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Morten Mørup

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17 papers
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17

TMLR Journal 2026 Journal Article

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

  • Kazu Ghalamkari
  • Jesper Løve Hinrich
  • Morten Mørup

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 E2M 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.

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TMLR Journal 2025 Journal Article

Estimating the Event-Related Potential from Few EEG Trials

  • Anders Vestergaard Nørskov
  • Kasper Jørgensen
  • Alexander Neergaard Zahid
  • Morten Mørup

Event-related potentials (ERP) are measurements of brain activity with wide applications in basic and clinical neuroscience, that are typically estimated using the average of many trials of electroencephalography signals (EEG) to sufficiently reduce noise and signal variability. We introduce EEG2ERP, a novel uncertainty-aware autoencoder approach that maps an arbitrary number of EEG trials to their associated ERP. To account for the ERP uncertainty we use bootstrapped training targets and introduce a separate variance decoder to model the uncertainty of the estimated ERP. We evaluate our approach in the challenging zero-shot scenario of generalizing to new subjects considering three different publicly available data sources; i) the comprehensive ERP CORE dataset that includes over 50,000 EEG trials across six ERP paradigms from 40 subjects, ii) the large P300 Speller BCI dataset, and iii) a neuroimaging dataset on face perception consisting of both EEG and magnetoencephalography (MEG) data. We consistently find that our method in the few trial regime provides substantially better ERP estimates than commonly used conventional and robust averaging procedures. EEG2ERP is the first deep learning approach to map EEG signals to their associated ERP, moving toward reducing the number of trials necessary for ERP research. Code is available at https://github.com/andersxa/EEG2ERP.

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ICLR Conference 2025 Conference Paper

How Low Can You Go? Searching for the Intrinsic Dimensionality of Complex Networks using Metric Node Embeddings

  • Nikolaos Nakis
  • Niels Raunkjær Holm
  • Andreas Lyhne Fiehn
  • Morten Mørup

Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified exact low-dimensional embeddings, the limits of the required embedding dimensions remain unclear. We presently prove that lower dimensional embeddings are possible when using Euclidean metric embeddings as opposed to vector-based Logistic PCA (LPCA) embeddings. In particular, we provide an efficient logarithmic search procedure for identifying the exact embedding dimension and demonstrate how metric embeddings enable inference of the exact embedding dimensions of large-scale networks by exploiting that the metric properties can be used to provide linearithmic scaling. Empirically, we show that our approach extracts substantially lower dimensional representations of networks than previously reported for small-sized networks. For the first time, we demonstrate that even large-scale networks can be effectively embedded in very low-dimensional spaces, and provide examples of scalable, exact reconstruction for graphs with up to a million nodes. Our approach highlights that the intrinsic dimensionality of networks is substantially lower than previously reported and provides a computationally efficient assessment of the exact embedding dimension also of large-scale networks. The surprisingly low dimensional representations achieved demonstrate that networks in general can be losslessly represented using very low dimensional feature spaces, which can be used to guide existing network analysis tasks from community detection and node classification to structure revealing exact network visualizations.

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AAAI Conference 2024 Conference Paper

Continuous-Time Graph Representation with Sequential Survival Process

  • Abdulkadir Çelikkanat
  • Nikolaos Nakis
  • Morten Mørup

Over the past two decades, there has been a tremendous increase in the growth of representation learning methods for graphs, with numerous applications across various fields, including bioinformatics, chemistry, and the social sciences. However, current dynamic network approaches focus on discrete-time networks or treat links in continuous-time networks as instantaneous events. Therefore, these approaches have limitations in capturing the persistence or absence of links that continuously emerge and disappear over time for particular durations. To address this, we propose a novel stochastic process relying on survival functions to model the durations of links and their absences over time. This forms a generic new likelihood specification explicitly accounting for intermittent edge-persistent networks, namely GraSSP: Graph Representation with Sequential Survival Process. We apply the developed framework to a recent continuous time dynamic latent distance model characterizing network dynamics in terms of a sequence of piecewise linear movements of nodes in latent space. We quantitatively assess the developed framework in various downstream tasks, such as link prediction and network completion, demonstrating that the developed modeling framework accounting for link persistence and absence well tracks the intrinsic trajectories of nodes in a latent space and captures the underlying characteristics of evolving network structure.

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NeurIPS Conference 2023 Conference Paper

CSLP-AE: A Contrastive Split-Latent Permutation Autoencoder Framework for Zero-Shot Electroencephalography Signal Conversion

  • Anders Nørskov
  • Alexander Neergaard Zahid
  • Morten Mørup

Electroencephalography (EEG) is a prominent non-invasive neuroimaging technique providing insights into brain function. Unfortunately, EEG data exhibit a high degree of noise and variability across subjects hampering generalizable signal extraction. Therefore, a key aim in EEG analysis is to extract the underlying neural activation (content) as well as to account for the individual subject variability (style). We hypothesize that the ability to convert EEG signals between tasks and subjects requires the extraction of latent representations accounting for content and style. Inspired by recent advancements in voice conversion technologies, we propose a novel contrastive split-latent permutation autoencoder (CSLP-AE) framework that directly optimizes for EEG conversion. Importantly, the latent representations are guided using contrastive learning to promote the latent splits to explicitly represent subject (style) and task (content). We contrast CSLP-AE to conventional supervised, unsupervised (AE), and self-supervised (contrastive learning) training and find that the proposed approach provides favorable generalizable characterizations of subject and task. Importantly, the procedure also enables zero-shot conversion between unseen subjects. While the present work only considers conversion of EEG, the proposed CSLP-AE provides a general framework for signal conversion and extraction of content (task activation) and style (subject variability) components of general interest for the modeling and analysis of biological signals.

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NeurIPS Conference 2016 Conference Paper

Completely random measures for modelling block-structured sparse networks

  • Tue Herlau
  • Mikkel Schmidt
  • Morten Mørup

Statistical methods for network data often parameterize the edge-probability by attributing latent traits such as block structure to the vertices and assume exchangeability in the sense of the Aldous-Hoover representation theorem. These assumptions are however incompatible with traits found in real-world networks such as a power-law degree-distribution. Recently, Caron & Fox (2014) proposed the use of a different notion of exchangeability after Kallenberg (2005) and obtained a network model which permits edge-inhomogeneity, such as a power-law degree-distribution whilst retaining desirable statistical properties. However, this model does not capture latent vertex traits such as block-structure. In this work we re-introduce the use of block-structure for network models obeying Kallenberg’s notion of exchangeability and thereby obtain a collapsed model which both admits the inference of block-structure and edge inhomogeneity. We derive a simple expression for the likelihood and an efficient sampling method. The obtained model is not significantly more difficult to implement than existing approaches to block-modelling and performs well on real network datasets.

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AILAW Journal 2013 Journal Article

Cross-categorization of legal concepts across boundaries of legal systems: in consideration of inferential links

  • Fumiko Kano Glückstad
  • Tue Herlau
  • Mikkel N. Schmidt
  • Morten Mørup

Abstract This work contrasts Giovanni Sartor’s view of inferential semantics of legal concepts (Sartor in Artif Intell Law 17: 217–251, 2009 ) with a probabilistic model of theory formation (Kemp et al. in Cognition 114: 165–196, 2010 ). The work further explores possibilities of implementing Kemp’s probabilistic model of theory formation in the context of mapping legal concepts between two individual legal systems. For implementing the legal concept mapping, we propose a cross-categorization approach that combines three mathematical models: the Bayesian Model of Generalization (BMG; Tenenbaum and Griffiths in Behav Brain Sci 4: 629–640, 2001 ), the probabilistic model of theory formation, i. e. , the Infinite Relational Model (IRM) first introduced by Kemp et al. (The twenty-first national conference on artificial intelligence, 2006, Cognition 114: 165–196, 2010 ) and its extended model, i. e. , the normal-IRM (n-IRM) proposed by Herlau et al. (IEEE International Workshop on Machine Learning for Signal Processing, 2012 ). We apply our cross-categorization approach to datasets where legal concepts related to educational systems are respectively defined by the Japanese- and the Danish authorities according to the International Standard Classification of Education. The main contribution of this work is the proposal of a conceptual framework of the cross-categorization approach that, inspired by Sartor (Artif Intell Law 17: 217–251, 2009 ), attempts to explain reasoner’s inferential mechanisms.

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ICML Conference 2013 Conference Paper

Modeling Temporal Evolution and Multiscale Structure in Networks

  • Tue Herlau
  • Morten Mørup
  • Mikkel N. Schmidt

Many real-world networks exhibit both temporal evolution and multiscale structure. We propose a model for temporally correlated multifurcating hierarchies in complex networks which jointly capture both effects. We use the Gibbs fragmentation tree as prior over multifurcating trees and a change-point model to account for the temporal evolution of each vertex. We demonstrate that our model is able to infer time-varying multiscale structure in synthetic as well as three real world time-evolving complex networks. Our modeling of the temporal evolution of hierarchies brings new insights into the changing roles and position of entities and possibilities for better understanding these dynamic complex systems.

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NeurIPS Conference 2010 Conference Paper

Infinite Relational Modeling of Functional Connectivity in Resting State fMRI

  • Morten Mørup
  • Kristoffer Madsen
  • Anne-Marie Dogonowski
  • Hartwig Siebner
  • Lars Hansen

Functional magnetic resonance imaging (fMRI) can be applied to study the functional connectivity of the neural elements which form complex network at a whole brain level. Most analyses of functional resting state networks (RSN) have been based on the analysis of correlation between the temporal dynamics of various regions of the brain. While these models can identify coherently behaving groups in terms of correlation they give little insight into how these groups interact. In this paper we take a different view on the analysis of functional resting state networks. Starting from the definition of resting state as functional coherent groups we search for functional units of the brain that communicate with other parts of the brain in a coherent manner as measured by mutual information. We use the infinite relational model (IRM) to quantify functional coherent groups of resting state networks and demonstrate how the extracted component interactions can be used to discriminate between functional resting state activity in multiple sclerosis and normal subjects.

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