Jesper Løve Hinrich

The core of my research is Mathematics and Statistical Science, in particular probabilistic machine learning. My work focuses on developing statistical methods for generating robust insights through Bayesian/probabilistic modelling, the incorporation of prior knowledge, and uncertainty quantification in relation to the data input and latent parameters.

I have a strong interesting in tensor modelling, with tensors being generalizations of vectors (1st order tensors) and matrices (2nd order tensor) to N-dimensional arrays (N'th order tensors), also known as multi-way or N-way arrays. A 3rd order tensor can thus be thought of as a data cube where each dimension of this cube corresponds to a mode of the tensor. Whereas conventional 2-way matrices are well understood the geometry and properties of higher order arrays are still far from fully understood. Tensors are common in modern life science data, such as;

• 1) Neuroimaging with data typically measured from different parts of the brain (e.g. voxels) over time for a number of trials or persons, providing a three way tensor for instance with modes voxels x time x persons.
  
  
• 2) Chemometrics in which for instance fluorescence spectroscopy gives rise to data of emission and excitation spectra across multiple samples, i.e. forming a 3-way array of emission spectra x excitation spectra x samples.
  
  
• 3) Genetics research where for instance gene expression data records which genes are expressed in a number of persons, as well as different parts of their body (tissue). Giving a person x gene x tissue tensor.
  
  

Several tensor analysis toolboxes are now publicly available. The most prominent ones being the n-way toolbox, Tensor Toolbox, Tensorlab and Tensorly . While extremely successful, these toolboxes do not allow for probabilistic (fully Bayesian) modeling and are based solely on maximum likelihood estimation. To mitigate this, the development of the Probabilistic Tensor Toolbox was initiated as part of my PhD and is in continuous - but intermittent - development.

A probabilistic approach allows for handling parameter uncertainty in a natural way and enables incorporation of more realistic noise model assumptions such as mode heteroscedastic, auto-regressive or Markovian noise.

Journal Publications

Armstrong, M. D. S., Hinrich, J. L., de la Mata, A. P., & Harynuk, J. J. (2023). PARAFAC2× N: Coupled decomposition of multi-modal data with drift in N modes. Analytica Chimica Acta, 1249, 340909. (Link)

Olsen, A. S., Høegh, R. M. T., Hinrich, J. L., Madsen, K. H., & Mørup, M. (2022). Combining Electro-and Magnetoencephalography Data using Directional Archetypal Analysis. Frontiers in Neuroscience, 1256. (Link)

Andersen, B. R., Ammitzbøll, I., Hinrich, J., Lehmann, S., Ringsted, C. V., Løkkegaard, E. C. L., & Tolsgaard, M. G. (2022). Using machine learning to identify quality-of-care predictors for emergency caesarean sections: a retrospective cohort study. BMJ open, 12(3), e049046. (Link)

Hinrich, J. L., Madsen, K. H., & Mørup, M. (2020). The probabilistic tensor decomposition toolbox. Machine Learning: Science and Technology, 1(2), 025011. (Link)

Andersen, B. R., Hinrich, J. L., Rasmussen, M. B., Lehmann, S., Ringsted, C., Løkkegaard, E., & Tolsgaard, M. G. (2019). Social ties between team members affect patient satisfaction: a data-driven approach to handling complex network analyses. Advances in Health Sciences Education, 1-26. (Link)

Krohne, L. G., Wang, Y., Hinrich, J. L., Mørup, M., Chan, R. C., & Madsen, K. H. (2019). Classification of social anhedonia using temporal and spatial network features from a social cognition fMRI task. Human brain mapping, 40(17), 4965-4981. (Link)

Hinrich JL, Bardenfleth SE, Røge RE, Churchill NW, Madsen KH, Mørup M. Archetypal Analysis for Modeling Multisubject fMRI Data. IEEE Journal of Selected Topics in Signal Processing. 2016 Oct;10(7):1160-71. (Link)

Conference Publication

Hinrich, J. L., & Mørup, M. (2019, September). Probabilistic Tensor Train Decomposition. In 2019 27th European Signal Processing Conference (EUSIPCO) (pp. 1-5). IEEE. (Link)

Jørgensen, P. J. H., Nielsen, S. F., Hinrich, J. L., Schmidt, M. N., Madsen, K. H., & Mørup, M. (2019). Analysis of Chromatographic Data using the Probabilistic PARAFAC2. In Thirty-Third Annual Conference on Neural Information Processing Systems. (Link)

Hinrich JL, Nielsen SF, Madsen KH, Mørup M. Variational bayesian partially observed non-negative tensor factorization. In 2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP) 2018 Sep 17 (pp. 1-6). IEEE. (Best Student Paper Award) (Link)

Hinrich JL, Mørup M. Probabilistic sparse non-negative matrix factorization. In International Conference on Latent Variable Analysis and Signal Separation 2018 Jul 2 (pp. 488-498). Springer, Cham. (Link)

Hinrich JL, Nielsen SF, Riis NA, Eriksen CT, Frøsig J, Kristensen MD, Schmidt MN, Madsen KH, Mørup M. Scalable Group Level Probabilistic Sparse Factor Analysis. 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, 2017, pp. 6314-6318. (In proceedings) (Preprint on Arxiv)

Beliveau V, Papoutsakis G, Hinrich JL, Mørup M. Sparse Probabilistic Parallel Factor Analysis for the Modeling of PET and Task-fMRI Data. In Medical Computer Vision and Bayesian and Graphical Models for Biomedical Imaging 2016 Oct 21 (pp. 186-198). Springer, Cham. (In proceedings)

Hinrich JL, Nielsen SF, Madsen KH, Morup M. Variational group-PCA for intrinsic dimensionality determination in fMRI data. In Pattern Recognition in Neuroimaging (PRNI), 2016 International Workshop on 2016 Jun 22 (pp. 1-4). IEEE.(In proceedings)