Philipp Berens

Philipp Berens, Kyle Cranmer, Neil D. Lawrence et al. · cambridge

This report documents the programme and the outcomes of Dagstuhl Seminar 22382 "Machine Learning for Science: Bridging Data-Driven and Mechanistic Modelling". Today's scientific challenges are characterised by complexity. Interconnected natural, technological, and human systems are influenced by forces acting across time- and spatial-scales, resulting in complex interactions and emergent behaviours. Understanding these phenomena -- and leveraging scientific advances to deliver innovative solutions to improve society's health, wealth, and well-being -- requires new ways of analysing complex systems. The transformative potential of AI stems from its widespread applicability across disciplines, and will only be achieved through integration across research domains. AI for science is a rendezvous point. It brings together expertise from $\mathrm{AI}$ and application domains; combines modelling knowledge with engineering know-how; and relies on collaboration across disciplines and between humans and machines. Alongside technical advances, the next wave of progress in the field will come from building a community of machine learning researchers, domain experts, citizen scientists, and engineers working together to design and deploy effective AI tools. This report summarises the discussions from the seminar and provides a roadmap to suggest how different communities can collaborate to deliver a new wave of progress in AI and its application for scientific discovery.

Valentyn Boreiko, Maximilian Augustin, Francesco Croce et al.

Visual counterfactual explanations (VCEs) in image space are an important tool to understand decisions of image classifiers as they show under which changes of the image the decision of the classifier would change. Their generation in image space is challenging and requires robust models due to the problem of adversarial examples. Existing techniques to generate VCEs in image space suffer from spurious changes in the background. Our novel perturbation model for VCEs together with its efficient optimization via our novel Auto-Frank-Wolfe scheme yields sparse VCEs which lead to subtle changes specific for the target class. Moreover, we show that VCEs can be used to detect undesired behavior of ImageNet classifiers due to spurious features in the ImageNet dataset.

Jan Niklas Böhm, Philipp Berens, Dmitry Kobak

Visualization methods based on the nearest neighbor graph, such as t-SNE or UMAP, are widely used for visualizing high-dimensional data. Yet, these approaches only produce meaningful results if the nearest neighbors themselves are meaningful. For images represented in pixel space this is not the case, as distances in pixel space are often not capturing our sense of similarity and therefore neighbors are not semantically close. This problem can be circumvented by self-supervised approaches based on contrastive learning, such as SimCLR, relying on data augmentation to generate implicit neighbors, but these methods do not produce two-dimensional embeddings suitable for visualization. Here, we present a new method, called t-SimCNE, for unsupervised visualization of image data. T-SimCNE combines ideas from contrastive learning and neighbor embeddings, and trains a parametric mapping from the high-dimensional pixel space into two dimensions. We show that the resulting 2D embeddings achieve classification accuracy comparable to the state-of-the-art high-dimensional SimCLR representations, thus faithfully capturing semantic relationships. Using t-SimCNE, we obtain informative visualizations of the CIFAR-10 and CIFAR-100 datasets, showing rich cluster structure and highlighting artifacts and outliers.

Max F. Burg, Thomas Zenkel, Michaela Vystrčilová et al.

Identifying cell types and understanding their functional properties is crucial for unraveling the mechanisms underlying perception and cognition. In the retina, functional types can be identified by carefully selected stimuli, but this requires expert domain knowledge and biases the procedure towards previously known cell types. In the visual cortex, it is still unknown what functional types exist and how to identify them. Thus, for unbiased identification of the functional cell types in retina and visual cortex, new approaches are needed. Here we propose an optimization-based clustering approach using deep predictive models to obtain functional clusters of neurons using Most Discriminative Stimuli (MDS). Our approach alternates between stimulus optimization with cluster reassignment akin to an expectation-maximization algorithm. The algorithm recovers functional clusters in mouse retina, marmoset retina and macaque visual area V4. This demonstrates that our approach can successfully find discriminative stimuli across species, stages of the visual system and recording techniques. The resulting most discriminative stimuli can be used to assign functional cell types fast and on the fly, without the need to train complex predictive models or show a large natural scene dataset, paving the way for experiments that were previously limited by experimental time. Crucially, MDS are interpretable: they visualize the distinctive stimulus patterns that most unambiguously identify a specific type of neuron.

Lisa M. Koch, Christian M. Schürch, Christian F. Baumgartner et al.

Distribution shifts remain a fundamental problem for the safe application of machine learning systems. If undetected, they may impact the real-world performance of such systems or will at least render original performance claims invalid. In this paper, we focus on the detection of subgroup shifts, a type of distribution shift that can occur when subgroups have a different prevalence during validation compared to the deployment setting. For example, algorithms developed on data from various acquisition settings may be predominantly applied in hospitals with lower quality data acquisition, leading to an inadvertent performance drop. We formulate subgroup shift detection in the framework of statistical hypothesis testing and show that recent state-of-the-art statistical tests can be effectively applied to subgroup shift detection on medical imaging data. We provide synthetic experiments as well as extensive evaluation on clinically meaningful subgroup shifts on histopathology as well as retinal fundus images. We conclude that classifier-based subgroup shift detection tests could be a particularly useful tool for post-market surveillance of deployed ML systems.

Jonas Beck, Michael Deistler, Yves Bernaerts et al.

Simulation-based Bayesian inference (SBI) can be used to estimate the parameters of complex mechanistic models given observed model outputs without requiring access to explicit likelihood evaluations. A prime example for the application of SBI in neuroscience involves estimating the parameters governing the response dynamics of Hodgkin-Huxley (HH) models from electrophysiological measurements, by inferring a posterior over the parameters that is consistent with a set of observations. To this end, many SBI methods employ a set of summary statistics or scientifically interpretable features to estimate a surrogate likelihood or posterior. However, currently, there is no way to identify how much each summary statistic or feature contributes to reducing posterior uncertainty. To address this challenge, one could simply compare the posteriors with and without a given feature included in the inference process. However, for large or nested feature sets, this would necessitate repeatedly estimating the posterior, which is computationally expensive or even prohibitive. Here, we provide a more efficient approach based on the SBI method neural likelihood estimation (NLE): We show that one can marginalize the trained surrogate likelihood post-hoc before inferring the posterior to assess the contribution of a feature. We demonstrate the usefulness of our method by identifying the most important features for inferring parameters of an example HH neuron model. Beyond neuroscience, our method is generally applicable to SBI workflows that rely on data features for inference used in other scientific fields.

Sarah Müller, Philipp Berens

Although deep learning models in medical imaging often achieve excellent classification performance, they can rely on shortcut learning, exploiting spurious correlations or confounding factors that are not causally related to the target task. This poses risks in clinical settings, where models must generalize across institutions, populations, and acquisition conditions. Feature disentanglement is a promising approach to mitigate shortcut learning by separating task-relevant information from confounder-related features in latent representations. In this study, we systematically evaluated feature disentanglement methods for mitigating shortcuts in medical imaging, including adversarial learning and latent space splitting based on dependence minimization. We assessed classification performance and disentanglement quality using latent space analyses across one artificial and two medical datasets with natural and synthetic confounders. We also examined robustness under varying levels of confounding and compared computational efficiency across methods. We found that shortcut mitigation methods improved classification performance under strong spurious correlations during training. Latent space analyses revealed differences in representation quality not captured by classification metrics, highlighting the strengths and limitations of each method. Model reliance on shortcuts depended on the degree of confounding in the training data. The best-performing models combine data-centric rebalancing with model-centric disentanglement, achieving stronger and more robust shortcut mitigation than rebalancing alone while maintaining similar computational efficiency. The project code is publicly available at https://github.com/berenslab/medical-shortcut-mitigation.

Sebastian Damrich, Philipp Berens, Dmitry Kobak

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much higher dimensionality. We show that in this case traditional persistent homology becomes very sensitive to noise and fails to detect the correct topology. The same holds true for existing refinements of persistent homology. As a remedy, we find that spectral distances on the k-nearest-neighbor graph of the data, such as diffusion distance and effective resistance, allow to detect the correct topology even in the presence of high-dimensional noise. Moreover, we derive a novel closed-form formula for effective resistance, and describe its relation to diffusion distances. Finally, we apply these methods to high-dimensional single-cell RNA-sequencing data and show that spectral distances allow robust detection of cell cycle loops.

Kerol Djoumessi, Philipp Berens

Convolutional neural networks (CNNs) achieve state-of-the-art performance in medical image analysis yet remain opaque, limiting adoption in high-stakes clinical settings. Existing approaches face a fundamental trade-off: post-hoc methods provide unfaithful approximate explanations, while inherently interpretable architectures are faithful but often sacrifice predictive performance. We introduce TTE-CAM, a test-time framework that bridges this gap by converting pretrained black-box CNNs into self-explainable models via a convolution-based replacement of their classification head, initialized from the original weights. The resulting model preserves black-box predictive performance while delivering built-in faithful explanations competitive with post-hoc methods, both qualitatively and quantitatively. The code is available at https://github.com/kdjoumessi/Test-Time-Explainability

Sacha Sokoloski, Philipp Berens

We introduce hierarchical mixtures of Gaussians (HMoGs), which unify dimensionality reduction and clustering into a single probabilistic model. HMoGs provide closed-form expressions for the model likelihood, exact inference over latent states and cluster membership, and exact algorithms for maximum-likelihood optimization. The novel exponential family parameterization of HMoGs greatly reduces their computational complexity relative to similar model-based methods, allowing them to efficiently model hundreds of latent dimensions, and thereby capture additional structure in high-dimensional data. We demonstrate HMoGs on synthetic experiments and MNIST, and show how joint optimization of dimensionality reduction and clustering facilitates increased model performance. We also explore how sparsity-constrained dimensionality reduction can further improve clustering performance while encouraging interpretability. By bridging classical statistical modelling with the scale of modern data and compute, HMoGs offer a practical approach to high-dimensional clustering that preserves statistical rigour, interpretability, and uncertainty quantification that is often missing from embedding-based, variational, and self-supervised methods.

Sarah Müller, Louisa Fay, Lisa M. Koch et al.

Medical imaging cohorts are often confounded by factors such as acquisition devices, hospital sites, patient backgrounds, and many more. As a result, deep learning models tend to learn spurious correlations instead of causally related features, limiting their generalizability to new and unseen data. This problem can be addressed by minimizing dependence measures between intermediate representations of task-related and non-task-related variables. These measures include mutual information, distance correlation, and the performance of adversarial classifiers. Here, we benchmark such dependence measures for the task of preventing shortcut learning. We study a simplified setting using Morpho-MNIST and a medical imaging task with CheXpert chest radiographs. Our results provide insights into how to mitigate confounding factors in medical imaging.

Indu Ilanchezian, Valentyn Boreiko, Laura Kühlewein et al.

Counterfactual reasoning is often used in clinical settings to explain decisions or weigh alternatives. Therefore, for imaging based specialties such as ophthalmology, it would be beneficial to be able to create counterfactual images, illustrating answers to questions like "If the subject had had diabetic retinopathy, how would the fundus image have looked?". Here, we demonstrate that using a diffusion model in combination with an adversarially robust classifier trained on retinal disease classification tasks enables the generation of highly realistic counterfactuals of retinal fundus images and optical coherence tomography (OCT) B-scans. The key to the realism of counterfactuals is that these classifiers encode salient features indicative for each disease class and can steer the diffusion model to depict disease signs or remove disease-related lesions in a realistic way. In a user study, domain experts also found the counterfactuals generated using our method significantly more realistic than counterfactuals generated from a previous method, and even indistinguishable from real images.

Sarah Müller, Lisa M. Koch, Hendrik P. A. Lensch et al.

Retinal fundus images play a crucial role in the early detection of eye diseases. However, the impact of technical factors on these images can pose challenges for reliable AI applications in ophthalmology. For example, large fundus cohorts are often confounded by factors like camera type, bearing the risk of learning shortcuts rather than the causal relationships behind the image generation process. Here, we introduce a population model for retinal fundus images that effectively disentangles patient attributes from camera effects, enabling controllable and highly realistic image generation. To achieve this, we propose a disentanglement loss based on distance correlation. Through qualitative and quantitative analyses, we show that our models encode desired information in disentangled subspaces and enable controllable image generation based on the learned subspaces, demonstrating the effectiveness of our disentanglement loss. The project's code is publicly available: https://github.com/berenslab/disentangling-retinal-images.

Kerol Djoumessi, Samuel Ofosu Mensah, Philipp Berens

In many medical imaging tasks, convolutional neural networks (CNNs) efficiently extract local features hierarchically. More recently, vision transformers (ViTs) have gained popularity, using self-attention mechanisms to capture global dependencies, but lacking the inherent spatial localization of convolutions. Therefore, hybrid models combining CNNs and ViTs have been developed to combine the strengths of both architectures. However, such hybrid models are difficult to interpret, which hinders their application in medical imaging. In this work, we introduce an interpretable-by-design hybrid fully convolutional CNN-Transformer architecture for retinal disease detection. Unlike widely used post-hoc saliency methods for ViTs, our approach generates faithful and localized evidence maps that directly reflect the mode's decision process. We evaluated our method on two medical tasks focused on disease detection using color fundus images. Our model achieves state-of-the-art predictive performance compared to black-box and interpretable models and provides class-specific sparse evidence maps in a single forward pass. The code is available at: https://github.com/kdjoumessi/Self-Explainable-CNN-Transformer.

Kerol Djoumessi, Bubacarr Bah, Laura Kühlewein et al.

Interpretability is a key requirement for the use of machine learning models in high-stakes applications, including medical diagnosis. Explaining black-box models mostly relies on post-hoc methods that do not faithfully reflect the model's behavior. As a remedy, prototype-based networks have been proposed, but their interpretability is limited as they have been shown to provide coarse, unreliable, and imprecise explanations. In this work, we introduce Proto-BagNets, an interpretable-by-design prototype-based model that combines the advantages of bag-of-local feature models and prototype learning to provide meaningful, coherent, and relevant prototypical parts needed for accurate and interpretable image classification tasks. We evaluated the Proto-BagNet for drusen detection on publicly available retinal OCT data. The Proto-BagNet performed comparably to the state-of-the-art interpretable and non-interpretable models while providing faithful, accurate, and clinically meaningful local and global explanations. The code is available at https://github.com/kdjoumessi/Proto-BagNets.

Samuel Ofosu Mensah, Maria Camila Roa Carvajal, Kerol Djoumessi et al.

Foundation models are used to extract transferable representations from large amounts of unlabeled data, typically via self-supervised learning (SSL). However, many of these models rely on architectures that offer limited interpretability, which is a critical issue in high-stakes domains such as medical imaging. We propose Dual-IFM, a foundation model that is interpretable-by-design in two ways: First, it provides local interpretability for individual images through class evidence maps that are faithful to the decision-making process. Second, it provides global interpretability for entire datasets through a 2D projection layer that allows for direct visualization of the model's representation space. We trained our model on over 800,000 color fundus photography from various sources to learn generalizable, interpretable representations for different downstream tasks. Our results show that our model reaches a performance range similar to that of state-of-the-art foundation models with up to $16\times$ the number of parameters, while providing interpretable predictions on out-of-distribution data. Our results suggest that large-scale SSL pretraining paired with inherent interpretability can lead to robust representations for retinal imaging.

Verena Jasmin Hallitschke, Carsten Eickhoff, Philipp Berens

Vision-language models hold considerable promise for ophthalmology, but their development depends on large-scale, high-quality image-text datasets that remain scarce. We present PubMed-Ophtha, a hierarchical dataset of 102,023 ophthalmological image-caption pairs extracted from 15,842 open-access articles in PubMed Central. Unlike existing datasets, figures are extracted directly from article PDFs at full resolution and decomposed into their constituent panels, panel identifiers, and individual images. Each image is annotated with its imaging modality -- color fundus photography, optical coherence tomography, retinal imaging, or other -- and a mark status indicating the presence of annotation marks such as arrows. Figure captions are split into panel-level subcaptions using a two-step LLM approach, achieving a mean average sentence BLEU score of 0.913 on human-annotated data. Panel and image detection models reach a mAP@0.50 of 0.909 and 0.892, respectively, and figure extraction achieves a median IoU of 0.997. To support reproducibility, we additionally release the human-annotated ground-truth data, all trained models, and the full dataset generation pipeline.

Jonathan Fuhr, Philipp Berens, Dominik Papies

The estimation of causal effects with observational data continues to be a very active research area. In recent years, researchers have developed new frameworks which use machine learning to relax classical assumptions necessary for the estimation of causal effects. In this paper, we review one of the most prominent methods - "double/debiased machine learning" (DML) - and empirically evaluate it by comparing its performance on simulated data relative to more traditional statistical methods, before applying it to real-world data. Our findings indicate that the application of a suitably flexible machine learning algorithm within DML improves the adjustment for various nonlinear confounding relationships. This advantage enables a departure from traditional functional form assumptions typically necessary in causal effect estimation. However, we demonstrate that the method continues to critically depend on standard assumptions about causal structure and identification. When estimating the effects of air pollution on housing prices in our application, we find that DML estimates are consistently larger than estimates of less flexible methods. From our overall results, we provide actionable recommendations for specific choices researchers must make when applying DML in practice.

Jonas Beck, Nathanael Bosch, Michael Deistler et al.

Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would allow for gradient-based parameter optimization, the nonlinear dynamics of ODEs often lead to many local minima and extreme sensitivity to initial conditions. We therefore propose diffusion tempering, a novel regularization technique for probabilistic numerical methods which improves convergence of gradient-based parameter optimization in ODEs. By iteratively reducing a noise parameter of the probabilistic integrator, the proposed method converges more reliably to the true parameters. We demonstrate that our method is effective for dynamical systems of different complexity and show that it obtains reliable parameter estimates for a Hodgkin-Huxley model with a practically relevant number of parameters.

Kerol Djoumessi, Philipp Berens

Convolutional neural networks (CNNs) are widely used for high-stakes applications like medicine, often surpassing human performance. However, most explanation methods rely on post-hoc attribution, approximating the decision-making process of already trained black-box models. These methods are often sensitive, unreliable, and fail to reflect true model reasoning, limiting their trustworthiness in critical applications. In this work, we introduce SoftCAM, a straightforward yet effective approach that makes standard CNN architectures inherently interpretable. By removing the global average pooling layer and replacing the fully connected classification layer with a convolution-based class evidence layer, SoftCAM preserves spatial information and produces explicit class activation maps that form the basis of the model's predictions. Evaluated on three medical datasets, SoftCAM maintains classification performance while significantly improving both the qualitative and quantitative explanation compared to existing post-hoc methods. Our results demonstrate that CNNs can be inherently interpretable without compromising performance, advancing the development of self-explainable deep learning for high-stakes decision-making.

Ifeoma Veronica Nwabufo, Jan Niklas Böhm, Philipp Berens et al.

Self-supervised learning methods based on data augmentations, such as SimCLR, BYOL, or DINO, allow obtaining semantically meaningful representations of image datasets and are widely used prior to supervised fine-tuning. A recent self-supervised learning method, $t$-SimCNE, uses contrastive learning to directly train a 2D representation suitable for visualisation. When applied to natural image datasets, $t$-SimCNE yields 2D visualisations with semantically meaningful clusters. In this work, we used $t$-SimCNE to visualise medical image datasets, including examples from dermatology, histology, and blood microscopy. We found that increasing the set of data augmentations to include arbitrary rotations improved the results in terms of class separability, compared to data augmentations used for natural images. Our 2D representations show medically relevant structures and can be used to aid data exploration and annotation, improving on common approaches for data visualisation.

Jeremiah Fadugba, Petru Manescu, Bolanle Oladejo et al.

Uncertainty estimation is critical for reliable medical image segmentation, particularly in retinal vessel analysis, where accurate predictions are essential for diagnostic applications. Deep Ensembles, where multiple networks are trained individually, are widely used to improve medical image segmentation performance. However, training and testing costs increase with the number of ensembles. In this work, we propose Ensemble Distillation as a robust alternative to commonly used uncertainty estimation techniques by distilling the knowledge of multiple ensemble models into a single model. Through extensive experiments on the DRIVE and FIVES datasets, we demonstrate that Ensemble Distillation achieves comparable performance via calibration and segmentation metrics, while significantly reducing computational complexity. These findings suggest that Ensemble distillation provides an efficient and reliable approach for uncertainty estimation in the segmentation of the retinal vessels, making it a promising tool for medical imaging applications.

Rita González-Márquez, Philipp Berens, Dmitry Kobak

Text embeddings, i.e. vector representations of entire texts, play an important role in many NLP applications, such as retrieval-augmented generation, sentiment analysis, clustering, or visualizing collections of texts for data exploration. Currently, top-performing embedding models are derived from pre-trained language models via extensive supervised fine-tuning using curated text pairs. This contrasts with computer vision, where self-supervised training based on data augmentations has demonstrated remarkable success. Here we systematically compare the two most well-known augmentation strategies for positive pair generation in contrastive learning of text embeddings. We assess embedding quality on MTEB and additional in-domain evaluations and show that cropping augmentation strongly outperforms the dropout-based approach. We find that on out-of-domain data, the quality of resulting embeddings is below the supervised SOTA models, but for in-domain data, self-supervised fine-tuning produces high-quality text embeddings after very short fine-tuning, sometimes only marginally below the supervised SOTA. Finally, we show that representation quality increases towards the last transformer layers, which undergo the largest change during fine-tuning; and that fine-tuning only those last layers is sufficient to reach similar embedding quality.

Samuel Ofosu Mensah, Kerol Djoumessi, Philipp Berens

Federated learning (FL) provides a promising paradigm for collaboratively training machine learning models across distributed data sources while maintaining privacy. Nevertheless, real-world FL often faces major challenges including communication overhead during the transfer of large model parameters and statistical heterogeneity, arising from non-identical independent data distributions across clients. In this work, we propose an FL framework that 1) provides inherent interpretations using prototypes, and 2) tackles statistical heterogeneity by utilising lightweight adapter modules to act as compressed surrogates of local models and guide clients to achieve generalisation despite varying client distribution. Each client locally refines its model by aligning class embeddings toward prototype representations and simultaneously adjust the lightweight adapter. Our approach replaces the need to communicate entire model weights with prototypes and lightweight adapters. This design ensures that each client's model aligns with a globally shared structure while minimising communication load and providing inherent interpretations. Moreover, we conducted our experiments on a real-world retinal fundus image dataset, which provides clinical-site information. We demonstrate inherent interpretable capabilities and perform a classification task, which shows improvements in accuracy over baseline algorithms.

Gustav Schmidt, Holger Heidrich, Philipp Berens et al.

Learning from noisy ordinal labels is a key challenge in medical imaging. In this work, we ask whether ordinal disease progression labels (better, worse, or stable) can be used to learn a representation allowing to classify disease state. For neovascular age-related macular degeneration (nAMD), we cast the problem of modeling disease progression between medical visits as a classification task with ordinal ranks. To enhance generalization, we tailor our model to the problem setting by (1) independent image encoding, (2) antisymmetric logit space equivariance, and (3) ordinal scale awareness. In addition, we address label noise by learning an uncertainty estimate for loss re-weighting. Our approach learns an interpretable disease representation enabling strong few-shot performance for the related task of nAMD activity classification from single images, despite being trained only on image pairs with ordinal disease progression labels.

Jeremiah Fadugba, Patrick Köhler, Lisa Koch et al.

Retinal blood vessel segmentation can extract clinically relevant information from fundus images. As manual tracing is cumbersome, algorithms based on Convolution Neural Networks have been developed. Such studies have used small publicly available datasets for training and measuring performance, running the risk of overfitting. Here, we provide a rigorous benchmark for various architectural and training choices commonly used in the literature on the largest dataset published to date. We train and evaluate five published models on the publicly available FIVES fundus image dataset, which exceeds previous ones in size and quality and which contains also images from common ophthalmological conditions (diabetic retinopathy, age-related macular degeneration, glaucoma). We compare the performance of different model architectures across different loss functions, levels of image qualitiy and ophthalmological conditions and assess their ability to perform well in the face of disease-induced domain shifts. Given sufficient training data, basic architectures such as U-Net perform just as well as more advanced ones, and transfer across disease-induced domain shifts typically works well for most architectures. However, we find that image quality is a key factor determining segmentation outcomes. When optimizing for segmentation performance, investing into a well curated dataset to train a standard architecture yields better results than tuning a sophisticated architecture on a smaller dataset or one with lower image quality. We distilled the utility of architectural advances in terms of their clinical relevance therefore providing practical guidance for model choices depending on the circumstances of the clinical setting

Ziwei Huang, Yanli Ran, Jonathan Oesterle et al.

Spatio-temporal receptive field (STRF) models are frequently used to approximate the computation implemented by a sensory neuron. Typically, such STRFs are assumed to be smooth and sparse. Current state-of-the-art approaches for estimating STRFs based on empirical Bayes are often not computationally efficient in high-dimensional settings, as encountered in sensory neuroscience. Here we pursued an alternative approach and encode prior knowledge for estimation of STRFs by choosing a set of basis functions with the desired properties: natural cubic splines. Our method is computationally efficient and can be easily applied to a wide range of existing models. We compared the performance of spline-based methods to non-spline ones on simulated and experimental data, showing that spline-based methods consistently outperform the non-spline versions.

Jan Niklas Böhm, Philipp Berens, Dmitry Kobak

Neighbor embeddings are a family of methods for visualizing complex high-dimensional datasets using $k$NN graphs. To find the low-dimensional embedding, these algorithms combine an attractive force between neighboring pairs of points with a repulsive force between all points. One of the most popular examples of such algorithms is t-SNE. Here we empirically show that changing the balance between the attractive and the repulsive forces in t-SNE using the exaggeration parameter yields a spectrum of embeddings, which is characterized by a simple trade-off: stronger attraction can better represent continuous manifold structures, while stronger repulsion can better represent discrete cluster structures and yields higher $k$NN recall. We find that UMAP embeddings correspond to t-SNE with increased attraction; mathematical analysis shows that this is because the negative sampling optimisation strategy employed by UMAP strongly lowers the effective repulsion. Likewise, ForceAtlas2, commonly used for visualizing developmental single-cell transcriptomic data, yields embeddings corresponding to t-SNE with the attraction increased even more. At the extreme of this spectrum lie Laplacian Eigenmaps. Our results demonstrate that many prominent neighbor embedding algorithms can be placed onto the attraction-repulsion spectrum, and highlight the inherent trade-offs between them.

Yves Bernaerts, Philipp Berens, Dmitry Kobak

Patch-seq, a recently developed experimental technique, allows neuroscientists to obtain transcriptomic and electrophysiological information from the same neurons. Efficiently analyzing and visualizing such paired multivariate data in order to extract biologically meaningful interpretations has, however, remained a challenge. Here, we use sparse deep neural networks with and without a two-dimensional bottleneck to predict electrophysiological features from the transcriptomic ones using a group lasso penalty, yielding concise and biologically interpretable two-dimensional visualizations. In two large example data sets, this visualization reveals known neural classes and their marker genes without biological prior knowledge. We also demonstrate that our method is applicable to other kinds of multimodal data, such as paired transcriptomic and proteomic measurements provided by CITE-seq.

Dmitry Kobak, George Linderman, Stefan Steinerberger et al.

T-distributed stochastic neighbour embedding (t-SNE) is a widely used data visualisation technique. It differs from its predecessor SNE by the low-dimensional similarity kernel: the Gaussian kernel was replaced by the heavy-tailed Cauchy kernel, solving the "crowding problem" of SNE. Here, we develop an efficient implementation of t-SNE for a $t$-distribution kernel with an arbitrary degree of freedom $ν$, with $ν\to\infty$ corresponding to SNE and $ν=1$ corresponding to the standard t-SNE. Using theoretical analysis and toy examples, we show that $ν<1$ can further reduce the crowding problem and reveal finer cluster structure that is invisible in standard t-SNE. We further demonstrate the striking effect of heavier-tailed kernels on large real-life data sets such as MNIST, single-cell RNA-sequencing data, and the HathiTrust library. We use domain knowledge to confirm that the revealed clusters are meaningful. Overall, we argue that modifying the tail heaviness of the t-SNE kernel can yield additional insight into the cluster structure of the data.

Lucas Theis, Philipp Berens, Emmanouil Froudarakis et al.

A fundamental challenge in calcium imaging has been to infer the timing of action potentials from the measured noisy calcium fluorescence traces. We systematically evaluate a range of spike inference algorithms on a large benchmark dataset recorded from varying neural tissue (V1 and retina) using different calcium indicators (OGB-1 and GCamp6). We show that a new algorithm based on supervised learning in flexible probabilistic models outperforms all previously published techniques, setting a new standard for spike inference from calcium signals. Importantly, it performs better than other algorithms even on datasets not seen during training. Future data acquired in new experimental conditions can easily be used to further improve its spike prediction accuracy and generalization performance. Finally, we show that comparing algorithms on artificial data is not informative about performance on real population imaging data, suggesting that a benchmark dataset may greatly facilitate future algorithmic developments.