arXiv subjects

Michael Scholkemper

Publications and source records attributed to Michael Scholkemper.

9 recordsLinked to original sources

arXiv2026

Extrapolation Guarantees for Perturbation Modeling Under the Additive Latent Shift Assumption

We consider the problem of modeling the effects of perturbations like gene knockouts on measurements such as single-cell RNA counts. Given data for some perturbations, we aim to predict the distribution of measurements for new combinations of perturbations. To address this challenging extrapolation task, we posit that perturbations act additively in a suitable, unknown embedding space. We formulate the data-generating process as a latent variable model, in which perturbations amount to mean shifts in latent space and can be combined additively. We then prove that, given sufficiently diverse training perturbations, the representation and perturbation effects are identifiable up to orthogonal transformation and use this to derive extrapolation guarantees for unseen perturbations that can be expressed as linear combinations of seen ones. To estimate the model from data, we propose the perturbation distribution autoencoder (PDAE), which is trained by maximizing the distributional similarity between true and simulated perturbation distributions. The trained model can then be used to predict previously unseen perturbation distributions. In support of our theoretical results, we demonstrate through simulations that PDAE can accurately predict the effects of unseen but identifiable perturbations, and showcase the method on combinatorial gene perturbation data.

stat.ML↗

arXiv2026

Causal Cellular Context Transfer Learning (C3TL): An Efficient Architecture for Prediction of Unseen Perturbation Effects

Predicting the effects of chemical and genetic perturbations on quantitative cell states is a central challenge in computational biology, molecular medicine and drug discovery. Recent work has leveraged large-scale single-cell data and massive foundation models to address this task. However, such computational resources and extensive datasets are not always accessible in academic or clinical settings, hence limiting utility. Here we propose a lightweight framework for perturbation effect prediction that exploits the structured nature of biological interventions and specific inductive biases/invariances. Our approach leverages available information concerning perturbation effects to allow generalization to novel contexts and requires only widely-available bulk molecular data. Extensive testing, comparing predictions of context-specific perturbation effects against real, large-scale interventional experiments, demonstrates accurate prediction in new contexts. The proposed approach is competitive with SOTA foundation models but requires simpler data, much smaller model sizes and less time. Focusing on robust bulk signals and efficient architectures, we show that accurate prediction of perturbation effects is possible without proprietary hardware or very large models, hence opening up ways to leverage causal learning approaches in biomedicine generally.

cs.LG↗

arXiv2025

Residual Connections and Normalization Can Provably Prevent Oversmoothing in GNNs

Residual connections and normalization layers have become standard design choices for graph neural networks (GNNs), and were proposed as solutions to the mitigate the oversmoothing problem in GNNs. However, how exactly these methods help alleviate the oversmoothing problem from a theoretical perspective is not well understood. In this work, we provide a formal and precise characterization of (linearized) GNNs with residual connections and normalization layers. We establish that (a) for residual connections, the incorporation of the initial features at each layer can prevent the signal from becoming too smooth, and determines the subspace of possible node representations; (b) batch normalization prevents a complete collapse of the output embedding space to a one-dimensional subspace through the individual rescaling of each column of the feature matrix. This results in the convergence of node representations to the top-$k$ eigenspace of the message-passing operator; (c) moreover, we show that the centering step of a normalization layer -- which can be understood as a projection -- alters the graph signal in message-passing in such a way that relevant information can become harder to extract. We therefore introduce a novel, principled normalization layer called GraphNormv2 in which the centering step is learned such that it does not distort the original graph signal in an undesirable way. Experimental results confirm the effectiveness of our method.

cs.LG↗

arXiv2024

A Wasserstein Graph Distance Based on Distributions of Probabilistic Node Embeddings

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive representations of graphs as Gaussian mixture models, fitted to distributions of sampled node embeddings over the same space. The Wasserstein distance between these Gaussian mixture distributions then yields an interpretable and easily computable distance measure, which can further be tailored for the comparison at hand by choosing appropriate embeddings. We propose two embeddings for this framework and show that under certain assumptions about the shape of the resulting Gaussian mixture components, further computational improvements of this Wasserstein distance can be achieved. An empirical validation of our findings on synthetic data and real-world Functional Brain Connectivity networks shows promising performance compared to existing embedding methods.

cs.CE↗

arXiv2023

Learning the effective order of a hypergraph dynamical system

Dynamical systems on hypergraphs can display a rich set of behaviours not observable for systems with pairwise interactions. Given a distributed dynamical system with a putative hypergraph structure, an interesting question is thus how much of this hypergraph structure is actually necessary to faithfully replicate the observed dynamical behaviour. To answer this question, we propose a method to determine the minimum order of a hypergraph necessary to approximate the corresponding dynamics accurately. Specifically, we develop an analytical framework that allows us to determine this order when the type of dynamics is known. We utilize these ideas in conjunction with a hypergraph neural network to directly learn the dynamics itself and the resulting order of the hypergraph from both synthetic and real data sets consisting of observed system trajectories.

cs.LG↗

arXiv2023

An Optimization-based Approach To Node Role Discovery in Networks: Approximating Equitable Partitions

Similar to community detection, partitioning the nodes of a network according to their structural roles aims to identify fundamental building blocks of a network. The found partitions can be used, e.g., to simplify descriptions of the network connectivity, to derive reduced order models for dynamical processes unfolding on processes, or as ingredients for various graph mining tasks. In this work, we offer a fresh look on the problem of role extraction and its differences to community detection and present a definition of node roles related to graph-isomorphism tests, the Weisfeiler-Leman algorithm and equitable partitions. We study two associated optimization problems (cost functions) grounded in ideas from graph isomorphism testing, and present theoretical guarantees associated to the solutions of these problems. Finally, we validate our approach via a novel "role-infused partition benchmark", a network model from which we can sample networks in which nodes are endowed with different roles in a stochastic way.

cs.SI↗

arXiv2022

Neighborhood Structure Configuration Models

We develop a new method to efficiently sample synthetic networks that preserve the d-hop neighborhood structure of a given network for any given d. The proposed algorithm trades off the diversity in network samples against the depth of the neighborhood structure that is preserved. Our key innovation is to employ a colored Configuration Model with colors derived from iterations of the so-called Color Refinement algorithm. We prove that with increasing iterations the preserved structural information increases: the generated synthetic networks and the original network become more and more similar, and are eventually indistinguishable in terms of centrality measures such as PageRank, HITS, Katz centrality and eigenvector centrality. Our work enables to efficiently generate samples with a precisely controlled similarity to the original network, especially for large networks.

cs.SI↗

arXiv2022

Blind Extraction of Equitable Partitions from Graph Signals

Finding equitable partitions is closely related to the extraction of graph symmetries and of interest in a variety of applications context such as node role detection, cluster synchronization, consensus dynamics, and network control problems. In this work we study a blind identification problem in which we aim to recover an equitable partition of a network without the knowledge of the network's edges but based solely on the observations of the outputs of an unknown graph filter. Specifically, we consider two settings. First, we consider a scenario in which we can control the input to the graph filter and present a method to extract the partition inspired by the well known Weisfeiler-Lehman (color refinement) algorithm. Second, we generalize this idea to a setting where only observe the outputs to random, low-rank excitations of the graph filter, and present a simple spectral algorithm to extract the relevant equitable partitions. Finally, we establish theoretical bounds on the error that this spectral detection scheme incurs and perform numerical experiments that illustrate our theoretical results and compare both algorithms.

math.OC↗

arXiv2021

Local, global and scale-dependent node roles

This paper re-examines the concept of node equivalences like structural equivalence or automorphic equivalence, which have originally emerged in social network analysis to characterize the role an actor plays within a social system, but have since then been of independent interest for graph-based learning tasks. Traditionally, such exact node equivalences have been defined either in terms of the one hop neighborhood of a node, or in terms of the global graph structure. Here we formalize exact node roles with a scale-parameter, describing up to what distance the ego network of a node should be considered when assigning node roles - motivated by the idea that there can be local roles of a node that should not be determined by nodes arbitrarily far away in the network. We present numerical experiments that show how already "shallow" roles of depth 3 or 4 carry sufficient information to perform node classification tasks with high accuracy. These findings corroborate the success of recent graph-learning approaches that compute approximate node roles in terms of embeddings, by nonlinearly aggregating node features in an (un)supervised manner over relatively small neighborhood sizes. Indeed, based on our ideas we can construct a shallow classifier achieving on par results with recent graph neural network architectures.

cs.SI↗