arXiv subjects

Søren Hauberg

Publications and source records attributed to Søren Hauberg.

At least 55 records · Page 3Linked to original sources

arXiv2022

Revisiting Active Sets for Gaussian Process Decoders

Decoders built on Gaussian processes (GPs) are enticing due to the marginalisation over the non-linear function space. Such models (also known as GP-LVMs) are often expensive and notoriously difficult to train in practice, but can be scaled using variational inference and inducing points. In this paper, we revisit active set approximations. We develop a new stochastic estimate of the log-marginal likelihood based on recently discovered links to cross-validation, and propose a computationally efficient approximation thereof. We demonstrate that the resulting stochastic active sets (SAS) approximation significantly improves the robustness of GP decoder training while reducing computational cost. The SAS-GP obtains more structure in the latent space, scales to many datapoints and learns better representations than variational autoencoders, which is rarely the case for GP decoders.

stat.ML↗

arXiv2022

Probabilistic thermal stability prediction through sparsity promoting transformer representation

Pre-trained protein language models have demonstrated significant applicability in different protein engineering task. A general usage of these pre-trained transformer models latent representation is to use a mean pool across residue positions to reduce the feature dimensions to further downstream tasks such as predicting bio-physics properties or other functional behaviours. In this paper we provide a two-fold contribution to machine learning (ML) driven drug design. Firstly, we demonstrate the power of sparsity by promoting penalization of pre-trained transformer models to secure more robust and accurate melting temperature (Tm) prediction of single-chain variable fragments with a mean absolute error of 0.23C. Secondly, we demonstrate the power of framing our prediction problem in a probabilistic framework. Specifically, we advocate for the need of adopting probabilistic frameworks especially in the context of ML driven drug design.

stat.ML↗

arXiv2022

Is an encoder within reach?

The encoder network of an autoencoder is an approximation of the nearest point projection onto the manifold spanned by the decoder. A concern with this approximation is that, while the output of the encoder is always unique, the projection can possibly have infinitely many values. This implies that the latent representations learned by the autoencoder can be misleading. Borrowing from geometric measure theory, we introduce the idea of using the reach of the manifold spanned by the decoder to determine if an optimal encoder exists for a given dataset and decoder. We develop a local generalization of this reach and propose a numerical estimator thereof. We demonstrate that this allows us to determine which observations can be expected to have a unique, and thereby trustworthy, latent representation. As our local reach estimator is differentiable, we investigate its usage as a regularizer and show that this leads to learned manifolds for which projections are more often unique than without regularization.

cs.LG↗

arXiv2022

Laplacian Autoencoders for Learning Stochastic Representations

Established methods for unsupervised representation learning such as variational autoencoders produce none or poorly calibrated uncertainty estimates making it difficult to evaluate if learned representations are stable and reliable. In this work, we present a Bayesian autoencoder for unsupervised representation learning, which is trained using a novel variational lower-bound of the autoencoder evidence. This is maximized using Monte Carlo EM with a variational distribution that takes the shape of a Laplace approximation. We develop a new Hessian approximation that scales linearly with data size allowing us to model high-dimensional data. Empirically, we show that our Laplacian autoencoder estimates well-calibrated uncertainties in both latent and output space. We demonstrate that this results in improved performance across a multitude of downstream tasks.

cs.LG↗

arXiv2022

Density estimation on smooth manifolds with normalizing flows

We present a framework for learning probability distributions on topologically non-trivial manifolds, utilizing normalizing flows. Current methods focus on manifolds that are homeomorphic to Euclidean space, enforce strong structural priors on the learned models or use operations that do not easily scale to high dimensions. In contrast, our method learns distributions on a data manifold by "gluing" together multiple local models, thus defining an open cover of the data manifold. We demonstrate the efficiency of our approach on synthetic data of known manifolds, as well as higher dimensional manifolds of unknown topology, where our method exhibits better sample efficiency and competitive or superior performance against baselines in a number of tasks.

cs.LG↗

arXiv2022

Probabilistic Spatial Transformer Networks

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.

cs.LG↗

arXiv2022

Mario Plays on a Manifold: Generating Functional Content in Latent Space through Differential Geometry

Deep generative models can automatically create content of diverse types. However, there are no guarantees that such content will satisfy the criteria necessary to present it to end-users and be functional, e.g. the generated levels could be unsolvable or incoherent. In this paper we study this problem from a geometric perspective, and provide a method for reliable interpolation and random walks in the latent spaces of Categorical VAEs based on Riemannian geometry. We test our method with "Super Mario Bros" and "The Legend of Zelda" levels, and against simpler baselines inspired by current practice. Results show that the geometry we propose is better able to interpolate and sample, reliably staying closer to parts of the latent space that decode to playable content.

cs.LG↗

arXiv2022

Pulling back information geometry

Latent space geometry has shown itself to provide a rich and rigorous framework for interacting with the latent variables of deep generative models. The existing theory, however, relies on the decoder being a Gaussian distribution as its simple reparametrization allows us to interpret the generating process as a random projection of a deterministic manifold. Consequently, this approach breaks down when applied to decoders that are not as easily reparametrized. We here propose to use the Fisher-Rao metric associated with the space of decoder distributions as a reference metric, which we pull back to the latent space. We show that we can achieve meaningful latent geometries for a wide range of decoder distributions for which the previous theory was not applicable, opening the door to `black box' latent geometries.

cs.LG↗

arXiv2022

Benchmarking Generative Latent Variable Models for Speech

Stochastic latent variable models (LVMs) achieve state-of-the-art performance on natural image generation but are still inferior to deterministic models on speech. In this paper, we develop a speech benchmark of popular temporal LVMs and compare them against state-of-the-art deterministic models. We report the likelihood, which is a much used metric in the image domain, but rarely, or incomparably, reported for speech models. To assess the quality of the learned representations, we also compare their usefulness for phoneme recognition. Finally, we adapt the Clockwork VAE, a state-of-the-art temporal LVM for video generation, to the speech domain. Despite being autoregressive only in latent space, we find that the Clockwork VAE can outperform previous LVMs and reduce the gap to deterministic models by using a hierarchy of latent variables.

eess.AS↗

arXiv2022

Visualizing Riemannian data with Rie-SNE

Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.

cs.LG↗

arXiv2022

What is a meaningful representation of protein sequences?

How we choose to represent our data has a fundamental impact on our ability to subsequently extract information from them. Machine learning promises to automatically determine efficient representations from large unstructured datasets, such as those arising in biology. However, empirical evidence suggests that seemingly minor changes to these machine learning models yield drastically different data representations that result in different biological interpretations of data. This begs the question of what even constitutes the most meaningful representation. Here, we approach this question for representations of protein sequences, which have received considerable attention in the recent literature. We explore two key contexts in which representations naturally arise: transfer learning and interpretable learning. In the first context, we demonstrate that several contemporary practices yield suboptimal performance, and in the latter we demonstrate that taking representation geometry into account significantly improves interpretability and lets the models reveal biological information that is otherwise obscured.

q-bio.BM↗

arXiv2022

Model-agnostic out-of-distribution detection using combined statistical tests

We present simple methods for out-of-distribution detection using a trained generative model. These techniques, based on classical statistical tests, are model-agnostic in the sense that they can be applied to any differentiable generative model. The idea is to combine a classical parametric test (Rao's score test) with the recently introduced typicality test. These two test statistics are both theoretically well-founded and exploit different sources of information based on the likelihood for the typicality test and its gradient for the score test. We show that combining them using Fisher's method overall leads to a more accurate out-of-distribution test. We also discuss the benefits of casting out-of-distribution detection as a statistical testing problem, noting in particular that false positive rate control can be valuable for practical out-of-distribution detection. Despite their simplicity and generality, these methods can be competitive with model-specific out-of-distribution detection algorithms without any assumptions on the out-distribution.

stat.ML↗

arXiv2022

Danish Airs and Grounds: A Dataset for Aerial-to-Street-Level Place Recognition and Localization

Place recognition and visual localization are particularly challenging in wide baseline configurations. In this paper, we contribute with the \emph{Danish Airs and Grounds} (DAG) dataset, a large collection of street-level and aerial images targeting such cases. Its main challenge lies in the extreme viewing-angle difference between query and reference images with consequent changes in illumination and perspective. The dataset is larger and more diverse than current publicly available data, including more than 50 km of road in urban, suburban and rural areas. All images are associated with accurate 6-DoF metadata that allows the benchmarking of visual localization methods. We also propose a map-to-image re-localization pipeline, that first estimates a dense 3D reconstruction from the aerial images and then matches query street-level images to street-level renderings of the 3D model. The dataset can be downloaded at: https://frederikwarburg.github.io/DAG

cs.CV↗

arXiv2022

Hierarchical VAEs Know What They Don't Know

Deep generative models have been demonstrated as state-of-the-art density estimators. Yet, recent work has found that they often assign a higher likelihood to data from outside the training distribution. This seemingly paradoxical behavior has caused concerns over the quality of the attained density estimates. In the context of hierarchical variational autoencoders, we provide evidence to explain this behavior by out-of-distribution data having in-distribution low-level features. We argue that this is both expected and desirable behavior. With this insight in hand, we develop a fast, scalable and fully unsupervised likelihood-ratio score for OOD detection that requires data to be in-distribution across all feature-levels. We benchmark the method on a vast set of data and model combinations and achieve state-of-the-art results on out-of-distribution detection.

cs.LG↗

arXiv2022

Robust uncertainty estimates with out-of-distribution pseudo-inputs training

Probabilistic models often use neural networks to control their predictive uncertainty. However, when making out-of-distribution (OOD)} predictions, the often-uncontrollable extrapolation properties of neural networks yield poor uncertainty predictions. Such models then don't know what they don't know, which directly limits their robustness w.r.t unexpected inputs. To counter this, we propose to explicitly train the uncertainty predictor where we are not given data to make it reliable. As one cannot train without data, we provide mechanisms for generating pseudo-inputs in informative low-density regions of the input space, and show how to leverage these in a practical Bayesian framework that casts a prior distribution over the model uncertainty. With a holistic evaluation, we demonstrate that this yields robust and interpretable predictions of uncertainty while retaining state-of-the-art performance on diverse tasks such as regression and generative modelling

cs.LG↗

arXiv2021

Latent Space Oddity: on the Curvature of Deep Generative Models

Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator imply that the latent space gives a distorted view of the input space. Under mild conditions, we show that this distortion can be characterized by a stochastic Riemannian metric, and demonstrate that distances and interpolants are significantly improved under this metric. This in turn improves probability distributions, sampling algorithms and clustering in the latent space. Our geometric analysis further reveals that current generators provide poor variance estimates and we propose a new generator architecture with vastly improved variance estimates. Results are demonstrated on convolutional and fully connected variational autoencoders, but the formalism easily generalize to other deep generative models.

stat.ML↗

arXiv2021

Bounds all around: training energy-based models with bidirectional bounds

Energy-based models (EBMs) provide an elegant framework for density estimation, but they are notoriously difficult to train. Recent work has established links to generative adversarial networks, where the EBM is trained through a minimax game with a variational value function. We propose a bidirectional bound on the EBM log-likelihood, such that we maximize a lower bound and minimize an upper bound when solving the minimax game. We link one bound to a gradient penalty that stabilizes training, thereby providing grounding for best engineering practice. To evaluate the bounds we develop a new and efficient estimator of the Jacobi-determinant of the EBM generator. We demonstrate that these developments significantly stabilize training and yield high-quality density estimation and sample generation.

cs.LG↗

arXiv2021

Bayesian Triplet Loss: Uncertainty Quantification in Image Retrieval

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.

cs.CV↗