arXiv subjects

Volker Roth

Publications and source records attributed to Volker Roth.

35 records · Page 2Linked to original sources

arXiv2019

On the Difference Between the Information Bottleneck and the Deep Information Bottleneck

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.

cs.LG↗

arXiv2019

Optimizing for Interpretability in Deep Neural Networks with Tree Regularization

Deep models have advanced prediction in many domains, but their lack of interpretability remains a key barrier to the adoption in many real world applications. There exists a large body of work aiming to help humans understand these black box functions to varying levels of granularity -- for example, through distillation, gradients, or adversarial examples. These methods however, all tackle interpretability as a separate process after training. In this work, we take a different approach and explicitly regularize deep models so that they are well-approximated by processes that humans can step-through in little time. Specifically, we train several families of deep neural networks to resemble compact, axis-aligned decision trees without significant compromises in accuracy. The resulting axis-aligned decision functions uniquely make tree regularized models easy for humans to interpret. Moreover, for situations in which a single, global tree is a poor estimator, we introduce a regional tree regularizer that encourages the deep model to resemble a compact, axis-aligned decision tree in predefined, human-interpretable contexts. Using intuitive toy examples as well as medical tasks for patients in critical care and with HIV, we demonstrate that this new family of tree regularizers yield models that are easier for humans to simulate than simpler L1 or L2 penalties without sacrificing predictive power.

cs.LG↗

arXiv2019

Greedy Structure Learning of Hierarchical Compositional Models

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.

cs.CV↗

arXiv2019

Tensor B-Spline Numerical Methods for PDEs: a High-Performance Alternative to FEM

Tensor B-spline methods are a high-performance alternative to solve partial differential equations (PDEs). This paper gives an overview on the principles of Tensor B-spline methodology, shows their use and analyzes their performance in application examples, and discusses its merits. Tensors preserve the dimensional structure of a discretized PDE, which makes it possible to develop highly efficient computational solvers. B-splines provide high-quality approximations, lead to a sparse structure of the system operator represented by shift-invariant separable kernels in the domain, and are mesh-free by construction. Further, high-order bases can easily be constructed from B-splines. In order to demonstrate the advantageous numerical performance of tensor B-spline methods, we studied the solution of a large-scale heat-equation problem (consisting of roughly 0.8 billion nodes!) on a heterogeneous workstation consisting of multi-core CPU and GPUs. Our experimental results nicely confirm the excellent numerical approximation properties of tensor B-splines, and their unique combination of high computational efficiency and low memory consumption, thereby showing huge improvements over standard finite-element methods (FEM).

math.NA↗

arXiv2018

Computational EEG in Personalized Medicine: A study in Parkinson's Disease

Recordings of electrical brain activity carry information about a person's cognitive health. For recording EEG signals, a very common setting is for a subject to be at rest with its eyes closed. Analysis of these recordings often involve a dimensionality reduction step in which electrodes are grouped into 10 or more regions (depending on the number of electrodes available). Then an average over each group is taken which serves as a feature in subsequent evaluation. Currently, the most prominent features used in clinical practice are based on spectral power densities. In our work we consider a simplified grouping of electrodes into two regions only. In addition to spectral features we introduce a secondary, non-redundant view on brain activity through the lens of Tsallis Entropy $S_{q=2}$. We further take EEG measurements not only in an eyes closed (ec) but also in an eyes open (eo) state. For our cohort of healthy controls (HC) and individuals suffering from Parkinson's disease (PD), the question we are asking is the following: How well can one discriminate between HC and PD within this simplified, binary grouping? This question is motivated by the commercial availability of inexpensive and easy to use portable EEG devices. If enough information is retained in this binary grouping, then such simple devices could potentially be used as personal monitoring tools, as standard screening tools by general practitioners or as digital biomarkers for easy long term monitoring during neurological studies.

q-bio.NC↗

arXiv2018

Informed MCMC with Bayesian Neural Networks for Facial Image Analysis

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.

cs.CV↗

arXiv2018

Estimating Causal Effects With Partial Covariates For Clinical Interpretability

Estimating the causal effects of an intervention in the presence of confounding is a frequently occurring problem in applications such as medicine. The task is challenging since there may be multiple confounding factors, some of which may be missing, and inferences must be made from high-dimensional, noisy measurements. In this paper, we propose a decision-theoretic approach to estimate the causal effects of interventions where a subset of the covariates is unavailable for some patients during testing. Our approach uses the information bottleneck principle to perform a discrete, low-dimensional sufficient reduction of the covariate data to estimate a distribution over confounders. In doing so, we can estimate the causal effect of an intervention where only partial covariate information is available. Our results on a causal inference benchmark and a real application for treating sepsis show that our method achieves state-of-the-art performance, without sacrificing interpretability.

stat.ME↗

arXiv2018

Learning Sparse Latent Representations with the Deep Copula Information Bottleneck

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.

stat.ML↗

arXiv2018

New Directions for Trust in the Certificate Authority Ecosystem

Many of the benefits we derive from the Internet require trust in the authenticity of HTTPS connections. Unfortunately, the public key certification ecosystem that underwrites this trust has failed us on numerous occasions. Towards an exploration of the root causes we present an update to the common knowledge about the Certificate Authority (CA) ecosystem. Based on our findings the certificate ecosystem currently undergoes a drastic transformation. Big steps towards ubiquitous encryption were made, however, on the expense of trust for authentication of communication partners. Furthermore we describe systemic problems rooted in misaligned incentives between players in the ecosystem. We depict that proposed security extensions do not correctly realign these incentives. As such we argue that it is worth considering alternative methods of authentication. As a first step in this direction we propose an insurance-based mechanism and we demonstrate that it is technically feasible.

cs.CR↗

arXiv2017

Beyond Sparsity: Tree Regularization of Deep Models for Interpretability

The lack of interpretability remains a key barrier to the adoption of deep models in many applications. In this work, we explicitly regularize deep models so human users might step through the process behind their predictions in little time. Specifically, we train deep time-series models so their class-probability predictions have high accuracy while being closely modeled by decision trees with few nodes. Using intuitive toy examples as well as medical tasks for treating sepsis and HIV, we demonstrate that this new tree regularization yields models that are easier for humans to simulate than simpler L1 or L2 penalties without sacrificing predictive power.

stat.ML↗

arXiv2016

Causal Compression

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.

stat.ML↗

arXiv2016

Towards Better Internet Citizenship: Reducing the Footprint of Internet-wide Scans by Topology Aware Prefix Selection

Internet service discovery is an emerging topic to study the deployment of protocols. Towards this end, our community periodically scans the entire advertised IPv4 address space. In this paper, we question this principle. Being good Internet citizens means that we should limit scan traffic to what is necessary. We conducted a study of scan data, which shows that several prefixes do not accommodate any host of interest and the network topology is fairly stable. We argue that this allows us to collect representative data by scanning less. In our paper, we explore the idea to scan all prefixes once and then identify prefixes of interest for future scanning. Based on our analysis of the censys.io data set (4.1 TB data encompassing 28 full IPv4 scans within 6 months) we found that we can reduce scan traffic between 25-90% and miss only 1-10% of the hosts, depending on desired trade-offs and protocols.

cs.NI↗

arXiv2015

Bayesian Markov Blanket Estimation

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.

stat.ML↗

arXiv2015

Probabilistic Clustering of Time-Evolving Distance Data

We present a novel probabilistic clustering model for objects that are represented via pairwise distances and observed at different time points. The proposed method utilizes the information given by adjacent time points to find the underlying cluster structure and obtain a smooth cluster evolution. This approach allows the number of objects and clusters to differ at every time point, and no identification on the identities of the objects is needed. Further, the model does not require the number of clusters being specified in advance -- they are instead determined automatically using a Dirichlet process prior. We validate our model on synthetic data showing that the proposed method is more accurate than state-of-the-art clustering methods. Finally, we use our dynamic clustering model to analyze and illustrate the evolution of brain cancer patients over time.

cs.LG↗

arXiv2013

A Secure Submission System for Online Whistleblowing Platforms

Whistleblower laws protect individuals who inform the public or an authority about governmental or corporate misconduct. Despite these laws, whistleblowers frequently risk reprisals and sites such as WikiLeaks emerged to provide a level of anonymity to these individuals. However, as countries increase their level of network surveillance and Internet protocol data retention, the mere act of using anonymizing software such as Tor, or accessing a whistleblowing website through an SSL channel might be incriminating enough to lead to investigations and repercussions. As an alternative submission system we propose an online advertising network called AdLeaks. AdLeaks leverages the ubiquity of unsolicited online advertising to provide complete sender unobservability when submitting disclosures. AdLeaks ads compute a random function in a browser and submit the outcome to the AdLeaks infrastructure. Such a whistleblower's browser replaces the output with encrypted information so that the transmission is indistinguishable from that of a regular browser. Its back-end design assures that AdLeaks must process only a fraction of the resulting traffic in order to receive disclosures with high probability. We describe the design of AdLeaks and evaluate its performance through analysis and experimentation.

cs.CR↗

arXiv2012

Copula Mixture Model for Dependency-seeking Clustering

We introduce a copula mixture model to perform dependency-seeking clustering when co-occurring samples from different data sources are available. The model takes advantage of the great flexibility offered by the copulas framework to extend mixtures of Canonical Correlation Analysis to multivariate data with arbitrary continuous marginal densities. We formulate our model as a non-parametric Bayesian mixture, while providing efficient MCMC inference. Experiments on synthetic and real data demonstrate that the increased flexibility of the copula mixture significantly improves the clustering and the interpretability of the results.

stat.ME↗

arXiv2012

A Complete Analysis of the l_1,p Group-Lasso

The Group-Lasso is a well-known tool for joint regularization in machine learning methods. While the l_{1,2} and the l_{1,\infty} version have been studied in detail and efficient algorithms exist, there are still open questions regarding other l_{1,p} variants. We characterize conditions for solutions of the l_{1,p} Group-Lasso for all p-norms with 1 <= p <= \infty, and we present a unified active set algorithm. For all p-norms, a highly efficient projected gradient algorithm is presented. This new algorithm enables us to compare the prediction performance of many variants of the Group-Lasso in a multi-task learning setting, where the aim is to solve many learning problems in parallel which are coupled via the Group-Lasso constraint. We conduct large-scale experiments on synthetic data and on two real-world data sets. In accordance with theoretical characterizations of the different norms we observe that the weak-coupling norms with p between 1.5 and 2 consistently outperform the strong-coupling norms with p >> 2.

cs.LG↗