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In human sleep staging models, augmenting the temporal context of the input to the range of tens of minutes has recently demonstrated performance improvement. In contrast, the temporal context of mouse sleep staging models is typically in the order of tens of seconds. While long-term time patterns are less clear in mouse sleep, increasing the temporal context further than that of the current mouse sleep staging models might still result in a performance increase, given that the current methods only model very short term patterns. In this study, we examine the influence of increasing the temporal context in mouse sleep staging up to 15 minutes in three mouse cohorts using two recent and high-performing human sleep staging models that account for long-term dependencies. These are compared to two prominent mouse sleep staging models that use a local context of 12 s and 20 s, respectively. An increase in context up to 28 s is observed to have a positive impact on sleep stage classification performance, especially in REM sleep. However, the impact is limited for longer context windows. One of the human sleep scoring models, L-SeqSleepNet, outperforms both mouse models in all cohorts. This suggests that mouse sleep staging can benefit from more temporal context than currently used., Comment: Accepted for publication in the 46th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (2024)

We present an expectation-maximization (EM) based unified framework for non-negative tensor decomposition that optimizes the Kullback-Leibler divergence. To avoid iterations in each M-step and learning rate tuning, we establish a general relationship between low-rank decomposition and many-body approximation. Using this connection, we exploit that the closed-form solution of the many-body approximation can be used to update all parameters simultaneously in the M-step. Our framework not only offers a unified methodology for a variety of low-rank structures, including CP, Tucker, and Train decompositions, but also their combinations forming mixtures of tensors as well as robust adaptive noise modeling. Empirically, we demonstrate that our framework provides superior generalization for discrete density estimation compared to conventional tensor-based approaches., Comment: 24 pages, 5 figures

Data fusion modeling can identify common features across diverse data sources while accounting for source-specific variability. Here we introduce the concept of a \textit{coupled generator decomposition} and demonstrate how it generalizes sparse principal component analysis (SPCA) for data fusion. Leveraging data from a multisubject, multimodal (electro- and magnetoencephalography (EEG and MEG)) neuroimaging experiment, we demonstrate the efficacy of the framework in identifying common features in response to face perception stimuli, while accommodating modality- and subject-specific variability. Through split-half cross-validation of EEG/MEG trials, we investigate the optimal model order and regularization strengths for models of varying complexity, comparing these to a group-level model assuming shared brain responses to stimuli. Our findings reveal altered $\sim170ms$ fusiform face area activation for scrambled faces, as opposed to real faces, particularly evident in the multimodal, multisubject model. Model parameters were inferred using stochastic optimization in PyTorch, demonstrating comparable performance to conventional quadratic programming inference for SPCA but with considerably faster execution. We provide an easily accessible toolbox for coupled generator decomposition that includes data fusion for SPCA, archetypal analysis and directional archetypal analysis. Overall, our approach offers a promising new avenue for data fusion.

Understanding the structure and dynamics of scientific research, i.e., the science of science (SciSci), has become an important area of research in order to address imminent questions including how scholars interact to advance science, how disciplines are related and evolve, and how research impact can be quantified and predicted. Central to the study of SciSci has been the analysis of citation networks. Here, two prominent modeling methodologies have been employed: one is to assess the citation impact dynamics of papers using parametric distributions, and the other is to embed the citation networks in a latent space optimal for characterizing the static relations between papers in terms of their citations. Interestingly, citation networks are a prominent example of single-event dynamic networks, i.e., networks for which each dyad only has a single event (i.e., the point in time of citation). We presently propose a novel likelihood function for the characterization of such single-event networks. Using this likelihood, we propose the Dynamic Impact Single-Event Embedding model (DISEE). The \textsc{\modelabbrev} model characterizes the scientific interactions in terms of a latent distance model in which random effects account for citation heterogeneity while the time-varying impact is characterized using existing parametric representations for assessment of dynamic impact. We highlight the proposed approach on several real citation networks finding that the DISEE well reconciles static latent distance network embedding approaches with classical dynamic impact assessments., Comment: Accepted for AISTATS 2024

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., Comment: Accepted to the 38th Annual AAAI Conference on Artificial Intelligence (AAAI24), Vancouver, British Columbia, 2024

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., Comment: Accepted for publication at the 37th Conference on Neural Information Processing Systems (NeurIPS 2023)

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., Comment: 11 pages, preprint of submitted article

Graph representation learning (GRL) has become a prominent tool for furthering the understanding of complex networks providing tools for network embedding, link prediction, and node classification. In this paper, we propose the Hybrid Membership-Latent Distance Model (HM-LDM) by exploring how a Latent Distance Model (LDM) can be constrained to a latent simplex. By controlling the edge lengths of the corners of the simplex, the volume of the latent space can be systematically controlled. Thereby communities are revealed as the space becomes more constrained, with hard memberships being recovered as the simplex volume goes to zero. We further explore a recent likelihood formulation for signed networks utilizing the Skellam distribution to account for signed weighted networks and extend the HM-LDM to the signed Hybrid Membership-Latent Distance Model (sHM-LDM). Importantly, the induced likelihood function explicitly attracts nodes with positive links and deters nodes from having negative interactions. We demonstrate the utility of HM-LDM and sHM-LDM on several real networks. We find that the procedures successfully identify prominent distinct structures, as well as how nodes relate to the extracted aspects providing favorable performances in terms of link prediction when compared to prominent baselines. Furthermore, the learned soft memberships enable easily interpretable network visualizations highlighting distinct patterns., Comment: For the published version of the paper please visit Advances in Complex Systems (ACS)

Graph representation learning has become a prominent tool for the characterization and understanding of the structure of networks in general and social networks in particular. Typically, these representation learning approaches embed the networks into a low-dimensional space in which the role of each individual can be characterized in terms of their latent position. A major current concern in social networks is the emergence of polarization and filter bubbles promoting a mindset of "us-versus-them" that may be defined by extreme positions believed to ultimately lead to political violence and the erosion of democracy. Such polarized networks are typically characterized in terms of signed links reflecting likes and dislikes. We propose the latent Signed relational Latent dIstance Model (SLIM) utilizing for the first time the Skellam distribution as a likelihood function for signed networks and extend the modeling to the characterization of distinct extreme positions by constraining the embedding space to polytopes. On four real social signed networks of polarization, we demonstrate that the model extracts low-dimensional characterizations that well predict friendships and animosity while providing interpretable visualizations defined by extreme positions when endowing the model with an embedding space restricted to polytopes., Comment: CAMERA READY version - Proceedings of the 26th International Conference on Artificial Intelligence and Statistics (AISTATS) 2023, Valencia, Spain. PMLR: Volume 206. Copyright 2023 by the author(s)

Networks have become indispensable and ubiquitous structures in many fields to model the interactions among different entities, such as friendship in social networks or protein interactions in biological graphs. A major challenge is to understand the structure and dynamics of these systems. Although networks evolve through time, most existing graph representation learning methods target only static networks. Whereas approaches have been developed for the modeling of dynamic networks, there is a lack of efficient continuous time dynamic graph representation learning methods that can provide accurate network characterization and visualization in low dimensions while explicitly accounting for prominent network characteristics such as homophily and transitivity. In this paper, we propose the Piecewise-Velocity Model (PiVeM) for the representation of continuous-time dynamic networks. It learns dynamic embeddings in which the temporal evolution of nodes is approximated by piecewise linear interpolations based on a latent distance model with piecewise constant node-specific velocities. The model allows for analytically tractable expressions of the associated Poisson process likelihood with scalable inference invariant to the number of events. We further impose a scalable Kronecker structured Gaussian Process prior to the dynamics accounting for community structure, temporal smoothness, and disentangled (uncorrelated) latent embedding dimensions optimally learned to characterize the network dynamics. We show that PiVeM can successfully represent network structure and dynamics in ultra-low two-dimensional spaces. It outperforms relevant state-of-art methods in downstream tasks such as link prediction. In summary, PiVeM enables easily interpretable dynamic network visualizations and characterizations that can further improve our understanding of the intrinsic dynamics of time-evolving networks., Comment: The work has got accepted to the first Learning on Graphs Conference (LoG)

A central aim of modeling complex networks is to accurately embed networks in order to detect structures and predict link and node properties. The latent space models (LSM) have become prominent frameworks for embedding networks and include the latent distance (LDM) and eigenmodel (LEM) as the most widely used LSM specifications. For latent community detection, the embedding space in LDMs has been endowed with a clustering model whereas LEMs have been constrained to part-based non-negative matrix factorization (NMF) inspired representations promoting community discovery. We presently reconcile LSMs with latent community detection by constraining the LDM representation to the D-simplex forming the hybrid-membership latent distance model (HM-LDM). We show that for sufficiently large simplex volumes this can be achieved without loss of expressive power whereas by extending the model to squared Euclidean distances, we recover the LEM formulation with constraints promoting part-based representations akin to NMF. Importantly, by systematically reducing the volume of the simplex, the model becomes unique and ultimately leads to hard assignments of nodes to simplex corners. We demonstrate experimentally how the proposed HM-LDM admits accurate node representations in regimes ensuring identifiability and valid community extraction. Importantly, HM-LDM naturally reconciles soft and hard community detection with network embeddings exploring a simple continuous optimization procedure on a volume constrained simplex that admits the systematic investigation of trade-offs between hard and mixed membership community detection., Comment: Camera-ready version. Accepted for oral presentation at the 11th International Conference on Complex Networks and their Applications, CNA 22

Graph Representation Learning (GRL) has become central for characterizing structures of complex networks and performing tasks such as link prediction, node classification, network reconstruction, and community detection. Whereas numerous generative GRL models have been proposed, many approaches have prohibitive computational requirements hampering large-scale network analysis, fewer are able to explicitly account for structure emerging at multiple scales, and only a few explicitly respect important network properties such as homophily and transitivity. This paper proposes a novel scalable graph representation learning method named the Hierarchical Block Distance Model (HBDM). The HBDM imposes a multiscale block structure akin to stochastic block modeling (SBM) and accounts for homophily and transitivity by accurately approximating the latent distance model (LDM) throughout the inferred hierarchy. The HBDM naturally accommodates unipartite, directed, and bipartite networks whereas the hierarchy is designed to ensure linearithmic time and space complexity enabling the analysis of very large-scale networks. We evaluate the performance of the HBDM on massive networks consisting of millions of nodes. Importantly, we find that the proposed HBDM framework significantly outperforms recent scalable approaches in all considered downstream tasks. Surprisingly, we observe superior performance even imposing ultra-low two-dimensional embeddings facilitating accurate direct and hierarchical-aware network visualization and interpretation., Comment: Preprint Version

Continuous Glucose Monitoring (CGM) has enabled important opportunities for diabetes management. This study explores the use of CGM data as input for digital decision support tools. We investigate how Recurrent Neural Networks (RNNs) can be used for Short Term Blood Glucose (STBG) prediction and compare the RNNs to conventional time-series forecasting using Autoregressive Integrated Moving Average (ARIMA). A prediction horizon up to 90 min into the future is considered. In this context, we evaluate both population-based and patient-specific RNNs and contrast them to patient-specific ARIMA models and a simple baseline predicting future observations as the last observed. We find that the population-based RNN model is the best performing model across the considered prediction horizons without the need of patient-specific data. This demonstrates the potential of RNNs for STBG prediction in diabetes patients towards detecting/mitigating severe events in the STBG, in particular hypoglycemic events. However, further studies are needed in regards to the robustness and practical use of the investigated STBG prediction models., Comment: Accepted to EMBC 2020

The PARAFAC2 is a multimodal factor analysis model suitable for analyzing multi-way data when one of the modes has incomparable observation units, for example because of differences in signal sampling or batch sizes. A fully probabilistic treatment of the PARAFAC2 is desirable in order to improve robustness to noise and provide a well founded principle for determining the number of factors, but challenging because the factor loadings are constrained to be orthogonal. We develop two probabilistic formulations of the PARAFAC2 along with variational procedures for inference: In the one approach, the mean values of the factor loadings are orthogonal leading to closed form variational updates, and in the other, the factor loadings themselves are orthogonal using a matrix Von Mises-Fisher distribution. We contrast our probabilistic formulation to the conventional direct fitting algorithm based on maximum likelihood. On simulated data and real fluorescence spectroscopy and gas chromatography-mass spectrometry data, we compare our approach to the conventional PARAFAC2 model estimation and find that the probabilistic formulation is more robust to noise and model order misspecification. The probabilistic PARAFAC2 thus forms a promising framework for modeling multi-way data accounting for uncertainty., Comment: 16 pages (incl. 4 pages of supplemental material), 5 figures

Many data-driven approaches exist to extract neural representations of functional magnetic resonance imaging (fMRI) data, but most of them lack a proper probabilistic formulation. We propose a group level scalable probabilistic sparse factor analysis (psFA) allowing spatially sparse maps, component pruning using automatic relevance determination (ARD) and subject specific heteroscedastic spatial noise modeling. For task-based and resting state fMRI, we show that the sparsity constraint gives rise to components similar to those obtained by group independent component analysis. The noise modeling shows that noise is reduced in areas typically associated with activation by the experimental design. The psFA model identifies sparse components and the probabilistic setting provides a natural way to handle parameter uncertainties. The variational Bayesian framework easily extends to more complex noise models than the presently considered., Comment: 10 pages plus 5 pages appendix, Submitted to ICASSP 17

Dynamic functional connectivity (FC) has in recent years become a topic of interest in the neuroimaging community. Several models and methods exist for both functional magnetic resonance imaging (fMRI) and electroencephalography (EEG), and the results point towards the conclusion that FC exhibits dynamic changes. The existing approaches modeling dynamic connectivity have primarily been based on time-windowing the data and k-means clustering. We propose a non-parametric generative model for dynamic FC in fMRI that does not rely on specifying window lengths and number of dynamic states. Rooted in Bayesian statistical modeling we use the predictive likelihood to investigate if the model can discriminate between a motor task and rest both within and across subjects. We further investigate what drives dynamic states using the model on the entire data collated across subjects and task/rest. We find that the number of states extracted are driven by subject variability and preprocessing differences while the individual states are almost purely defined by either task or rest. This questions how we in general interpret dynamic FC and points to the need for more research on what drives dynamic FC., Comment: 8 pages, 1 figure. Presented at the Machine Learning and Interpretation in Neuroimaging Workshop (MLINI-2015), 2015 (arXiv:1605.04435)

Dropout has recently emerged as a powerful and simple method for training neural networks preventing co-adaptation by stochastically omitting neurons. Dropout is currently not grounded in explicit modelling assumptions which so far has precluded its adoption in Bayesian modelling. Using Bayesian entropic reasoning we show that dropout can be interpreted as optimal inference under constraints. We demonstrate this on an analytically tractable regression model providing a Bayesian interpretation of its mechanism for regularizing and preventing co-adaptation as well as its connection to other Bayesian techniques. We also discuss two general approximate techniques for applying Bayesian dropout for general models, one based on an analytical approximation and the other on stochastic variational techniques. These techniques are then applied to a Baysian logistic regression problem and are shown to improve performance as the model become more misspecified. Our framework roots dropout as a theoretically justified and practical tool for statistical modelling allowing Bayesians to tap into the benefits of dropout training., Comment: 21 pages, 3 figures. Manuscript prepared 2014 and awaiting submission

Many statistical methods for network data parameterize the edge-probability by attributing latent traits to the vertices such as block structure and assume exchangeability in the sense of the Aldous-Hoover representation theorem. Empirical studies of networks indicate that many real-world networks have a power-law distribution of the vertices which in turn implies the number of edges scale slower than quadratically in the number of vertices. These assumptions are fundamentally irreconcilable as the Aldous-Hoover theorem implies quadratic scaling of the number of edges. Recently Caron and Fox (2014) proposed the use of a different notion of exchangeability due to Kallenberg (2009) and obtained a network model which admits power-law behaviour while 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 model which 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.

Bayesian mixture models are widely applied for unsupervised learning and exploratory data analysis. Markov chain Monte Carlo based on Gibbs sampling and split-merge moves are widely used for inference in these models. However, both methods are restricted to limited types of transitions and suffer from torpid mixing and low accept rates even for problems of modest size. We propose a method that considers a broader range of transitions that are close to equilibrium by exploiting multiple chains in parallel and using the past states adaptively to inform the proposal distribution. The method significantly improves on Gibbs and split-merge sampling as quantified using convergence diagnostics and acceptance rates. Adaptive MCMC methods which use past states to inform the proposal distribution has given rise to many ingenious sampling schemes for continuous problems and the present work can be seen as an important first step in bringing these benefits to partition-based problems, Comment: Manuscript is in preparation, 26 pages including figures

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to non-parametric Bayesian modeling of complex networks: Using an infinite mixture model as running example we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model's fit and predictive performance. We explain how advanced non-parametric models for complex networks can be derived and point out relevant literature.

In Stochastic blockmodels, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A recent extension by Karrer and Newman incorporates a node degree correction to model degree heterogeneity within each group. Although this demonstrably leads to better performance on several networks it is not obvious whether modelling node degree is always appropriate or necessary. We formulate the degree corrected stochastic blockmodel as a non-parametric Bayesian model, incorporating a parameter to control the amount of degree correction which can then be inferred from data. Additionally, our formulation yields principled ways of inferring the number of groups as well as predicting missing links in the network which can be used to quantify the model's predictive performance. On synthetic data we demonstrate that including the degree correction yields better performance both on recovering the true group structure and predicting missing links when degree heterogeneity is present, whereas performance is on par for data with no degree heterogeneity within clusters. On seven real networks (with no ground truth group structure available) we show that predictive performance is about equal whether or not degree correction is included; however, for some networks significantly fewer clusters are discovered when correcting for degree indicating that the data can be more compactly explained by clusters of heterogenous degree nodes., Comment: Originally presented at the Complex Networks workshop NIPS 2013

Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a hierarchically structured model. We propose two non-parametric Bayesian hierarchical network models based on Gibbs fragmentation tree priors, and demonstrate their ability to capture nested patterns in simulated networks. On real networks we demonstrate detection of hierarchical structure and show predictive performance on par with the state of the art. We envision that our methods can be employed in exploratory analysis of large scale complex networks for example to model human brain connectivity.

Learning latent structure in complex networks has become an important problem fueled by many types of networked data originating from practically all fields of science. In this paper, we propose a new non-parametric Bayesian multiple-membership latent feature model for networks. Contrary to existing multiple-membership models that scale quadratically in the number of vertices the proposed model scales linearly in the number of links admitting multiple-membership analysis in large scale networks. We demonstrate a connection between the single membership relational model and multiple membership models and show on "real" size benchmark network data that accounting for multiple memberships improves the learning of latent structure as measured by link prediction while explicitly accounting for multiple membership result in a more compact representation of the latent structure of networks., Comment: 8 pages, 4 figures

We present three generalisations of Kernel Principal Components Analysis (KPCA) which incorporate knowledge of the class labels of a subset of the data points. The first, MV-KPCA, penalises within class variances similar to Fisher discriminant analysis. The second, LSKPCA is a hybrid of least squares regression and kernel PCA. The final LR-KPCA is an iteratively reweighted version of the previous which achieves a sigmoid loss function on the labeled points. We provide a theoretical risk bound as well as illustrative experiments on real and toy data sets.

The problem of incomplete data - i.e., data with missing or unknown values - in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, communication networks, etc. We consider the problem of how to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP). In the presence of missing data, CP can be formulated as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) that uses a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 x 1000 x 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP-WOPT on two real-world applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process.

We present multiplicative updates for solving hard and soft margin support vector machines (SVM) with non-negative kernels. They follow as a natural extension of the updates for non-negative matrix factorization. No additional param- eter setting, such as choosing learning, rate is required. Ex- periments demonstrate rapid convergence to good classifiers. We analyze the rates of asymptotic convergence of the up- dates and establish tight bounds. We test the performance on several datasets using various non-negative kernels and report equivalent generalization errors to that of a standard SVM., Comment: 4 pages, 1 figure, 1 table