Martin Jørgensen

Pola Schwöbel, Martin Jørgensen, Sebastian W. Ober et al.

Data augmentation is often used to incorporate inductive biases into models. Traditionally, these are hand-crafted and tuned with cross validation. The Bayesian paradigm for model selection provides a path towards end-to-end learning of invariances using only the training data, by optimising the marginal likelihood. Computing the marginal likelihood is hard for neural networks, but success with tractable approaches that compute the marginal likelihood for the last layer only raises the question of whether this convenient approach might be employed for learning invariances. We show partial success on standard benchmarks, in the low-data regime and on a medical imaging dataset by designing a custom optimisation routine. Introducing a new lower bound to the marginal likelihood allows us to perform inference for a larger class of likelihood functions than before. On the other hand, we demonstrate failure modes on the CIFAR10 dataset, where the last layer approximation is not sufficient due to the increased complexity of our neural network. Our results indicate that once more sophisticated approximations become available the marginal likelihood is a promising approach for invariance learning in neural networks.

Frederik Warburg, Martin Jørgensen, Javier Civera et al.

Uncertainty quantification in image retrieval is crucial for downstream decisions, yet it remains a challenging and largely unexplored problem. Current methods for estimating uncertainties are poorly calibrated, computationally expensive, or based on heuristics. We present a new method that views image embeddings as stochastic features rather than deterministic features. Our two main contributions are (1) a likelihood that matches the triplet constraint and that evaluates the probability of an anchor being closer to a positive than a negative; and (2) a prior over the feature space that justifies the conventional l2 normalization. To ensure computational efficiency, we derive a variational approximation of the posterior, called the Bayesian triplet loss, that produces state-of-the-art uncertainty estimates and matches the predictive performance of current state-of-the-art methods.

Martin Jørgensen, Søren Hauberg

Causal discovery estimates the underlying physical process that generates the observed data: does X cause Y or does Y cause X? Current methodologies use structural conditions to turn the causal query into a statistical query, when only observational data is available. But what if these statistical queries are sensitive to causal invariants? This study investigates one such invariant: the causal relationship between X and Y is invariant to the marginal distributions of X and Y. We propose an algorithm that uses a non-parametric estimator that is robust to changes in the marginal distributions. This way we may marginalize the marginals, and inspect what relationship is intrinsically there. The resulting causal estimator is competitive with current methodologies and has high emphasis on the uncertainty in the causal query; an aspect just as important as the query itself.

Martin Jørgensen, Marc Peter Deisenroth, Hugh Salimbeni

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also known as the diffusion, and modelling it by means of Wishart processes. Further, we present a semi-parametric approach that allows the framework to scale to high dimensions. This successfully lead us onto how to model both latent and auto-regressive temporal systems with conditional heteroskedastic noise. We provide experimental evidence that modelling diffusion often improves performance and that this randomness in the differential equation can be essential to avoid overfitting.

Martin Jørgensen, Søren Hauberg

We present a probabilistic model where the latent variable respects both the distances and the topology of the modeled data. The model leverages the Riemannian geometry of the generated manifold to endow the latent space with a well-defined stochastic distance measure, which is modeled locally as Nakagami distributions. These stochastic distances are sought to be as similar as possible to observed distances along a neighborhood graph through a censoring process. The model is inferred by variational inference based on observations of pairwise distances. We demonstrate how the new model can encode invariances in the learned manifolds.

Pola Schwöbel, Frederik Warburg, Martin Jørgensen et al.

Spatial Transformer Networks (STNs) estimate image transformations that can improve downstream tasks by `zooming in' on relevant regions in an image. However, STNs are hard to train and sensitive to mis-predictions of transformations. To circumvent these limitations, we propose a probabilistic extension that estimates a stochastic transformation rather than a deterministic one. Marginalizing transformations allows us to consider each image at multiple poses, which makes the localization task easier and the training more robust. As an additional benefit, the stochastic transformations act as a localized, learned data augmentation that improves the downstream tasks. We show across standard imaging benchmarks and on a challenging real-world dataset that these two properties lead to improved classification performance, robustness and model calibration. We further demonstrate that the approach generalizes to non-visual domains by improving model performance on time-series data.

Nicki S. Detlefsen, Martin Jørgensen, Søren Hauberg

We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to make unbiased weight updates to a variance network. Further, we formulate a heuristic for robustly fitting both the mean and variance networks post hoc. Finally, we take inspiration from posterior Gaussian processes and propose a network architecture with similar extrapolation properties to Gaussian processes. The proposed methodologies are complementary, and improve upon baseline methods individually. Experimentally, we investigate the impact on predictive uncertainty on multiple datasets and tasks ranging from regression, active learning and generative modeling. Experiments consistently show significant improvements in predictive uncertainty estimation over state-of-the-art methods across tasks and datasets.