Aleksander Wieczorek

Maxim Samarin, Vitali Nesterov, Mario Wieser et al.

Identifying meaningful and independent factors of variation in a dataset is a challenging learning task frequently addressed by means of deep latent variable models. This task can be viewed as learning symmetry transformations preserving the value of a chosen property along latent dimensions. However, existing approaches exhibit severe drawbacks in enforcing the invariance property in the latent space. We address these shortcomings with a novel approach to cycle consistency. Our method involves two separate latent subspaces for the target property and the remaining input information, respectively. In order to enforce invariance as well as sparsity in the latent space, we incorporate semantic knowledge by using cycle consistency constraints relying on property side information. The proposed method is based on the deep information bottleneck and, in contrast to other approaches, allows using continuous target properties and provides inherent model selection capabilities. We demonstrate on synthetic and molecular data that our approach identifies more meaningful factors which lead to sparser and more interpretable models with improved invariance properties.

Mario Wieser, Sonali Parbhoo, Aleksander Wieczorek et al.

Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation cannot be formulated analytically. We propose to learn the symmetry transformation with a model consisting of two latent subspaces, where the first subspace captures the target and the second subspace the remaining invariant information. Our approach is based on the deep information bottleneck in combination with a continuous mutual information regulariser. Unlike previous methods, we focus on the challenging task of minimising mutual information in continuous domains. To this end, we base the calculation of mutual information on correlation matrices in combination with a bijective variable transformation. Extensive experiments demonstrate that our model outperforms state-of-the-art methods on artificial and molecular datasets.

Aleksander Wieczorek, Volker Roth

Combining the Information Bottleneck model with deep learning by replacing mutual information terms with deep neural nets has proved successful in areas ranging from generative modelling to interpreting deep neural networks. In this paper, we revisit the Deep Variational Information Bottleneck and the assumptions needed for its derivation. The two assumed properties of the data $X$, $Y$ and their latent representation $T$ take the form of two Markov chains $T-X-Y$ and $X-T-Y$. Requiring both to hold during the optimisation process can be limiting for the set of potential joint distributions $P(X,Y,T)$. We therefore show how to circumvent this limitation by optimising a lower bound for $I(T;Y)$ for which only the latter Markov chain has to be satisfied. The actual mutual information consists of the lower bound which is optimised in DVIB and cognate models in practice and of two terms measuring how much the former requirement $T-X-Y$ is violated. Finally, we propose to interpret the family of information bottleneck models as directed graphical models and show that in this framework the original and deep information bottlenecks are special cases of a fundamental IB model.

Adam Kortylewski, Mario Wieser, Andreas Morel-Forster et al.

Computer vision tasks are difficult because of the large variability in the data that is induced by changes in light, background, partial occlusion as well as the varying pose, texture, and shape of objects. Generative approaches to computer vision allow us to overcome this difficulty by explicitly modeling the physical image formation process. Using generative object models, the analysis of an observed image is performed via Bayesian inference of the posterior distribution. This conceptually simple approach tends to fail in practice because of several difficulties stemming from sampling the posterior distribution: high-dimensionality and multi-modality of the posterior distribution as well as expensive simulation of the rendering process. The main difficulty of sampling approaches in a computer vision context is choosing the proposal distribution accurately so that maxima of the posterior are explored early and the algorithm quickly converges to a valid image interpretation. In this work, we propose to use a Bayesian Neural Network for estimating an image dependent proposal distribution. Compared to a standard Gaussian random walk proposal, this accelerates the sampler in finding regions of the posterior with high value. In this way, we can significantly reduce the number of samples needed to perform facial image analysis.

Sonali Parbhoo, Mario Wieser, Aleksander Wieczorek et al.

Estimating the causal effects of an intervention from high-dimensional observational data is difficult due to the presence of confounding. The task is often complicated by the fact that we may have a systematic missingness in our data at test time. Our approach uses the information bottleneck to perform a low-dimensional compression of covariates by explicitly considering the relevance of information. Based on the sufficiently reduced covariate, we transfer the relevant information to cases where data is missing at test time, allowing us to reliably and accurately estimate the effects of an intervention, even where data is incomplete. Our results on causal inference benchmarks and a real application for treating sepsis show that our method achieves state-of-the art performance, without sacrificing interpretability.

Aleksander Wieczorek, Mario Wieser, Damian Murezzan et al.

Deep latent variable models are powerful tools for representation learning. In this paper, we adopt the deep information bottleneck model, identify its shortcomings and propose a model that circumvents them. To this end, we apply a copula transformation which, by restoring the invariance properties of the information bottleneck method, leads to disentanglement of the features in the latent space. Building on that, we show how this transformation translates to sparsity of the latent space in the new model. We evaluate our method on artificial and real data.

Adam Kortylewski, Aleksander Wieczorek, Mario Wieser et al.

In this work, we consider the problem of learning a hierarchical generative model of an object from a set of images which show examples of the object in the presence of variable background clutter. Existing approaches to this problem are limited by making strong a-priori assumptions about the object's geometric structure and require segmented training data for learning. In this paper, we propose a novel framework for learning hierarchical compositional models (HCMs) which do not suffer from the mentioned limitations. We present a generalized formulation of HCMs and describe a greedy structure learning framework that consists of two phases: Bottom-up part learning and top-down model composition. Our framework integrates the foreground-background segmentation problem into the structure learning task via a background model. As a result, we can jointly optimize for the number of layers in the hierarchy, the number of parts per layer and a foreground-background segmentation based on class labels only. We show that the learned HCMs are semantically meaningful and achieve competitive results when compared to other generative object models at object classification on a standard transfer learning dataset.

Aleksander Wieczorek, Volker Roth

We propose a new method of discovering causal relationships in temporal data based on the notion of causal compression. To this end, we adopt the Pearlian graph setting and the directed information as an information theoretic tool for quantifying causality. We introduce chain rule for directed information and use it to motivate causal sparsity. We show two applications of the proposed method: causal time series segmentation which selects time points capturing the incoming and outgoing causal flow between time points belonging to different signals, and causal bipartite graph recovery. We prove that modelling of causality in the adopted set-up only requires estimating the copula density of the data distribution and thus does not depend on its marginals. We evaluate the method on time resolved gene expression data.

Dinu Kaufmann, Sonali Parbhoo, Aleksander Wieczorek et al.

This paper considers a Bayesian view for estimating a sub-network in a Markov random field. The sub-network corresponds to the Markov blanket of a set of query variables, where the set of potential neighbours here is big. We factorize the posterior such that the Markov blanket is conditionally independent of the network of the potential neighbours. By exploiting this blockwise decoupling, we derive analytic expressions for posterior conditionals. Subsequently, we develop an inference scheme which makes use of the factorization. As a result, estimation of a sub-network is possible without inferring an entire network. Since the resulting Gibbs sampler scales linearly with the number of variables, it can handle relatively large neighbourhoods. The proposed scheme results in faster convergence and superior mixing of the Markov chain than existing Bayesian network estimation techniques.