arXiv subjects

Marta Pelizzola

Publications and source records attributed to Marta Pelizzola.

5 recordsLinked to original sources

arXiv2026

Integrating opportunities and parametrized signatures for improved mutational processes estimation in extended sequence contexts

Mutational signatures describe the pattern of mutations over the different mutation types. Each mutation type is determined by a base substitution and the flanking nucleotides to the left and right of that base substitution. Due to the widespread interest in mutational signatures, several efforts have been devoted to the development of methods for robust and stable signature estimation. Here, we combine various extensions of the standard framework to estimate mutational signatures. These extensions include (a) incorporating opportunities to the analysis, (b) allowing for extended sequence contexts, (c) using the Negative Binomial model, and (d) parametrizing the signatures. We show that the combination of these four extensions gives very robust and reliable mutational signatures. In particular, we highlight the importance of including mutational opportunities and parametrizing the signatures when the mutation types describe an extended sequence context with two or three flanking nucleotides to each side of the base substitution.

q-bio.PE↗

arXiv2026

MM-algorithms for traditional and convex NMF with Tweedie and Negative Binomial cost functions and empirical evaluation

Non-negative matrix factorisation (NMF) is a widely used tool for unsupervised learning and feature extraction, with applications ranging from genomics to text analysis and signal processing. Standard formulations of NMF are typically derived under Gaussian or Poisson noise assumptions, which may be inadequate for data exhibiting overdispersion or other complex mean-variance relationships. In this paper, we develop a unified framework for both traditional and convex NMF under a broad class of distributional assumptions, including Negative Binomial and Tweedie models, where the connection between the Tweedie and the $β$-divergence is also highlighted. Using a Majorize-Minimisation approach, we derive multiplicative update rules for all considered models, and novel updates for convex NMF with Poisson and Negative Binomial cost functions. We provide a unified implementation of all considered models, including the first implementations of several convex NMF models. Empirical evaluations on mutational and word count data demonstrate that the choice of noise model critically affects model fit and feature recovery, and that convex NMF can provide an efficient and robust alternative to traditional NMF in scenarios where the number of classes is large. The code for our proposed updates is available in the R package nmfgenr and can be found at https://github.com/MartaPelizzola/nmfgenr.

cs.LG↗

arXiv2024

On the Relation Between Autoencoders and Non-negative Matrix Factorization, and Their Application for Mutational Signature Extraction

The aim of this study is to provide a foundation to understand the relationship between non-negative matrix factorization (NMF) and non-negative autoencoders enabling proper interpretation and understanding of autoencoder-based alternatives to NMF. Since its introduction, NMF has been a popular tool for extracting interpretable, low-dimensional representations of high-dimensional data. However, recently, several studies have proposed to replace NMF with autoencoders. This increasing popularity of autoencoders warrants an investigation on whether this replacement is in general valid and reasonable. Moreover, the exact relationship between non-negative autoencoders and NMF has not been thoroughly explored. Thus, a main aim of this study is to investigate in detail the relationship between non-negative autoencoders and NMF. We find that the connection between the two models can be established through convex NMF, which is a restricted case of NMF. In particular, convex NMF is a special case of an autoencoder. The performance of NMF and autoencoders is compared within the context of extraction of mutational signatures from cancer genomics data. We find that the reconstructions based on NMF are more accurate compared to autoencoders, while the signatures extracted using both methods show comparable consistencies and values when externally validated. These findings suggest that the non-negative autoencoders investigated in this article do not provide an improvement of NMF in the field of mutational signature extraction.

stat.AP↗

arXiv2022

Model selection and robust inference of mutational signatures using Negative Binomial non-negative matrix factorization

The spectrum of mutations in a collection of cancer genomes can be described by a mixture of a few mutational signatures. The mutational signatures can be found using non-negative matrix factorization (NMF). To extract the mutational signatures we have to assume a distribution for the observed mutational counts and a number of mutational signatures. In most applications, the mutational counts are assumed to be Poisson distributed, and the rank is chosen by comparing the fit of several models with the same underlying distribution and different values for the rank using classical model selection procedures. However, the counts are often overdispersed, and thus the Negative Binomial distribution is more appropriate. We propose a Negative Binomial NMF with a patient specific dispersion parameter to capture the variation across patients. We also introduce a novel model selection procedure inspired by cross-validation to determine the number of signatures. Using simulations, we study the influence of the distributional assumption on our method together with other classical model selection procedures and we show that our model selection procedure is more robust at determining the correct number of signatures under model misspecification. We also show that our model selection procedure is more accurate than state-of-the-art methods for finding the true number of signatures. Other methods are highly overestimating the number of signatures when overdispersion is present. We apply our proposed analysis on a wide range of simulated data and on two real data sets from breast and prostate cancer patients. The code for our model selection procedure and negative binomial NMF is available in the R package SigMoS and can be found at https://github.com/MartaPelizzola/SigMoS.

stat.ME↗

arXiv2019

Modifying the Chi-square and the CMH test for population genetic inference: adapting to over-dispersion

Evolve and resequence studies provide a popular approach to simulate evolution in the lab and explore its genetic basis. In this context, the chi-square test, Fishers exact test, as well as the Cochran-Mantel-Haenszel test are commonly used to infer genomic positions affected by selection from temporal changes in allele frequency. However, the null model associated with these tests does not match the null hypothesis of actual interest. Indeed due to genetic drift and possibly other additional noise components such as pool sequencing, the null variance in the data can be substantially larger than accounted forby these common test statistics. This leads to p-values that are systematically too small and therefore a huge number of false positive results. Even, if the ranking rather than the actual p-values is of interest, a naive application of the mentioned tests will give misleading results, as the amount of over-dispersion varies from locus to locus. We therefore propose adjusted statistics that take the over-dispersion into account while keeping the formulas simple. This is particularly useful in genome-wide applications, where millions of SNPs can be handled with little computational effort. We then apply the adapted test statistics to real data fromDrosophila, and investigate how in-formation from intermediate generations can be included when avail-able. The obtained formulas may also be useful in other situations, provided that the null variance either is known or can be estimated.

stat.AP↗