arXiv subjects

Jesper Løve Hinrich

Publications and source records attributed to Jesper Løve Hinrich.

5 recordsLinked to original sources

arXiv2026

Efficient and Generalizable Archetypal Analysis for Discrete Data

Archetypal Analysis (AA) represents observations as convex combinations of extremal data-driven profiles, yielding interpretable low-dimensional descriptions of complex datasets. Classical AA relies on a least-squares objective, which is poorly suited to discrete observations such as binary, count, and categorical data. We introduce an efficient likelihood-based framework for AA supporting Bernoulli, Poisson, and multinomial observation models. Our optimization scheme employs local quadratic approximations of the negative log-likelihood, enabling constrained updates through sequential minimal optimization (SMO) and an active-set method. Scalability is improved by bounding the active set while preserving simplex feasibility. We further introduce a cross-validated predictive likelihood criterion for selecting the number of archetypes, providing a principled alternative to reconstruction-error heuristics and stability-based diagnostics. Synthetic experiments demonstrate computational efficiency and accurate recovery of model complexity. Applications to single-cell RNA sequencing, microbiome composition, and somatic mutation data show that the learned archetypes capture interpretable domain-specific structures while achieving competitive likelihood fits and stable solutions. Overall, the proposed framework enables efficient likelihood-based archetypal analysis of discrete data, complemented by predictive likelihood-based model selection.

stat.ML↗

arXiv2026

Exploiting chemical shift variability enables recovery of overlapping metabolites from 1H nuclear magnetic resonance spectra

Overlapping peaks and sample-dependent chemical shift variability prevent reliable metabolite recovery from complex biological spectra. This problem is critical in one-dimensional proton (1D 1H) NMR which has become the standard method providing fast acquisition and information-rich spectra in metabolomics and foodomics. This study demonstrates how chemical shifts can be utilised as a strength in 1D 1H NMR, when suitably modeled through the proposed Bayesian Shift-Invariant Non-negative Matrix Factorization (BSI-NMF) procedure. We find that BSI-NMF accurately recovers the underlying chemical signals in 1D 1H NMR spectra missed by existing analyses approaches across simulations, laboratory created datasets, and a large urine dataset obtained from 2439 people across Europe. Our study highlights how shifts in the chemical signatures - until now perceived as a nuisance - can in fact when suitably modelled be instrumental for unique recovery of metabolites. This creates an opportunity to experimentally induce chemical shifts changes to facilitate unique recovery of spectra.

q-bio.QM↗

arXiv2026

E$^2$M: Double Bounded $α$-Divergence Optimization for Tensor-based Discrete Density Estimation

Tensor-based discrete density estimation requires flexible modeling and proper divergence criteria to enable effective learning; however, traditional approaches using $α$-divergence face analytical challenges due to the $α$-power terms in the objective function, which hinder the derivation of closed-form update rules. We present a generalization of the expectation-maximization (EM) algorithm, called the E$^2$M algorithm. It circumvents this issue by first relaxing the optimization into the minimization of a surrogate objective based on the Kullback-Leibler (KL) divergence, which is tractable via the standard EM algorithm, and subsequently applying a tensor many-body approximation in the M-step to enable simultaneous closed-form updates of all parameters. Our approach offers flexible modeling for not only a variety of low-rank structures, including the CP, Tucker, and Tensor Train formats, but also their mixtures, thus allowing us to leverage the strengths of different low-rank structures. We evaluate the effectiveness of our approach on synthetic and real datasets, highlighting its comparable convergence to gradient-based procedures, robustness to outliers, and favorable density estimation performance compared to prominent existing tensor-based methods.

stat.ML↗

arXiv2023

Probabilistic Block Term Decomposition for the Modelling of Higher-Order Arrays

Tensors are ubiquitous in science and engineering and tensor factorization approaches have become important tools for the characterization of higher order structure. Factorizations includes the outer-product rank Canonical Polyadic Decomposition (CPD) as well as the multi-linear rank Tucker decomposition in which the Block-Term Decomposition (BTD) is a structured intermediate interpolating between these two representations. Whereas CPD, Tucker, and BTD have traditionally relied on maximum-likelihood estimation, Bayesian inference has been use to form probabilistic CPD and Tucker. We propose, an efficient variational Bayesian probabilistic BTD, which uses the von-Mises Fisher matrix distribution to impose orthogonality in the multi-linear Tucker parts forming the BTD. On synthetic and two real datasets, we highlight the Bayesian inference procedure and demonstrate using the proposed pBTD on noisy data and for model order quantification. We find that the probabilistic BTD can quantify suitable multi-linear structures providing a means for robust inference of patterns in multi-linear data.

stat.ML↗

arXiv2022

PARAFAC2$\times$N: Coupled Decomposition of Multi-modal Data with Drift in N Modes

Reliable analysis of comprehensive two-dimensional gas chromatography - time-of-flight mass spectrometry (GC$\times$GC-TOFMS) data is considered to be a major bottleneck for its widespread application. For multiple samples, GC$\times$GC-TOFMS data for specific chromatographic regions manifests as a 4th order tensor of I mass spectral acquisitions, J mass channels, K modulations, and L samples. Chromatographic drift is common along both the first-dimension (modulations), and along the second-dimension (mass spectral acquisitions), while drift along the mass channel and sample dimensions is for all practical purposes nonexistent. A number of solutions to handling GC$\times$GC-TOFMS data have been proposed: these involve reshaping the data to make it amenable to either 2nd order decomposition techniques based on Multivariate Curve Resolution (MCR), or 3rd order decomposition techniques such as Parallel Factor Analysis 2 (PARAFAC2). PARAFAC2 has been utilised to model chromatographic drift along one mode, which has enabled its use for robust decomposition of multiple GC-MS experiments. Although extensible, it is not straightforward to implement a PARAFAC2 model that accounts for drift along multiple modes. In this submission, we demonstrate a new approach and a general theory for modelling data with drift along multiple modes, for applications in multidimensional chromatography with multivariate detection.

stat.AP↗