arXiv subjects

Lorenzo Cappello

Publications and source records attributed to Lorenzo Cappello.

9 recordsLinked to original sources

arXiv2026

Computationally efficient segmentation for non-stationary time series with oscillatory patterns

We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of sinusoidal functions with unknown frequencies and amplitudes plus noise. The inference for this model is non-trivial. However, discretising the parameter space allows us to recast this complex estimation problem into a more tractable linear model, where the covariates are Fourier basis functions. Then, any change-point detection algorithms for segmentation can be used. The advantage of our proposal is that it bypasses the need for trans-dimensional Markov chain Monte Carlo algorithms used by state-of-the-art methods. Through simulations, we demonstrate that our method is significantly faster than existing approaches while maintaining comparable numerical accuracy. We also provide high probability bounds on the change-point localization error. We apply our methodology to climate and EEG sleep data.

stat.ME↗

arXiv2025

Bayesian Predictive Inference Beyond Martingales

There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of predictive distributions for the observations is required, and inference on the unknown estimand can be performed, cheaply in parallel, using bootstrap-type schemes. Understanding which classes of predictive distributions can be used within this framework, is still a key open question. We relax commonly used probabilistic assumptions on the observations, namely exchangeability and conditional identical distribution, and on their predictive distributions, being measure-valued martingales, by introducing the new class of Almost Conditional Identically Distributed (a.c.i.d.) random variables. This class assumes that the predictive distributions are measure-valued almost supermartingales, and is parametrized by a sequence of parameters $(\xi_n)_{n>0}$, which regulate the decay of conditional dependence among future observations. Under mild summability assumptions on $(\xi_n)_{n>0}$, the resulting sequence of observations is shown to be asymptotically exchangeable, hence amenable to Bayesian Predictive Inference techniques. A.c.i.d. random variables arise naturally in recursive algorithms, and include classic approaches in Statistics and Learning Theory, such as kernel estimators, and more novel ones, such as the parametric Bayesian bootstraps.

math.ST↗

arXiv2025

A Bayesian framework for change-point detection with uncertainty quantification

We introduce a novel Bayesian method that can detect multiple structural breaks in the mean and variance of a length $T$ time-series. Our method quantifies uncertainty by returning $\alpha$-level credible sets around the estimated locations of the breaks. In the case of a single change in the mean and/or the variance of an independent sub-Gaussian sequence, we prove that our method attains a localization rate that is minimax optimal up to a $\log T$ factor. For an $\alpha$-mixing sequence with dependence, we prove this optimality holds up to $\log^2 T$ factor. For $d$-dimensional mean changes, we show that if $d \gg \log T$ and the mean signal is dense, then our method exactly recovers the location of the change. Our method detects multiple change-points by modularly ``stacking'' single change-point models and searching for a variational approximation to the posterior distribution. This approach is applicable to both continuous and count data. Extensive simulation studies demonstrate that our method is competitive with the state-of-the-art in terms of speed and performance, and we produce credible sets that are an order of magnitude smaller than our competitors without sacrificing nominal coverage guarantees. We apply our method to real data by detecting i) the gating of an ion channel in the outer membrane of a bacterial cell, and ii) changes in the lithological structure of an oil well.

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arXiv2022

Bayesian variance change point detection with credible sets

This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a measure of uncertainty is necessary when change point methods are deployed in sensitive applications, for example, when one is interested in determining whether an organ is viable for transplant. The key of our proposal is framing the problem as a product of multiple single changes in the scale parameter. We fit the model through an iterative procedure similar to what is done for additive models. The novelty is that each iteration returns a probability distribution on time instances, which captures the uncertainty in the change point location. Leveraging a recent result in the literature, we can show that our proposal is a variational approximation of the exact model posterior distribution. We study the algorithm's convergence and the change point localization rate. Extensive experiments in simulation studies illustrate the performance of our method and the possibility of generalizing it to more complex data-generating mechanisms. We apply the new model to an experiment involving a novel technique to assess the viability of a liver and oceanographic data.

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arXiv2021

Statistical Challenges in Tracking the Evolution of SARS-CoV-2

Genomic surveillance of SARS-CoV-2 has been instrumental in tracking the spread and evolution of the virus during the pandemic. The availability of SARS-CoV-2 molecular sequences isolated from infected individuals, coupled with phylodynamic methods, have provided insights into the origin of the virus, its evolutionary rate, the timing of introductions, the patterns of transmission, and the rise of novel variants that have spread through populations. Despite enormous global efforts of governments, laboratories, and researchers to collect and sequence molecular data, many challenges remain in analyzing and interpreting the data collected. Here, we describe the models and methods currently used to monitor the spread of SARS-CoV-2, discuss long-standing and new statistical challenges, and propose a method for tracking the rise of novel variants during the epidemic.

stat.AP↗

arXiv2021

The Tajima heterochronous n-coalescent: inference from heterochronously sampled molecular data

The observed sequence variation at a locus informs about the evolutionary history of the sample and past population size dynamics. The Kingman coalescent is used in a generative model of molecular sequence variation to infer evolutionary parameters. However, it is well understood that inference under this model does not scale well with sample size. Here, we build on recent work based on a lower resolution coalescent process, the Tajima coalescent, to model longitudinal samples. While the Kingman coalescent models the ancestry of labeled individuals, the heterochronous Tajima coalescent models the ancestry of individuals labeled by their sampling time. We propose a new inference scheme for the reconstruction of effective population size trajectories based on this model with the potential to improve computational efficiency. Modeling of longitudinal samples is necessary for applications (e.g. ancient DNA and RNA from rapidly evolving pathogens like viruses) and statistically desirable (variance reduction and parameter identifiability). We propose an efficient algorithm to calculate the likelihood and employ a Bayesian nonparametric procedure to infer the population size trajectory. We provide a new MCMC sampler to explore the space of heterochronous Tajima's genealogies and model parameters. We compare our procedure with state-of-the-art methodologies in simulations and applications.

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arXiv2021

Scalable Bayesian change point detection with spike and slab priors

We study the use of spike and slab priors for consistent estimation of the number of change points and their locations. Leveraging recent results in the variable selection literature, we show that an estimator based on spike and slab priors achieves optimal localization rate in the multiple offline change point detection problem. Based on this estimator, we propose a Bayesian change point detection method, which is one of the fastest Bayesian methodologies, and it is more robust to misspecification of the error terms than the competing methods. We demonstrate through empirical work the good performance of our approach vis-a-vis some state-of-the-art benchmarks.

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arXiv2020

Adaptive preferential sampling in phylodynamics

Longitudinal molecular data of rapidly evolving viruses and pathogens provide information about disease spread and complement traditional surveillance approaches based on case count data. The coalescent is used to model the genealogy that represents the sample ancestral relationships. The basic assumption is that coalescent events occur at a rate inversely proportional to the effective population size $N_{e}(t)$, a time-varying measure of genetic diversity. When the sampling process (collection of samples over time) depends on $N_{e}(t)$, the coalescent and the sampling processes can be jointly modeled to improve estimation of $N_{e}(t)$. Failing to do so can lead to bias due to model misspecification. However, the way that the sampling process depends on the effective population size may vary over time. We introduce an approach where the sampling process is modeled as an inhomogeneous Poisson process with rate equal to the product of $N_{e}(t)$ and a time-varying coefficient, making minimal assumptions on their functional shapes via Markov random field priors. We provide scalable algorithms for inference, show the model performance vis-a-vis alternative methods in a simulation study, and apply our model to SARS-CoV-2 sequences from Los Angeles and Santa Clara counties. The methodology is implemented and available in the R package adapref.

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arXiv2019

Sequential importance sampling for multi-resolution Kingman-Tajima coalescent counting

Statistical inference of evolutionary parameters from molecular sequence data relies on coalescent models to account for the shared genealogical ancestry of the samples. However, inferential algorithms do not scale to available data sets. A strategy to improve computational efficiency is to rely on simpler coalescent and mutation models, resulting in smaller hidden state spaces. An estimate of the cardinality of the state-space of genealogical trees at different resolutions is essential to decide the best modeling strategy for a given dataset. To our knowledge, there is neither an exact nor approximate method to determine these cardinalities. We propose a sequential importance sampling algorithm to estimate the cardinality of the space of genealogical trees under different coalescent resolutions. Our sampling scheme proceeds sequentially across the set of combinatorial constraints imposed by the data. We analyse the cardinality of different genealogical tree spaces on simulations to study the settings that favor coarser resolutions. We estimate the cardinality of genealogical tree spaces from mtDNA data from the 1000 genomes and a sample from a Melanesian population to illustrate the settings in which it is advantageous to employ coarser resolutions.

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