arXiv subjects

Leiv Rønneberg

Publications and source records attributed to Leiv Rønneberg.

8 recordsLinked to original sources

arXiv2026

Posterior uncertainty for kernel density estimates

Recent work in predictive Bayesian inference has enabled novel Bayesian interpretations of many well-known stochastic one-step-ahead predictive algorithms. In this paper, we study classic kernel density estimation in the predictive Bayesian framework. We prove that their predictive measures converge weakly almost surely $\unicode{x2013}$ meaning that their associated predictive resampling sequences are almost surely asymptotically exchangeable $\unicode{x2013}$ and we provide estimators for moments of the limiting random probability measure. We also show that the resampling sequences do not satisfy standard assumptions like being conditionally identically distributed (c.i.d.) or almost c.i.d. (a.c.i.d.), thus providing a non-trivial example of a predictive sequence which is not a.c.i.d. but nevertheless converges weakly almost surely. For Gaussian kernels, we show that the limiting directing measure is almost surely absolutely continuous with respect to the Lebesgue measure, meaning it emits a probability density. This enables us to derive credibility intervals for kernel density estimates, which we illustrate on two real datasets.

stat.ME↗

arXiv2026

Stepwise Variational Inference with Vine Copulas

We propose stepwise variational inference (VI) with vine copulas: a universal VI procedure that combines vine copulas with a novel stepwise estimation procedure of the variational parameters. Vine copulas consist of a nested sequence of trees built from copulas, where more complex latent dependence can be modeled with increasing number of trees. We propose to estimate the vine copula approximate posterior in a stepwise fashion, tree by tree along the vine structure. Further, we show that the usual backward Kullback-Leibler divergence cannot recover the correct parameters in the vine copula model, thus the evidence lower bound is defined based on the Rényi divergence. Finally, an intuitive stopping criterion for adding further trees to the vine eliminates the need to pre-define a complexity parameter of the variational distribution, as required for most other approaches. Thus, our method interpolates between mean-field VI (MFVI) and full latent dependence. In many applications, in particular sparse Gaussian processes, our method is parsimonious with parameters, while outperforming MFVI.

stat.ML↗

arXiv2026

Dirichlet Scale Mixture Priors for Bayesian Neural Networks

Neural networks are the cornerstone of modern machine learning, yet can be difficult to interpret, give overconfident predictions and are vulnerable to adversarial attacks. Bayesian neural networks (BNNs) provide some alleviation of these limitations, but have problems of their own. The key step of specifying prior distributions in BNNs is no trivial task, yet is often skipped out of convenience. In this work, we propose a new class of prior distributions for BNNs, the Dirichlet scale mixture (DSM) prior, that addresses current limitations in Bayesian neural networks through structured, sparsity-inducing shrinkage. Theoretically, we derive general dependence structures and shrinkage results for DSM priors and show how they manifest under the geometry induced by neural networks. In experiments on simulated and real world data we find that the DSM priors encourages sparse networks through implicit feature selection, show robustness under adversarial attacks and deliver competitive predictive performance with substantially fewer effective parameters. In particular, their advantages appear most pronounced in correlated, moderately small data regimes, and are more amenable to weight pruning. Moreover, by adopting heavy-tailed shrinkage mechanisms, our approach aligns with recent findings that such priors can mitigate the cold posterior effect, offering a principled alternative to the commonly used Gaussian priors.

stat.ML↗

arXiv2025

Multi-Output Robust and Conjugate Gaussian Processes

Multi-output Gaussian process (MOGP) regression allows modelling dependencies among multiple correlated response variables. Similarly to standard Gaussian processes, MOGPs are sensitive to model misspecification and outliers, which can distort predictions within individual outputs. This situation can be further exacerbated by multiple anomalous response variables whose errors propagate due to correlations between outputs. To handle this situation, we extend and generalise the robust and conjugate Gaussian process (RCGP) framework introduced by Altamirano et al. (2024). This results in the multi-output RCGP (MO-RCGP): a provably robust MOGP that is conjugate, and jointly captures correlations across outputs. We thoroughly evaluate our approach through applications in finance and cancer research.

stat.ML↗

arXiv2024

Heterogeneous Clinical Trial Outcomes via Multi-Output Gaussian Processes

We make use of Kronecker structure for scaling Gaussian Process models to large-scale, heterogeneous, clinical data sets. Repeated measures, commonly performed in clinical research, facilitate computational acceleration for nonlinear Bayesian nonparametric models and enable exact sampling for non-conjugate inference, when combinations of continuous and discrete endpoints are observed. Model inference is performed in Stan, and comparisons are made with brms on simulated data and two real clinical data sets, following a radiological image quality theme. Scalable Gaussian Process models compare favourably with parametric models on real data sets with 17,460 observations. Different GP model specifications are explored, with components analogous to random effects, and their theoretical properties are described.

stat.ME↗

arXiv2024

Permutation invariant multi-output Gaussian Processes for drug combination prediction in cancer

Dose-response prediction in cancer is an active application field in machine learning. Using large libraries of \textit{in-vitro} drug sensitivity screens, the goal is to develop accurate predictive models that can be used to guide experimental design or inform treatment decisions. Building on previous work that makes use of permutation invariant multi-output Gaussian Processes in the context of dose-response prediction for drug combinations, we develop a variational approximation to these models. The variational approximation enables a more scalable model that provides uncertainty quantification and naturally handles missing data. Furthermore, we propose using a deep generative model to encode the chemical space in a continuous manner, enabling prediction for new drugs and new combinations. We demonstrate the performance of our model in a simple setting using a high-throughput dataset and show that the model is able to efficiently borrow information across outputs.

q-bio.QM↗

arXiv2023

FlexKnot and Gaussian Process for 21 cm global signal analysis and foreground separation

The cosmological 21 cm signal is one of the most promising avenues to study the Epoch of Reionization. One class of experiments aiming to detect this signal is global signal experiments measuring the sky-averaged 21 cm brightness temperature as a function of frequency. A crucial step in the interpretation and analysis of such measurements is separating foreground contributions from the remainder of the signal, requiring accurate models for both components. Current models for the signal (non-foreground) component, which may contain cosmological and systematic contributions, are incomplete and unable to capture the full signal. We propose two new methods for extracting this component from the data: Firstly, we employ a foreground-orthogonal Gaussian Process to extract the part of the signal that cannot be explained by the foregrounds. Secondly, we use a FlexKnot parameterization to model the full signal component in a free-form manner, not assuming any particular shape or functional form. This method uses Bayesian model selection to find the simplest signal that can explain the data. We test our methods on both, synthetic data and publicly available EDGES low-band data. We find that the Gaussian Process can clearly capture the foreground-orthogonal signal component of both data sets. The FlexKnot method correctly recovers the full shape of the input signal used in the synthetic data and yields a multi-modal distribution of different signal shapes that can explain the EDGES observations.

astro-ph.CO↗

arXiv2019

Composite local low-rank structure in learning drug sensitivity

The molecular characterization of tumor samples by multiple omics data sets of different types or modalities (e.g. gene expression, mutation, CpG methylation) has become an invaluable source of information for assessing the expected performance of individual drugs and their combinations. Merging the relevant information from the omics data modalities provides the statistical basis for determining suitable therapies for specific cancer patients. Different data modalities may each have their specific structures that need to be taken into account during inference. In this paper, we assume that each omics data modality has a low-rank structure with only few relevant features that affect the prediction and we propose to use a composite local nuclear norm penalization for learning drug sensitivity. Numerical results show that the composite low-rank structure can improve the prediction performance compared to using a global low-rank approach or elastic net regression.

stat.AP↗