arXiv subjects

Jonas Beck

Publications and source records attributed to Jonas Beck.

11 recordsLinked to original sources

arXiv2026

Detecting Early and Late Divergences in Survival Curves Using Nonparametric Effect Measures

Clinical trials often show treatment curves that diverge early and converge later, or vice versa patterns that are poorly captured by the proportional-hazards assumption. We develop a joint inferential framework for two nonparametric functionals of censored survival data: the Kaplan--Meier-based Mann--Whitney effect and a novel temporal contrast separating early and late differences. The approach provides interpretable, probability-scale effect measures and enables joint inference for global and temporal contrasts under right censoring. In simulation studies, the method outperforms the log-rank test under non-proportional hazards while maintaining nominal type-I error. A real-world application illustrates how the temporal contrast reveals clinically meaningful early treatment advantages that remain hidden in standard analyses

stat.ME↗

arXiv2026

Learning Hybrid Biophysical Neuron Models with Neural ODEs

Biophysical neuron models link measurements of neural activity to underlying cellular mechanisms. Yet, a central challenge is that the kinetics of many ion channels are poorly characterized, and practical simplifications -- omitting channels or reducing morphological detail -- introduce systematic gaps between model and biology. Bridging these gaps requires approaches that can flexibly discover unmodeled dynamics while preserving mechanistic interpretability. Here, we introduce a hybrid modeling framework that embeds neural ordinary differential equations into conductance-based biophysical models to capture unknown currents or mis-specified channel kinetics. By parameterizing the neural ODE in terms of voltage-dependent steady-state and time-constant functions, we recover interpretable gating dynamics directly from voltage recordings without assuming a functional form. We show that the hybrid model fits the gating kinetics of 2400 ion channel models and recovers unknown gating dynamics from single current-clamp recordings, generalizing to out-of-distribution stimulus regimes under realistic inputs and parameter misspecification. We also use our method to reduce a multicompartment model of a cortical neuron into a single-compartment hybrid model with a learned axial current, yielding up to an order of magnitude lower computational cost. Together, our results establish a plug-and-play framework for selectively replacing unknown components of conductance-based models with neural ODEs while preserving their mechanistic structure.

q-bio.NC↗

arXiv2026

On the Regularity and Interpolation of Coupled Cluster Amplitudes in Canonical Orbital Basis

Arguably the most widely used approaches for obtaining highly accurate molecular ground-state energies are coupled cluster methods. Despite introducing two layers of approximation, a linear and a nonlinear one, coupled cluster methods remain computationally intensive, with the complexity scaling as $O(poly(N))$, where $N$ is the number of electrons. Moreover, this method must be applied over a large set of different nuclear coordinates in order to study certain chemical phenomena. Therefore, in this work, we investigate the regularity of single-reference coupled cluster amplitudes with respect to nuclear coordinate displacements, with the aim of enabling interpolation or extrapolation approaches that rely on only a limited number of reference geometries. We show that, in theory, under certain non-degeneracy assumptions on the Hartree-Fock level of theory, and the coupled cluster level of theory the amplitudes behave real analytic. Furthermore, we analyze the artifacts that arise in practical calculations that use canonical orbitals, which hinder this high degree of regularity, and suggest strategies to mitigate these issues. Finally, we validate our findings through numerical experiments by interpolating the amplitudes and comparing the performance of the interpolants with that of the exact amplitudes.

math.NA↗

arXiv2026

Mixed neural posterior estimation for simulators with discrete and continuous parameters

Neural Posterior Estimation (NPE) enables rapid parameter inference for complex simulators with intractable likelihoods. NPE trains an inference network to estimate a probability density over parameters given data, typically assumed to be \emph{continuous}. However, many scientific models involve parameter spaces that are \emph{mixed}, that is, they contain both discrete and continuous dimensions. We address this limitation by extending NPE to mixed parameter spaces through an inference network that jointly handles discrete and continuous parameters. The inference network factorizes the joint posterior into discrete and continuous components, combining an autoregressive classifier for the discrete parameters with a generative model for the continuous parameters, trained jointly under a single simulation-based objective. In addition, we propose a diagnostic tool to assess the calibration of the mixed posterior approximation. Across tractable toy examples and real-world scientific simulators, our joint inference approach yields accurate and calibrated posteriors. The inference framework is available in the \texttt{sbi} Python package.

cs.LG↗

arXiv2026

Nonparametric Statistical Inference for Multivariate Niche Overlap

In ecological studies niche overlap is often used to quantify species interaction and dynamics. This paper develops a robust, nonparametric statistical framework for quantifying and analyzing multivariate niche overlap. Parametric methods are often constrained by restrictive assumptions and tend to underperform in complex multivariate settings. We introduce a nonparametric overlap index and propose estimators for it. Further, we investigate asymptotic properties of the estimators. We also propose bootstrap-based inference procedures that enable statistical testing and simultaneous confidence intervals in small sample settings. Extensive numerical examples demonstrate that our proposed methods maintain correct size and exhibit robust power across various scenarios. We illustrate the practical utility of our methodology using stable isotope measurements from multiple fish species and provide distinct ecological insights regarding species niche differentiation.

stat.ME↗

arXiv2025

Kekul\'e order from diffuse nesting near higher-order Van Hove points

Translation symmetry-breaking order is assumed to be suppressed by the lack of Fermi surface nesting near certain higher-order Van Hove singularities (HOVHS). We show the anisotropic band-flattening inherent to such HOVHS, combined with broadening of the Fermi surface due to elevated critical temperatures, results in the Fermi surface becoming approximately nested at a wavevector unrelated to the precise shape of the Fermi surface - leading to a $\sqrt{3}\times\sqrt{3}$ Kekul\'e density wave formation. The effect is demonstrated using unbiased renormalization group calculations for a model of the breathing kagome lattice. Our mechanism - termed diffuse nesting - represents an entirely new notion in the study of Fermi surface instabilities.

cond-mat.str-el↗

arXiv2024

sbi reloaded: a toolkit for simulation-based inference workflows

Scientists and engineers use simulators to model empirically observed phenomena. However, tuning the parameters of a simulator to ensure its outputs match observed data presents a significant challenge. Simulation-based inference (SBI) addresses this by enabling Bayesian inference for simulators, identifying parameters that match observed data and align with prior knowledge. Unlike traditional Bayesian inference, SBI only needs access to simulations from the model and does not require evaluations of the likelihood function. In addition, SBI algorithms do not require gradients through the simulator, allow for massive parallelization of simulations, and can perform inference for different observations without further simulations or training, thereby amortizing inference. Over the past years, we have developed, maintained, and extended sbi, a PyTorch-based package that implements Bayesian SBI algorithms based on neural networks. The sbi toolkit implements a wide range of inference methods, neural network architectures, sampling methods, and diagnostic tools. In addition, it provides well-tested default settings, but also offers flexibility to fully customize every step of the simulation-based inference workflow. Taken together, the sbi toolkit enables scientists and engineers to apply state-of-the-art SBI methods to black-box simulators, opening up new possibilities for aligning simulations with empirically observed data.

cs.LG↗

arXiv2024

Diffusion Tempering Improves Parameter Estimation with Probabilistic Integrators for Ordinary Differential Equations

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.

cs.LG↗

arXiv2024

Phase diagram of the $J$-$J_d$ Heisenberg Model on the Maple-Leaf Lattice: Neural networks and density matrix renormalization group

We microscopically analyze the nearest neighbor Heisenberg model on the maple-leaf lattice through neural quantum states (NQS) and infinite density matrix renormalization group (iDMRG). Embarking to parameter regimes beyond the exact dimer singlet ground state with a dimer bond spin exchange coupling $J_d$ varied against the exchange strength $J$ of all other bonds, iDMRG (NQS) finds a dimer state paramagnetic phase for $J_d/J > 1.464$ ($J_d/J > 1.39$) and a canted $120^\circ$ magnetic order for $J_d/J < 1.419$ ($J_d/J < 1.23$). Assessing training convergence inaccuracies of NQS and the influence of finite cylindric circumference for iDMRG, we discuss the possible existence of an intermediate phase between magnet and dimer paramagnet.

cond-mat.str-el↗

arXiv2023

Combining Stochastic Tendency and Distribution Overlap Towards Improved Nonparametric Effect Measures and Inference

A fundamental functional in nonparametric statistics is the Mann-Whitney functional ${\theta} = P (X < Y )$ , which constitutes the basis for the most popular nonparametric procedures. The functional ${\theta}$ measures a location or stochastic tendency effect between two distributions. A limitation of ${\theta}$ is its inability to capture scale differences. If differences of this nature are to be detected, specific tests for scale or omnibus tests need to be employed. However, the latter often suffer from low power, and they do not yield interpretable effect measures. In this manuscript, we extend ${\theta}$ by additionally incorporating the recently introduced distribution overlap index (nonparametric dispersion measure) $I_2$ that can be expressed in terms of the quantile process. We derive the joint asymptotic distribution of the respective estimators of ${\theta}$ and $I_2$ and construct confidence regions. Extending the Wilcoxon- Mann-Whitney test, we introduce a new test based on the joint use of these functionals. It results in much larger consistency regions while maintaining competitive power to the rank sum test for situations in which {\theta} alone would suffice. Compared with classical omnibus tests, the simulated power is much improved. Additionally, the newly proposed inference method yields effect measures whose interpretation is surprisingly straightforward.

stat.ME↗

arXiv2022

Efficient identification of informative features in simulation-based inference

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.

cs.LG↗