arXiv subjects

Jens Sjölund

Publications and source records attributed to Jens Sjölund.

At least 37 records · Page 2Linked to original sources

arXiv2025

Probabilistic Zeeman-Doppler imaging of stellar magnetic fields: I. Analysis of tau Scorpii in the weak-field limit

Zeeman-Doppler imaging (ZDI) is used to study the surface magnetic field topology of stars, based on high-resolution spectropolarimetric time series observations. Multiple ZDI inversions have been conducted for the early B-type star tau Sco, which has been found to exhibit a weak but complex non-dipolar surface magnetic field. The classical ZDI framework suffers from a significant limitation in that it provides little to no reliable uncertainty quantification for the reconstructed magnetic field maps, with essentially all published results being confined to point estimates. To fill this gap, we propose a Bayesian framework for probabilistic ZDI. Here, the proposed framework is demonstrated on tau Sco in the weak-field limit. We propose three distinct statistical models, and use archival ESPaDOnS high-resolution Stokes V observations to carry out the probabilistic magnetic inversion in closed form. The surface magnetic field is parameterised by a high-dimensional spherical-harmonic expansion. By comparing three different prior distributions over the latent variables in the spherical-harmonic decomposition, our results showcase the ZDI sensitivity to various hyperparameters. The mean magnetic field maps are qualitatively similar to previously published point estimates, but analysis of the magnetic energy distribution indicates high uncertainty and higher energy content at low angular degrees l. Our results effectively demonstrate that, for stars in the weak-field regime, reliable uncertainty quantification of recovered magnetic field maps can be obtained in closed form with natural assumptions on the statistical model. Future work will explore extending this framework beyond the weak-field approximation and incorporating prior uncertainty over multiple stellar parameters in more complex magnetic inversion problems.

astro-ph.SR↗

arXiv2025

Symmetrizable systems

Transforming an asymmetric system into a symmetric system makes it possible to exploit the simplifying properties of symmetry in control problems. We define and characterize the family of symmetrizable systems, which can be transformed into symmetric systems by a linear transformation of their inputs and outputs. In the special case of complete symmetry, the set of symmetrizable systems is convex and verifiable by a semidefinite program. We show that a Khatri-Rao rank needs to be satisfied for a system to be symmetrizable and conclude that linear systems are generically neither symmetric nor symmetrizable.

math.OC↗

arXiv2025

Ising on the Graph: Task-specific Graph Subsampling via the Ising Model

Reducing a graph while preserving its overall properties is an important problem with many applications. Typically, reduction approaches either remove edges (sparsification) or merge nodes (coarsening) in an unsupervised way with no specific downstream task in mind. In this paper, we present an approach for subsampling graph structures using an Ising model defined on either the nodes or edges and learning the external magnetic field of the Ising model using a graph neural network. Our approach is task-specific as it can learn how to reduce a graph for a specific downstream task in an end-to-end fashion without requiring a differentiable loss function for the task. We showcase the versatility of our approach on four distinct applications: image segmentation, explainability for graph classification, 3D shape sparsification, and sparse approximate matrix inverse determination.

cs.LG↗

arXiv2025

Personalized Privacy Amplification via Importance Sampling

For scalable machine learning on large data sets, subsampling a representative subset is a common approach for efficient model training. This is often achieved through importance sampling, whereby informative data points are sampled more frequently. In this paper, we examine the privacy properties of importance sampling, focusing on an individualized privacy analysis. We find that, in importance sampling, privacy is well aligned with utility but at odds with sample size. Based on this insight, we propose two approaches for constructing sampling distributions: one that optimizes the privacy-efficiency trade-off; and one based on a utility guarantee in the form of coresets. We evaluate both approaches empirically in terms of privacy, efficiency, and accuracy on the differentially private $k$-means problem. We observe that both approaches yield similar outcomes and consistently outperform uniform sampling across a wide range of data sets. Our code is available on GitHub: https://github.com/smair/personalized-privacy-amplification-via-importance-sampling

cs.CR↗

arXiv2025

Real-Time Diffusion Policies for Games: Enhancing Consistency Policies with Q-Ensembles

Diffusion models have shown impressive performance in capturing complex and multi-modal action distributions for game agents, but their slow inference speed prevents practical deployment in real-time game environments. While consistency models offer a promising approach for one-step generation, they often suffer from training instability and performance degradation when applied to policy learning. In this paper, we present CPQE (Consistency Policy with Q-Ensembles), which combines consistency models with Q-ensembles to address these challenges.CPQE leverages uncertainty estimation through Q-ensembles to provide more reliable value function approximations, resulting in better training stability and improved performance compared to classic double Q-network methods. Our extensive experiments across multiple game scenarios demonstrate that CPQE achieves inference speeds of up to 60 Hz -- a significant improvement over state-of-the-art diffusion policies that operate at only 20 Hz -- while maintaining comparable performance to multi-step diffusion approaches. CPQE consistently outperforms state-of-the-art consistency model approaches, showing both higher rewards and enhanced training stability throughout the learning process. These results indicate that CPQE offers a practical solution for deploying diffusion-based policies in games and other real-time applications where both multi-modal behavior modeling and rapid inference are critical requirements.

cs.AI↗

arXiv2025

Conditioning diffusion models by explicit forward-backward bridging

Given an unconditional diffusion model targeting a joint model $π(x, y)$, using it to perform conditional simulation $π(x \mid y)$ is still largely an open question and is typically achieved by learning conditional drifts to the denoising SDE after the fact. In this work, we express \emph{exact} conditional simulation within the \emph{approximate} diffusion model as an inference problem on an augmented space corresponding to a partial SDE bridge. This perspective allows us to implement efficient and principled particle Gibbs and pseudo-marginal samplers marginally targeting the conditional distribution $π(x \mid y)$. Contrary to existing methodology, our methods do not introduce any additional approximation to the unconditional diffusion model aside from the Monte Carlo error. We showcase the benefits and drawbacks of our approach on a series of synthetic and real data examples.

stat.ML↗

arXiv2025

Conditional sampling within generative diffusion models

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their success in these domains, an important open challenge remains: extending these techniques to sample from conditional distributions, as required in, for example, Bayesian inverse problems. In this paper, we present a comprehensive review of existing computational approaches to conditional sampling within generative diffusion models. Specifically, we highlight key methodologies that either utilise the joint distribution, or rely on (pre-trained) marginal distributions with explicit likelihoods, to construct conditional generative samplers.

stat.ML↗

arXiv2025

Entropy-regularized Diffusion Policy with Q-Ensembles for Offline Reinforcement Learning

This paper presents advanced techniques of training diffusion policies for offline reinforcement learning (RL). At the core is a mean-reverting stochastic differential equation (SDE) that transfers a complex action distribution into a standard Gaussian and then samples actions conditioned on the environment state with a corresponding reverse-time SDE, like a typical diffusion policy. We show that such an SDE has a solution that we can use to calculate the log probability of the policy, yielding an entropy regularizer that improves the exploration of offline datasets. To mitigate the impact of inaccurate value functions from out-of-distribution data points, we further propose to learn the lower confidence bound of Q-ensembles for more robust policy improvement. By combining the entropy-regularized diffusion policy with Q-ensembles in offline RL, our method achieves state-of-the-art performance on most tasks in D4RL benchmarks. Code is available at https://github.com/ruoqizzz/Entropy-Regularized-Diffusion-Policy-with-QEnsemble.

cs.LG↗

arXiv2024

Learning incomplete factorization preconditioners for GMRES

Incomplete LU factorizations of sparse matrices are widely used as preconditioners in Krylov subspace methods to speed up solving linear systems. Unfortunately, computing the preconditioner itself can be time-consuming and sensitive to hyper-parameters. Instead, we replace the hand-engineered algorithm with a graph neural network that is trained to approximate the matrix factorization directly. To apply the output of the neural network as a preconditioner, we propose an output activation function that guarantees that the predicted factorization is invertible. Further, applying a graph neural network architecture allows us to ensure that the output itself is sparse which is desirable from a computational standpoint. We theoretically analyze and empirically evaluate different loss functions to train the learned preconditioners and show their effectiveness in decreasing the number of GMRES iterations and improving the spectral properties on synthetic data. The code is available at https://github.com/paulhausner/neural-incomplete-factorization.

cs.LG↗

arXiv2024

Neural incomplete factorization: learning preconditioners for the conjugate gradient method

The convergence of the conjugate gradient method for solving large-scale and sparse linear equation systems depends on the spectral properties of the system matrix, which can be improved by preconditioning. In this paper, we develop a computationally efficient data-driven approach to accelerate the generation of effective preconditioners. We, therefore, replace the typically hand-engineered preconditioners by the output of graph neural networks. Our method generates an incomplete factorization of the matrix and is, therefore, referred to as neural incomplete factorization (NeuralIF). Optimizing the condition number of the linear system directly is computationally infeasible. Instead, we utilize a stochastic approximation of the Frobenius loss which only requires matrix-vector multiplications for efficient training. At the core of our method is a novel message-passing block, inspired by sparse matrix theory, that aligns with the objective of finding a sparse factorization of the matrix. We evaluate our proposed method on both synthetic problem instances and on problems arising from the discretization of the Poisson equation on varying domains. Our experiments show that by using data-driven preconditioners within the conjugate gradient method we are able to speed up the convergence of the iterative procedure. The code is available at https://github.com/paulhausner/neural-incomplete-factorization.

math.OC↗

arXiv2024

Online learning in motion modeling for intra-interventional image sequences

Image monitoring and guidance during medical examinations can aid both diagnosis and treatment. However, the sampling frequency is often too low, which creates a need to estimate the missing images. We present a probabilistic motion model for sequential medical images, with the ability to both estimate motion between acquired images and forecast the motion ahead of time. The core is a low-dimensional temporal process based on a linear Gaussian state-space model with analytically tractable solutions for forecasting, simulation, and imputation of missing samples. The results, from two experiments on publicly available cardiac datasets, show reliable motion estimates and an improved forecasting performance using patient-specific adaptation by online learning.

cs.CV↗

arXiv2024

Efficient Radiation Treatment Planning based on Voxel Importance

Radiation treatment planning involves optimization over a large number of voxels, many of which carry limited information about the clinical problem. We propose an approach to reduce the large optimization problem by only using a representative subset of informative voxels. This way, we drastically improve planning efficiency while maintaining the plan quality. Within an initial probing step, we pre-solve an easier optimization problem involving a simplified objective from which we derive an importance score per voxel. This importance score is then turned into a sampling distribution, which allows us to subsample a small set of informative voxels using importance sampling. By solving a - now reduced - version of the original optimization problem using this subset, we effectively reduce the problem's size and computational demands while accounting for regions where satisfactory dose deliveries are challenging. In contrast to other stochastic (sub-)sampling methods, our technique only requires a single probing and sampling step to define a reduced optimization problem. This problem can be efficiently solved using established solvers without the need of modifying or adapting them. Empirical experiments on open benchmark data highlight substantially reduced optimization times, up to 50 times faster than the original ones, for intensity-modulated radiation therapy (IMRT), all while upholding plan quality comparable to traditional methods. Our novel approach has the potential to significantly accelerate radiation treatment planning by addressing its inherent computational challenges. We reduce the treatment planning time by reducing the size of the optimization problem rather than modifying and improving the optimization method. Our efforts are thus complementary to many previous developments.

physics.med-ph↗

arXiv2024

Archetypal Analysis++: Rethinking the Initialization Strategy

Archetypal analysis is a matrix factorization method with convexity constraints. Due to local minima, a good initialization is essential, but frequently used initialization methods yield either sub-optimal starting points or are prone to get stuck in poor local minima. In this paper, we propose archetypal analysis++ (AA++), a probabilistic initialization strategy for archetypal analysis that sequentially samples points based on their influence on the objective function, similar to $k$-means++. In fact, we argue that $k$-means++ already approximates the proposed initialization method. Furthermore, we suggest to adapt an efficient Monte Carlo approximation of $k$-means++ to AA++. In an extensive empirical evaluation of 15 real-world data sets of varying sizes and dimensionalities and considering two pre-processing strategies, we show that AA++ almost always outperforms all baselines, including the most frequently used ones.

cs.LG↗

arXiv2024

Photo-Realistic Image Restoration in the Wild with Controlled Vision-Language Models

Though diffusion models have been successfully applied to various image restoration (IR) tasks, their performance is sensitive to the choice of training datasets. Typically, diffusion models trained in specific datasets fail to recover images that have out-of-distribution degradations. To address this problem, this work leverages a capable vision-language model and a synthetic degradation pipeline to learn image restoration in the wild (wild IR). More specifically, all low-quality images are simulated with a synthetic degradation pipeline that contains multiple common degradations such as blur, resize, noise, and JPEG compression. Then we introduce robust training for a degradation-aware CLIP model to extract enriched image content features to assist high-quality image restoration. Our base diffusion model is the image restoration SDE (IR-SDE). Built upon it, we further present a posterior sampling strategy for fast noise-free image generation. We evaluate our model on both synthetic and real-world degradation datasets. Moreover, experiments on the unified image restoration task illustrate that the proposed posterior sampling improves image generation quality for various degradations.

cs.CV↗

arXiv2024

Controlling Vision-Language Models for Multi-Task Image Restoration

Vision-language models such as CLIP have shown great impact on diverse downstream tasks for zero-shot or label-free predictions. However, when it comes to low-level vision such as image restoration their performance deteriorates dramatically due to corrupted inputs. In this paper, we present a degradation-aware vision-language model (DA-CLIP) to better transfer pretrained vision-language models to low-level vision tasks as a multi-task framework for image restoration. More specifically, DA-CLIP trains an additional controller that adapts the fixed CLIP image encoder to predict high-quality feature embeddings. By integrating the embedding into an image restoration network via cross-attention, we are able to pilot the model to learn a high-fidelity image reconstruction. The controller itself will also output a degradation feature that matches the real corruptions of the input, yielding a natural classifier for different degradation types. In addition, we construct a mixed degradation dataset with synthetic captions for DA-CLIP training. Our approach advances state-of-the-art performance on both \emph{degradation-specific} and \emph{unified} image restoration tasks, showing a promising direction of prompting image restoration with large-scale pretrained vision-language models. Our code is available at https://github.com/Algolzw/daclip-uir.

cs.CV↗

arXiv2024

On Feynman--Kac training of partial Bayesian neural networks

Recently, partial Bayesian neural networks (pBNNs), which only consider a subset of the parameters to be stochastic, were shown to perform competitively with full Bayesian neural networks. However, pBNNs are often multi-modal in the latent variable space and thus challenging to approximate with parametric models. To address this problem, we propose an efficient sampling-based training strategy, wherein the training of a pBNN is formulated as simulating a Feynman--Kac model. We then describe variations of sequential Monte Carlo samplers that allow us to simultaneously estimate the parameters and the latent posterior distribution of this model at a tractable computational cost. Using various synthetic and real-world datasets we show that our proposed training scheme outperforms the state of the art in terms of predictive performance.

cs.LG↗

arXiv2024

ICML 2023 Topological Deep Learning Challenge : Design and Results

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

cs.LG↗

arXiv2023

Variational Elliptical Processes

We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational tractability. Elliptical processes are based on a representation of elliptical distributions as a continuous mixture of Gaussian distributions. We parameterize this mixture distribution as a spline normalizing flow, which we train using variational inference. The proposed form of the variational posterior enables a sparse variational elliptical process applicable to large-scale problems. We highlight advantages compared to Gaussian processes through regression and classification experiments. Elliptical processes can supersede Gaussian processes in several settings, including cases where the likelihood is non-Gaussian or when accurate tail modeling is essential.

cs.LG↗