modal music retrieval are related to connecting sheet music images to audio recordings. A typical and recent approach to this is to learn, via deep neural networks, a joint embedding space that correlates short fixed-size snippets of audio and sheet music by means of an appropriate similarity structure. However, two challenges that arise out of this strategy are the requirement of strongly aligned data to train the networks, and the inherent discrepancies of musical content between audio and sheet music snippets caused by local and global tempo differences. In this paper, we address these two shortcomings by designing a cross-modal recurrent network that learns joint embeddings that can summarize longer passages of corresponding audio and sheet music. The benefits of our method are that it only requires weakly aligned audio-sheet music pairs, as well as that the recurrent network handles the non-linearities caused by tempo variations between audio and sheet music. We conduct a number of experiments on synthetic and real piano data and scores, showing that our proposed recurrent method leads to more accurate retrieval in all possible configurations.

cs.SD↗

arXiv2023

Towards Robust and Truly Large-Scale Audio-Sheet Music Retrieval

A range of applications of multi-modal music information retrieval is centred around the problem of connecting large collections of sheet music (images) to corresponding audio recordings, that is, identifying pairs of audio and score excerpts that refer to the same musical content. One of the typical and most recent approaches to this task employs cross-modal deep learning architectures to learn joint embedding spaces that link the two distinct modalities - audio and sheet music images. While there has been steady improvement on this front over the past years, a number of open problems still prevent large-scale employment of this methodology. In this article we attempt to provide an insightful examination of the current developments on audio-sheet music retrieval via deep learning methods. We first identify a set of main challenges on the road towards robust and large-scale cross-modal music retrieval in real scenarios. We then highlight the steps we have taken so far to address some of these challenges, documenting step-by-step improvement along several dimensions. We conclude by analysing the remaining challenges and present ideas for solving these, in order to pave the way to a unified and robust methodology for cross-modal music retrieval.

cs.SD↗

arXiv2023

Self-Supervised Contrastive Learning for Robust Audio-Sheet Music Retrieval Systems

Linking sheet music images to audio recordings remains a key problem for the development of efficient cross-modal music retrieval systems. One of the fundamental approaches toward this task is to learn a cross-modal embedding space via deep neural networks that is able to connect short snippets of audio and sheet music. However, the scarcity of annotated data from real musical content affects the capability of such methods to generalize to real retrieval scenarios. In this work, we investigate whether we can mitigate this limitation with self-supervised contrastive learning, by exposing a network to a large amount of real music data as a pre-training step, by contrasting randomly augmented views of snippets of both modalities, namely audio and sheet images. Through a number of experiments on synthetic and real piano data, we show that pre-trained models are able to retrieve snippets with better precision in all scenarios and pre-training configurations. Encouraged by these results, we employ the snippet embeddings in the higher-level task of cross-modal piece identification and conduct more experiments on several retrieval configurations. In this task, we observe that the retrieval quality improves from 30% up to 100% when real music data is present. We then conclude by arguing for the potential of self-supervised contrastive learning for alleviating the annotated data scarcity in multi-modal music retrieval models.

cs.SD↗

arXiv2023

Deviance Matrix Factorization

We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages classical statistical methodology from generalized linear models (GLMs) and provides an efficient algorithm that is flexible enough to allow for structural zeros via entry weights. Moreover, by adapting results from GLM theory, we provide support for these decompositions by (i) showing strong consistency under the GLM setup, (ii) checking the adequacy of a chosen exponential family via a generalized Hosmer-Lemeshow test, and (iii) determining the rank of the decomposition via a maximum eigenvalue gap method. To further support our findings, we conduct simulation studies to assess robustness to decomposition assumptions and extensive case studies using benchmark datasets from image face recognition, natural language processing, network analysis, and biomedical studies. Our theoretical and empirical results indicate that the proposed decomposition is more flexible, general, and robust, and can thus provide improved performance when compared to similar methods. To facilitate applications, an R package with efficient model fitting and family and rank determination is also provided.

stat.ML↗

arXiv2022

Soft-SVM Regression For Binary Classification

The binomial deviance and the SVM hinge loss functions are two of the most widely used loss functions in machine learning. While there are many similarities between them, they also have their own strengths when dealing with different types of data. In this work, we introduce a new exponential family based on a convex relaxation of the hinge loss function using softness and class-separation parameters. This new family, denoted Soft-SVM, allows us to prescribe a generalized linear model that effectively bridges between logistic regression and SVM classification. This new model is interpretable and avoids data separability issues, attaining good fitting and predictive performance by automatically adjusting for data label separability via the softness parameter. These results are confirmed empirically through simulations and case studies as we compare regularized logistic, SVM, and Soft-SVM regressions and conclude that the proposed model performs well in terms of both classification and prediction errors.

stat.ML↗

arXiv2021

Exploiting Temporal Dependencies for Cross-Modal Music Piece Identification

This paper addresses the problem of cross-modal musical piece identification and retrieval: finding the appropriate recording(s) from a database given a sheet music query, and vice versa, working directly with audio and scanned sheet music images. The fundamental approach to this is to learn a cross-modal embedding space with a suitable similarity structure for audio and sheet image snippets, using a deep neural network, and identifying candidate pieces by cross-modal near neighbour search in this space. However, this method is oblivious of temporal aspects of music. In this paper, we introduce two strategies that address this shortcoming. First, we present a strategy that aligns sequences of embeddings learned from sheet music scans and audio snippets. A series of experiments on whole piece and fragment-level retrieval on 24 hours worth of classical piano recordings demonstrates significant improvement. Second, we show that the retrieval can be further improved by introducing an attention mechanism to the embedding learning model that reduces the effects of tempo variations in music. To conclude, we assess the scalability of our method and discuss potential measures to make it suitable for truly large-scale applications.

eess.AS↗

arXiv2019

Learning Soft-Attention Models for Tempo-invariant Audio-Sheet Music Retrieval

Connecting large libraries of digitized audio recordings to their corresponding sheet music images has long been a motivation for researchers to develop new cross-modal retrieval systems. In recent years, retrieval systems based on embedding space learning with deep neural networks got a step closer to fulfilling this vision. However, global and local tempo deviations in the music recordings still require careful tuning of the amount of temporal context given to the system. In this paper, we address this problem by introducing an additional soft-attention mechanism on the audio input. Quantitative and qualitative results on synthesized piano data indicate that this attention increases the robustness of the retrieval system by focusing on different parts of the input representation based on the tempo of the audio. Encouraged by these results, we argue for the potential of attention models as a very general tool for many MIR tasks.

cs.IR↗

arXiv2018

A Bayesian Covariance Graphical And Latent Position Model For Multivariate Financial Time Series

Current understanding holds that financial contagion is driven mainly by the system-wide interconnectedness of institutions. A distinction has been made between systematic and idiosyncratic channels of contagion, with shocks transmitted through the latter expected to be substantially more likely to lead to systemic crisis than through the former. Idiosyncratic connectivity is thought to be driven not simply by obviously shared characteristics among institutions, but more by latent characteristics that lead to the holding of related securities. We develop a graphical model for multivariate financial time series with interest in uncovering the latent positions of nodes in a network intended to capture idiosyncratic relationships. We propose a hierarchical model consisting of a VAR, a covariance graphical model (CGM) and a latent position model (LPM). The VAR enables us to extract useful information on the idiosyncratic components, which are used by the CGM to model the network and the LPM uncovers the spatial position of the nodes. We also develop a Markov chain Monte Carlo algorithm that iterates between sampling parameters of the CGM and the LPM, using samples from the latter to update prior information for covariance graph selection. We show empirically that modeling the idiosyncratic channel of contagion using our approach can relate latent institutional features to systemic vulnerabilities prior to a crisis.

stat.AP↗

arXiv2017

Bayesian Network Regularized Regression for Modeling Urban Crime Occurrences

Analyses of occurrences of residential burglary in urban areas have shown that crime rates are not spatially homogeneous: rates vary across the network of city streets, resulting in some areas being far more susceptible to crime than others. The explanation for why a certain segment of the city experiences high crime may be different than why a neighboring area experiences high crime. Motivated by the importance of understanding spatial patterns such as these, we consider a statistical model of burglary defined on the street network of Boston, Massachusetts. Leveraging ideas from functional data analysis, our proposed solution consists of a generalized linear model with vertex-indexed covariates, allowing for an interpretation of the covariate effects at the street level. We employ a regularization procedure cast as a prior distribution on the regression coefficients under a Bayesian setup, so that the predicted responses vary smoothly according to the connectivity of the city. We introduce a novel variable selection procedure, examine computationally efficient methods for sampling from the posterior distribution of the model parameters, and demonstrate the flexibility of our proposed modeling structure. The resulting model and interpretations provide insight into the spatial network patterns and dynamics of residential burglary in Boston.

stat.AP↗

arXiv2016

Gene-Proximity Models For Genome-Wide Association Studies

Motivated by the important problem of detecting association between genetic markers and binary traits in genome-wide association studies, we present a novel Bayesian model that establishes a hierarchy between markers and genes by defining weights according to gene lengths and distances from genes to markers. The proposed hierarchical model uses these weights to define unique prior probabilities of association for markers based on their proximities to genes that are believed to be relevant to the trait of interest. We use an expectation-maximization algorithm in a filtering step to first reduce the dimensionality of the data and then sample from the posterior distribution of the model parameters to estimate posterior probabilities of association for the markers. We offer practical and meaningful guidelines for the selection of the model tuning parameters and propose a pipeline that exploits a singular value decomposition on the raw data to make our model run efficiently on large data sets. We demonstrate the performance of the model in a simulation study and conclude by discussing the results of a case study using a real-world dataset provided by the Wellcome Trust Case Control Consortium.

stat.AP↗

arXiv2014

Bayesian Degree-Corrected Stochastic Blockmodels for Community Detection

Community detection in networks has drawn much attention in diverse fields, especially social sciences. Given its significance, there has been a large body of literature with approaches from many fields. Here we present a statistical framework that is representative, extensible, and that yields an estimator with good properties. Our proposed approach considers a stochastic blockmodel based on a logistic regression formulation with node correction terms. We follow a Bayesian approach that explicitly captures the community behavior via prior specification. We further adopt a data augmentation strategy with latent Polya-Gamma variables to obtain posterior samples. We conduct inference based on a principled, canonically mapped centroid estimator that formally addresses label non-identifiability and captures representative community assignments. We demonstrate the proposed model and estimation on real-world as well as simulated benchmark networks and show that the proposed model and estimator are more flexible, representative, and yield smaller error rates when compared to the MAP estimator from classical degree-corrected stochastic blockmodels.

stat.ME↗

arXiv2014

Perturbation Detection Through Modeling of Gene Expression on a Latent Biological Pathway Network: A Bayesian hierarchical approach

Cellular response to a perturbation is the result of a dynamic system of biological variables linked in a complex network. A major challenge in drug and disease studies is identifying the key factors of a biological network that are essential in determining the cell's fate. Here our goal is the identification of perturbed pathways from high-throughput gene expression data. We develop a three-level hierarchical model, where (i) the first level captures the relationship between gene expression and biological pathways using confirmatory factor analysis, (ii) the second level models the behavior within an underlying network of pathways induced by an unknown perturbation using a conditional autoregressive model, and (iii) the third level is a spike-and-slab prior on the perturbations. We then identify perturbations through posterior-based variable selection. We illustrate our approach using gene transcription drug perturbation profiles from the DREAM7 drug sensitivity predication challenge data set. Our proposed method identified regulatory pathways that are known to play a causative role and that were not readily resolved using gene set enrichment analysis or exploratory factor models. Simulation results are presented assessing the performance of this model relative to a network-free variant and its robustness to inaccuracies in biological databases.

stat.AP↗

arXiv2013

An Expectation-Maximization Algorithm for the Matrix Normal Distribution

Dramatic increases in the size and dimensionality of many recent data sets make crucial the need for sophisticated methods that can exploit inherent structure and handle missing values. In this article we derive an expectation-maximization (EM) algorithm for the matrix normal distribution, a distribution well-suited for naturally structured data such as spatio-temporal data. We review previously established maximum likelihood matrix normal estimates, and then consider the situation involving missing data. We apply our EM method in a simulation study exploring errors across different dimensions and proportions of missing data. We compare these errors and computational running times to those from two alternative methods. Finally, we implement the proposed EM method on a satellite image dataset to investigate land-cover classification separability.

stat.ME↗