Searcharxiv⌕ Search

arXiv subjects

Grégory Nuel

Publications and source records attributed to Grégory Nuel.

17 recordsLinked to original sources

Observed Fisher Information in hidden Markov models - Application to a noisy Gaussian random walk

In this work we provide analytical and closed-form expressions for the exact computation of the score and the observed Fisher information matrix in a Gaussian random walk observed through Gaussian noise. Our method is based on the Oakes' identity and, as for the computation of the log-likelihood, its complexity in time is linear in the length of the sequence with the forward-backward (or Baum-Welch) algorithm. We illustrate the method over various simulation studies and provide parameter estimates computed with the Newton-Raphson algorithm along with confidence intervals.

stat.CO↗

Change-point detection in regression models for ordered data via the max-EM algorithm

We consider the problem of breakpoint detection in a regression modeling framework. To that end, we introduce a novel method, the max-EM algorithm which combines a constrained Hidden Markov Model with the Classification-EM (CEM) algorithm. This algorithm has linear complexity and provides accurate breakpoints detection and parameter estimations. We derive a theoretical result that shows that the likelihood of the data as a function of the regression parameters and the breakpoints location is increased at each step of the algorithm. We also present two initialization methods for the location of the breakpoints in order to deal with local maxima issues. Finally, a statistical test in the one breakpoint situation is developed. Simulation experiments based on linear, logistic, Poisson and Accelerated Failure Time regression models show that the final method that includes the initialization procedure and the max-EM algorithm has a strong performance both in terms of parameters estimation and breakpoints detection. The statistical test is also evaluated and exhibits a correct rejection rate under the null hypothesis and a strong power under various alternatives. Two real dataset are analyzed, the UCI bike sharing and the health disease data, where the interest of the method to detect heterogeneity in the distribution of the data is illustrated.

stat.CO↗

An updated State-of-the-Art Overview of transcriptomic Deconvolution Methods

Although bulk transcriptomic analyses have significantly contributed to an enhanced comprehension of multifaceted diseases, their exploration capacity is impeded by the heterogeneous compositions of biological samples. Indeed, by averaging expression of multiple cell types, RNA-Seq analysis is oblivious to variations in cellular changes, hindering the identification of the internal constituents of tissues, involved in disease progression. On the other hand, single-cell techniques are still time, manpower and resource-consuming analyses.To address the intrinsic limitations of both bulk and single-cell methodologies, computational deconvolution techniques have been developed to estimate the frequencies of cell subtypes within complex tissues. These methods are especially valuable for dissecting intricate tissue niches, with a particular focus on tumour microenvironments (TME).In this paper, we offer a comprehensive overview of deconvolution techniques, classifying them based on their methodological characteristics, the type of prior knowledge required for the algorithm, and the statistical constraints they address. Within each category identified, we delve into the theoretical aspects for implementing the underlying method, while providing an in-depth discussion of their main advantages and disadvantages in supplementary materials.Notably, we emphasise the advantages of cutting-edge deconvolution tools based on probabilistic models, as they offer robust statistical frameworks that closely align with biological realities. We anticipate that this review will provide valuable guidelines for computational bioinformaticians in order to select the appropriate method in alignment with their statistical and biological objectives.We ultimately end this review by discussing open challenges that must be addressed to accurately quantify closely related cell types from RNA sequencing data, and the complementary role of single-cell RNA-Seq to that purpose.

q-bio.QM↗

DeCovarT, a multidimensional probalistic model for the deconvolution of heterogeneous transcriptomic samples

Although bulk transcriptomic analyses have greatly contributed to a better understanding of complex diseases, their sensibility is hampered by the highly heterogeneous cellular compositions of biological samples. To address this limitation, computational deconvolution methods have been designed to automatically estimate the frequencies of the cellular components that make up tissues, typically using reference samples of physically purified populations. However, they perform badly at differentiating closely related cell populations. We hypothesised that the integration of the covariance matrices of the reference samples could improve the performance of deconvolution algorithms. We therefore developed a new tool, DeCovarT, that integrates the structure of individual cellular transcriptomic network to reconstruct the bulk profile. Specifically, we inferred the ratios of the mixture components by a standard maximum likelihood estimation (MLE) method, using the Levenberg-Marquardt algorithm to recover the maximum from the parametric convolutional distribution of our model. We then consider a reparametrisation of the log-likelihood to explicitly incorporate the simplex constraint on the ratios. Preliminary numerical simulations suggest that this new algorithm outperforms previously published methods, particularly when individual cellular transcriptomic profiles strongly overlap.

q-bio.QM↗

A flexible smoother adapted to censored data with outliers and its application to SARS-CoV-2 monitoring in wastewater

A sentinel network, Obépine, has been designed to monitor SARS-CoV-2 viral load in wastewaters arriving at wastewater treatment plants (WWTPs) in France as an indirect macro-epidemiological parameter. The sources of uncertainty in such monitoring system are numerous and the concentration measurements it provides are left-censored and contain outliers, which biases the results of usual smoothing methods. Hence the need for an adapted pre-processing in order to evaluate the real daily amount of virus arriving to each WWTP. We propose a method based on an auto-regressive model adapted to censored data with outliers. Inference and prediction are produced via a discretised smoother which makes it a very flexible tool. This method is both validated on simulations and on real data from Obépine. The resulting smoothed signal shows a good correlation with other epidemiological indicators and is currently used by Obépine to provide an estimate of virus circulation over the watersheds corresponding to about 200 WWTPs.

stat.AP↗

Regression modelling of interval censored data based on the adaptive ridge procedure

A new method for the analysis of time to ankylosis complication on a dataset of replanted teeth is proposed. In this context of left-censored, interval-censored and right-censored data, a Cox model with piecewise constant baseline hazard is introduced. Estimation is carried out with the EM algorithm by treating the true event times as unobserved variables. This estimation procedure is shown to produce a block diagonal Hessian matrix of the baseline parameters. Taking advantage of this interesting feature of the estimation method a L0 penalised likelihood method is implemented in order to automatically determine the number and locations of the cuts of the baseline hazard. This procedure allows to detect specific areas of time where patients are at greater risks for ankylosis. The method can be directly extended to the inclusion of exact observations and to a cure fraction. Theoretical results are obtained which allow to derive statistical inference of the model parameters from asymptotic likelihood theory. Through simulation studies, the penalisation technique is shown to provide a good fit of the baseline hazard and precise estimations of the resulting regression parameters.

stat.ME↗

Regularized Bidimensional Estimation of the Hazard Rate

In epidemiological or demographic studies, with variable age at onset, a typical quantity of interest is the incidence of a disease (for example the cancer incidence). In these studies, the individuals are usually highly heterogeneous in terms of dates of birth (the cohort) and with respect to the calendar time (the period) and appropriate estimation methods are needed. In this article a new estimation method is presented which extends classical age-period-cohort analysis by allowing interactions between age, period and cohort effects. This paper introduces a bidimensional regularized estimate of the hazard rate where a penalty is introduced on the likelihood of the model. This penalty can be designed either to smooth the hazard rate or to enforce consecutive values of the hazard to be equal, leading to a parsimonious representation of the hazard rate. In the latter case, we make use of an iterative penalized likelihood scheme to approximate the L0 norm, which makes the computation tractable. The method is evaluated on simulated data and applied on breast cancer survival data from the SEER program.

math.ST↗

Spline Regression with Automatic Knot Selection

In this paper we introduce a new method for automatically selecting knots in spline regression. The approach consists in setting a large number of initial knots and fitting the spline regression through a penalized likelihood procedure called adaptive ridge. The proposed method is similar to penalized spline regression methods (e.g. P-splines), with the noticeable difference that the output is a sparse spline regression with a small number of knots. We show that our method called A-spline, for adaptive splines yields sparse regression models with high interpretability, while having similar predictive performance similar to penalized spline regression methods. A-spline is applied both to simulated and real dataset. A fast and publicly available implementation in R is provided along with this paper.

stat.AP↗

Fixed effects selection in the linear mixed-effects model using adaptive ridge procedure for L0 penalty performance

This paper is concerned with the selection of fixed effects along with the estimation of fixed effects, random effects and variance components in the linear mixed-effects model. We introduce a selection procedure based on an adaptive ridge (AR) penalty of the profiled likelihood, where the covariance matrix of the random effects is Cholesky factorized. This selection procedure is intended to both low and high-dimensional settings where the number of fixed effects is allowed to grow exponentially with the total sample size, yielding technical difficulties due to the non-convex optimization problem induced by L0 penalties. Through extensive simulation studies, the procedure is compared to the LASSO selection and appears to enjoy the model selection consistency as well as the estimation consistency.

stat.ME↗

Profiled deviance for the multivariate linear mixed-effects model fitting

This paper focuses on the multivariate linear mixed-effects model, including all the correlations between the random effects when the marginal residual terms are assumed uncorrelated and homoscedastic with possibly different standard deviations. The random effects covariance matrix is Cholesky factorized to directly estimate the variance components of these random effects. This strategy enables a consistent estimate of the random effects covariance matrix which, generally, has a poor estimate when it is grossly (or directly) estimated, using the estimating methods such as the EM algorithm. By using simulated data sets, we compare the estimates based on the present method with the EM algorithm-based estimates. We provide an illustration by using the real-life data concerning the study of the child's immune against malaria in Benin (West Africa).

stat.ME↗

Calibration of a two-state pitch-wise HMM method for note segmentation in Automatic Music Transcription systems

Many methods for automatic music transcription involves a multi-pitch estimation method that estimates an activity score for each pitch. A second processing step, called note segmentation, has to be performed for each pitch in order to identify the time intervals when the notes are played. In this study, a pitch-wise two-state on/off firstorder Hidden Markov Model (HMM) is developed for note segmentation. A complete parametrization of the HMM sigmoid function is proposed, based on its original regression formulation, including a parameter alpha of slope smoothing and beta? of thresholding contrast. A comparative evaluation of different note segmentation strategies was performed, differentiated according to whether they use a fixed threshold, called "Hard Thresholding" (HT), or a HMM-based thresholding method, called "Soft Thresholding" (ST). This evaluation was done following MIREX standards and using the MAPS dataset. Also, different transcription scenarios and recording natures were tested using three units of the Degradation toolbox. Results show that note segmentation through a HMM soft thresholding with a data-based optimization of the {alpha,beta} parameter couple significantly enhances transcription performance.

stat.ME↗

A Change-Point Model for Detecting Heterogeneity in Ordered Survival Responses

In this article we suggest a new statistical approach considering survival heterogeneity as a breakpoint model in an ordered sequence of time to event variables. The survival responses need to be ordered according to a numerical covariate. Our esti- mation method will aim at detecting heterogeneity that could arise through the or- dering covariate. We formally introduce our model as a constrained Hidden Markov Model (HMM) where the hidden states are the unknown segmentation (breakpoint locations) and the observed states are the survival responses. We derive an efficient Expectation-Maximization (EM) framework for maximizing the likelihood of this model for a wide range of baseline hazard forms (parametrics or nonparametric). The posterior distribution of the breakpoints is also derived and the selection of the number of segments using penalized likelihood criterion is discussed. The performance of our survival breakpoint model is finally illustrated on a diabetes dataset where the observed survival times are ordered according to the calendar time of disease onset.

stat.AP↗

Joint estimation of causal effects from observational and intervention gene expression data

Background: Inference of gene regulatory networks from transcriptomic data has been a wide research area in recent years. Proposed methods are mainly based on the use of graphical Gaussian models for observational wild-type data and provide undirected graphs that are not able to accurately highlight the causal relationships among genes. In the present work, we seek to improve estimation of causal effects among genes by jointly modeling observational transcriptomic data with intervention data obtained by performing knock-outs or knock-downs on a subset of genes. By examining the impact of such expression perturbations on other genes, a more accurate reflection of regulatory relationships may be obtained than through the use of wild-type data alone. Results: Using the framework of Gaussian Bayesian networks, we propose a Markov chain Monte Carlo algorithm with a Mallows model and an analytical likelihood maximization to sample from the posterior distribution of causal node orderings, and in turn, to estimate causal effects. The main advantage of the proposed algorithm over previously proposed methods is that it has the flexibility to accommodate any kind of intervention design, including partial or multiple knock-out experiments. Methods were compared on simulated data as well as data from the DREAM 2007 challenge. Conclusions: The simulation study confirmed the impossibility of estimating causal orderings of genes with observation data only. The proposed algorithm was found, in most cases, to perform better than the previously proposed methods in terms of accuracy for the estimation of causal effects. In addition, multiple knock-outs proved to bring valuable additional information compared to single knock-outs. The choice of optimal intervention design therefore appears to be a crucial aspect for causal inference and an interesting challenge for future research.

stat.AP↗

Joint likelihood calculation for intervention and observational data from a Gaussian Bayesian network

Methodological development for the inference of gene regulatory networks from transcriptomic data is an active and important research area. Several approaches have been proposed to infer relationships among genes from observational steady-state expression data alone, mainly based on the use of graphical Gaussian models. However, these methods rely on the estimation of partial correlations and are only able to provide undirected graphs that cannot highlight causal relationships among genes. A major upcoming challenge is to jointly analyze observational transcriptomic data and intervention data obtained by performing knock-out or knock-down experiments in order to uncover causal gene regulatory relationships. To this end, in this technical note we present an explicit formula for the likelihood function for any complex intervention design in the context of Gaussian Bayesian networks, as well as its analytical maximization. This allows a direct calculation of the causal effects for known graph structure. We also show how to obtain the Fisher information in this context, which will be extremely useful for the choice of optimal intervention designs in the future.

stat.AP↗

Exact Computation of Kullback-Leibler Distance for Hidden Markov Trees and Models

We suggest new recursive formulas to compute the exact value of the Kullback-Leibler distance (KLD) between two general Hidden Markov Trees (HMTs). For homogeneous HMTs with regular topology, such as homogeneous Hidden Markov Models (HMMs), we obtain a closed-form expression for the KLD when no evidence is given. We generalize our recursive formulas to the case of HMMs conditioned on the observable variables. Our proposed formulas are validated through several numerical examples in which we compare the exact KLD value with Monte Carlo estimations.

cs.IT↗

Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source

We present two novel approaches for the computation of the exact distribution of a pattern in a long sequence. Both approaches take into account the sparse structure of the problem and are two-part algorithms. The first approach relies on a partial recursion after a fast computation of the second largest eigenvalue of the transition matrix of a Markov chain embedding. The second approach uses fast Taylor expansions of an exact bivariate rational reconstruction of the distribution. We illustrate the interest of both approaches on a simple toy-example and two biological applications: the transcription factors of the Human Chromosome 5 and the PROSITE signatures of functional motifs in proteins. On these example our methods demonstrate their complementarity and their hability to extend the domain of feasibility for exact computations in pattern problems to a new level.

math.PR↗

On the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source

In this paper, we develop an explicit formula allowing to compute the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source. We derive efficient algorithms allowing to deal both with low or high complexity patterns and either homogeneous or heterogenous Markov models. We then apply these results to the distribution of DNA patterns in genomic sequences where we show that moment-based developments (namely: Edgeworth's expansion and Gram-Charlier type B series) allow to improve the reliability of common asymptotic approximations like Gaussian or Poisson approximations.

math.PR↗