Alexander Jung

Alexander Jung, Cezar Crăciunoiu, Nikolaos Karaolidis et al.

Specializing an OS to optimize the performance of a particular application is typically a manual process that requires great expertise. Specialization through configuration lends itself well to automation; however, it is challenging due to the sheer size of the configuration space of modern OSes, the difficulty to quantify that space, the long time it takes to evaluate a configuration, and the large number of invalid configurations. Hence, existing attempts at specializing OSes automatically are limited to switching features on and off to minimize memory consumption or attack surface, and cannot target metrics such as performance. We present Wayfinder, a framework specializing the configuration of OSes completely automatically and without expert knowledge. It can specialize all aspects of an OS configuration (compile-/boot-/run-time) towards any quantifiable performance, resource consumption, or security metric, for an application processing a given workload on a given hardware setup. Wayfinder consists of an automated OS benchmarking platform, and a neural network-based search algorithm driving the specialization process. This is achieved by learning on the fly which configuration parameters and values impact performance the most, and which ones lead to runtime failures. Optionally, a model pre-trained on one application can be reused to accelerate the specialization of related applications. We evaluate Wayfinder on two OSes, four applications, and two target metrics: Wayfinder fully automatically identifies specialized configurations with up to 24% application performance improvement and 8.5% memory usage reduction compared to default configurations. We highlight the benefits of our neural network, reaching good solutions faster than competing approaches (random and Bayesian), and successfully transferring knowledge between related applications.

Reza Mirzaeifard, Naveen K. D. Venkategowda, Alexander Jung et al.

This paper proposes a proximal variant of the alternating direction method of multipliers (ADMM) for distributed optimization. Although the current versions of ADMM algorithm provide promising numerical results in producing solutions that are close to optimal for many convex and non-convex optimization problems, it remains unclear if they can converge to a stationary point for weakly convex and locally non-smooth functions. Through our analysis using the Moreau envelope function, we demonstrate that MADM can indeed converge to a stationary point under mild conditions. Our analysis also includes computing the bounds on the amount of change in the dual variable update step by relating the gradient of the Moreau envelope function to the proximal function. Furthermore, the results of our numerical experiments indicate that our method is faster and more robust than widely-used approaches.

Ekkehard Schnoor, Jawher Said, Malik Tiomoko et al.

Concept Activation Vectors (CAVs) are a fundamental tool for concept-based explainability in deep learning, yet their practical utility is limited by statistical instability. We analyze the stochastic nature of CAVs and the Testing with CAVs (TCAV) method, deriving the distributions of major CAV classes including PatternCAV, FastCAV, and ridge regression-based CAVs. We then identify a fundamental flaw in the standard TCAV score: its reliance on a discontinuous indicator function induces non-decaying variance in critical regimes. To address this, we introduce $α$-TCAV, a generalized framework that replaces the indicator with a parameterized smooth function, yielding a unified probabilistic formulation that subsumes both TCAV and Multi-TCAV. We characterize the induced distributions of sensitivity scores and different TCAV variants, showing that established state-of-the-art choices lack theoretical justification. We provide principled guidance on tuning the parameter in $α$-TCAV -- either to imitate Multi-TCAV at substantially lower computational cost, or to obtain a calibrated Bayes-optimal probabilistic measure of a concept's influence. Finally, our analysis yields practical recommendations that challenge established routines: most notably, allocating the full sampling budget to a single CAV rather than splitting it across several.

Shamsiiat Abdurakhmanova, Amirhossein Mohammadi, Yasmin SarcheshmehPour et al.

Many important machine learning applications involve networks of devices-such as wearables or smartphones-that generate local data and train personalized models. A key challenge is determining which peers are most beneficial for collaboration. We propose a simple and privacy-preserving method to select relevant collaborators by evaluating how much a model improves after a single gradient step using another devices data-without sharing raw data. This method naturally extends to non-parametric models by replacing the gradient step with a non-parametric generalization. Our approach enables model-agnostic, data-driven peer selection for personalized federated learning (PersFL).

Salma Rachidi, Aso Bozorgpanah, Eric Fey et al.

Machine learning (ML) promises better clinical decision-making, yet opaque model behavior limits the adoption in healthcare. We propose two novel regularization techniques for ensuring the interpretability of ML models trained on real-world data. In particular, we consider the prediction of five-year survival for multiple myeloma patients using clinical data from Helsinki University Hospital. To ensure the interpretability of the trained models, we use two alternative constructions for a penalty term used for regularization. The first one penalizes deviations from the predictions obtained from an interpretable logistic regression method with two manually chosen features. The second construction requires consistency of model predictions with the revised international staging system (R-ISS). We verify the usefulness of the proposed regularization techniques in numerical experiments using data from 812 patients. They achieve an accuracy up to 0.721 on a test set and SHAP values show that the models rely on the selected important features.

Timo Saala, Lucie Flek, Alexander Jung et al.

Correlations between input parameters play a crucial role in many scientific classification tasks, since these are often related to fundamental laws of nature. For example, in high energy physics, one of the common deep learning use-cases is the classification of signal and background processes in particle collisions. In many such cases, the fundamental principles of the correlations between observables are often better understood than the actual distributions of the observables themselves. In this work, we present a new adversarial attack algorithm called Random Distribution Shuffle Attack (RDSA), emphasizing the correlations between observables in the network rather than individual feature characteristics. Correct application of the proposed novel attack can result in a significant improvement in classification performance - particularly in the context of data augmentation - when using the generated adversaries within adversarial training. Given that correlations between input features are also crucial in many other disciplines. We demonstrate the RDSA effectiveness on six classification tasks, including two particle collision challenges (using CERN Open Data), hand-written digit recognition (MNIST784), human activity recognition (HAR), weather forecasting (Rain in Australia), and ICU patient mortality (MIMIC-IV), demonstrating a general use case beyond fundamental physics for this new type of adversarial attack algorithms.

Diana Pfau, Alexander Jung

AI systems increasingly shape critical decisions across personal and societal domains. While empirical risk minimization (ERM) drives much of the AI success, it typically prioritizes accuracy over trustworthiness, often resulting in biases, opacity, and other adverse effects. This paper discusses how key requirements for trustworthy AI can be translated into design choices for the components of ERM. We hope to provide actionable guidance for building AI systems that meet emerging standards for trustworthiness of AI.

Pasi Pyrrö, Hassan Naseri, Alexander Jung

The visual inspection of aerial drone footage is an integral part of land search and rescue (SAR) operations today. Since this inspection is a slow, tedious and error-prone job for humans, we propose a novel deep learning algorithm to automate this aerial person detection (APD) task. We experiment with model architecture selection, online data augmentation, transfer learning, image tiling and several other techniques to improve the test performance of our method. We present the novel Aerial Inspection RetinaNet (AIR) algorithm as the combination of these contributions. The AIR detector demonstrates state-of-the-art performance on a commonly used SAR test data set in terms of both precision (~21 percentage point increase) and speed. In addition, we provide a new formal definition for the APD problem in SAR missions. That is, we propose a novel evaluation scheme that ranks detectors in terms of real-world SAR localization requirements. Finally, we propose a novel postprocessing method for robust, approximate object localization: the merging of overlapping bounding boxes (MOB) algorithm. This final processing stage used in the AIR detector significantly improves its performance and usability in the face of real-world aerial SAR missions.

Yasmin SarcheshmehPour, Yu Tian, Linli Zhang et al.

We study optimization methods to train local (or personalized) models for decentralized collections of local datasets with an intrinsic network structure. This network structure arises from domain-specific notions of similarity between local datasets. Examples for such notions include spatio-temporal proximity, statistical dependencies or functional relations. Our main conceptual contribution is to formulate federated learning as generalized total variation (GTV) minimization. This formulation unifies and considerably extends existing federated learning methods. It is highly flexible and can be combined with a broad range of parametric models, including generalized linear models or deep neural networks. Our main algorithmic contribution is a fully decentralized federated learning algorithm. This algorithm is obtained by applying an established primal-dual method to solve GTV minimization. It can be implemented as message passing and is robust against inexact computations that arise from limited computational resources including processing time or bandwidth. Our main analytic contribution is an upper bound on the deviation between the local model parameters learnt by our algorithm and an oracle-based clustered federated learning method. This upper bound reveals conditions on the local models and the network structure of local datasets such that GTV minimization is able to pool (nearly) homogeneous local datasets.

Alexander Jung, Yasmin SarcheshmehPour

We study the statistical and computational properties of a network Lasso method for local graph clustering. The clusters delivered by nLasso can be characterized elegantly via network flows between cluster boundary and seed nodes. While spectral clustering methods are guided by a minimization of the graph Laplacian quadratic form, nLasso minimizes the total variation of cluster indicator signals. As demonstrated theoretically and numerically, nLasso methods can handle very sparse clusters (chain-like) which are difficult for spectral clustering. We also verify that a primal-dual method for nonsmooth optimization allows to approximate nLasso solutions with optimal worst-case convergence rate.

Alexander Jung, Pedro H. J. Nardelli

Automated decision making is used routinely throughout our everyday life. Recommender systems decide which jobs, movies, or other user profiles might be interesting to us. Spell checkers help us to make good use of language. Fraud detection systems decide if a credit card transactions should be verified more closely. Many of these decision making systems use machine learning methods that fit complex models to massive datasets. The successful deployment of machine learning (ML) methods to many (critical) application domains crucially depends on its explainability. Indeed, humans have a strong desire to get explanations that resolve the uncertainty about experienced phenomena like the predictions and decisions obtained from ML methods. Explainable ML is challenging since explanations must be tailored (personalized) to individual users with varying backgrounds. Some users might have received university-level education in ML, while other users might have no formal training in linear algebra. Linear regression with few features might be perfectly interpretable for the first group but might be considered a black-box by the latter. We propose a simple probabilistic model for the predictions and user knowledge. This model allows to study explainable ML using information theory. Explaining is here considered as the task of reducing the "surprise" incurred by a prediction. We quantify the effect of an explanation by the conditional mutual information between the explanation and prediction, given the user background.

Alexander Jung, Ivan Baranov

Clustering methods group a set of data points into a few coherent groups or clusters of similar data points. As an example, consider clustering pixels in an image (or video) if they belong to the same object. Different clustering methods are obtained by using different notions of similarity and different representations of data points.

Alexander Jung

A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges within a cluster and between different clusters. We assume that the cluster assignments are known for at least one data point in each cluster. In such a partially labeled stochastic block model, clustering amounts to estimating the cluster assignments of the remaining data points. We study total variation minimization as a method for this clustering task. We implement the resulting clustering algorithm as a highly scalable message-passing protocol. We also provide a condition on the model parameters such that total variation minimization allows for accurate clustering.

Alexander Jung

Many machine learning problems and methods are combinations of three components: data, hypothesis space and loss function. Different machine learning methods are obtained as combinations of different choices for the representation of data, hypothesis space and loss function. After reviewing the mathematical structure of these three components, we discuss intrinsic trade-offs between statistical and computational properties of machine learning methods.

Alexander Jung

Many applications generate data with an intrinsic network structure such as time series data, image data or social network data. The network Lasso (nLasso) has been proposed recently as a method for joint clustering and optimization of machine learning models for networked data. The nLasso extends the Lasso from sparse linear models to clustered graph signals. This paper explores the duality of nLasso and network flow optimization. We show that, in a very precise sense, nLasso is equivalent to a minimum-cost flow problem on the data network structure. Our main technical result is a concise characterization of nLasso solutions via existence of certain network flows. The main conceptual result is a useful link between nLasso methods and basic graph algorithms such as clustering or maximum flow.

Roope Tervo, Joonas Karjalainen, Alexander Jung

Prediction of power outages caused by convective storms which are highly localised in space and time is of crucial importance to power grid operators. We propose a new machine learning approach to predict the damage caused by storms. This approach hinges identifying and tracking of storm cells using weather radar images on the application of machine learning techniques. Overall prediction process consists of identifying storm cells from CAPPI weather radar images by contouring them with a solid 35 dBZ threshold, predicting a track of storm cells and classifying them based on their damage potential to power grid operators. Tracked storm cells are then classified by combining data obtained from weather radar, ground weather observations and lightning detectors. We compare random forest classifiers and deep neural networks as alternative methods to classify storm cells. The main challenge is that the training data are heavily imbalanced as extreme weather events are rare.

Alexander Jung

We propose networked exponential families to jointly leverage the information in the topology as well as the attributes (features) of networked data points. Networked exponential families are a flexible probabilistic model for heterogeneous datasets with intrinsic network structure. These models can be learnt efficiently using network Lasso which implicitly pools or clusters the data points according to the intrinsic network structure and the local likelihood. The resulting method can be formulated as a non-smooth convex optimization problem which we solve using a primal-dual splitting method. This primal-dual method is appealing for big data applications as it can be implemented as a highly scalable message passing algorithm.

Alexander Jung, Nguyen Tran

The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from learning sparse (generalized) linear models to network models. Efficient implementations of the nLasso have been obtained using convex optimization methods lending to scalable message passing protocols. In this paper, we analyze the statistical properties of nLasso when applied to localized linear regression problems involving networked data. Our main result is a sufficient condition on the network structure and available label information such that nLasso accurately learns a localized linear regression model from a few labeled data points. We also provide an implementation of nLasso for localized linear regression by specializing a primaldual method for solving the convex (non-smooth) nLasso problem.

Nguyen Tran, Henrik Ambos, Alexander Jung

We apply the network Lasso to classify partially labeled data points which are characterized by high-dimensional feature vectors. In order to learn an accurate classifier from limited amounts of labeled data, we borrow statistical strength, via an intrinsic network structure, across the dataset. The resulting logistic network Lasso amounts to a regularized empirical risk minimization problem using the total variation of a classifier as a regularizer. This minimization problem is a non-smooth convex optimization problem which we solve using a primal-dual splitting method. This method is appealing for big data applications as it can be implemented as a highly scalable message passing algorithm.

Alexander Jung, Alfred O. Hero, Alexandru Mara et al.

We propose and analyze a method for semi-supervised learning from partially-labeled network-structured data. Our approach is based on a graph signal recovery interpretation under a clustering hypothesis that labels of data points belonging to the same well-connected subset (cluster) are similar valued. This lends naturally to learning the labels by total variation (TV) minimization, which we solve by applying a recently proposed primal-dual method for non-smooth convex optimization. The resulting algorithm allows for a highly scalable implementation using message passing over the underlying empirical graph, which renders the algorithm suitable for big data applications. By applying tools of compressed sensing, we derive a sufficient condition on the underlying network structure such that TV minimization recovers clusters in the empirical graph of the data. In particular, we show that the proposed primal-dual method amounts to maximizing network flows over the empirical graph of the dataset. Moreover, the learning accuracy of the proposed algorithm is linked to the set of network flows between data points having known labels. The effectiveness and scalability of our approach is verified by numerical experiments.

Markku Hinkka, Teemu Lehto, Keijo Heljanko et al.

Process Mining consists of techniques where logs created by operative systems are transformed into process models. In process mining tools it is often desired to be able to classify ongoing process instances, e.g., to predict how long the process will still require to complete, or to classify process instances to different classes based only on the activities that have occurred in the process instance thus far. Recurrent neural networks and its subclasses, such as Gated Recurrent Unit (GRU) and Long Short-Term Memory (LSTM), have been demonstrated to be able to learn relevant temporal features for subsequent classification tasks. In this paper we apply recurrent neural networks to classifying process instances. The proposed model is trained in a supervised fashion using labeled process instances extracted from event log traces. This is the first time we know of GRU having been used in classifying business process instances. Our main experimental results shows that GRU outperforms LSTM remarkably in training time while giving almost identical accuracies to LSTM models. Additional contributions of our paper are improving the classification model training time by filtering infrequent activities, which is a technique commonly used, e.g., in Natural Language Processing (NLP).

Roope Tervo, Joonas Karjalainen, Alexander Jung

We consider the problem of predicting power outages in an electrical power grid due to hazards produced by convective storms. These storms produce extreme weather phenomena such as intense wind, tornadoes and lightning over a small area. In this paper, we discuss the application of state-of-the-art machine learning techniques, such as random forest classifiers and deep neural networks, to predict the amount of damage caused by storms. We cast this application as a classification problem where the goal is to classify storm cells into a finite number of classes, each corresponding to a certain amount of expected damage. The classification method use as input features estimates for storm cell location and movement which has to be extracted from the raw data. A main challenge of this application is that the training data is heavily imbalanced as the occurrence of extreme weather events is rare. In order to address this issue, we applied SMOTE technique.

Oleksii Abramenko, Alexander Jung

We formulate the problem of sampling and recovering clustered graph signal as a multi-armed bandit (MAB) problem. This formulation lends naturally to learning sampling strategies using the well-known gradient MAB algorithm. In particular, the sampling strategy is represented as a probability distribution over the individual arms of the MAB and optimized using gradient ascent. Some illustrative numerical experiments indicate that the sampling strategies based on the gradient MAB algorithm outperform existing sampling methods.

Alexander Jung

Machine learning (ML) has become a commodity in our every-day lives. We routinely ask ML empowered smartphones to suggest lovely food places or to guide us through a strange place. ML methods have also become standard tools in many fields of science and engineering. A plethora of ML applications transform human lives at unprecedented pace and scale. This book portrays ML as the combination of three basic components: data, model and loss. ML methods combine these three components within computationally efficient implementations of the basic scientific principle "trial and error". This principle consists of the continuous adaptation of a hypothesis about a phenomenon that generates data. ML methods use a hypothesis to compute predictions for future events. We believe that thinking about ML as combinations of three components given by data, model, and loss helps to navigate the steadily growing offer for ready-to-use ML methods. Our three-component picture of ML allows a unified treatment of a wide range of concepts and techniques which seem quite unrelated at first sight. The regularization effect of early stopping in iterative methods is due to the shrinking of the effective hypothesis space. Privacy-preserving ML is obtained by particular choices for the features of data points. Explainable ML methods are characterized by particular choices for the hypothesis space. To make good use of ML tools it is instrumental to understand its underlying principles at different levels of detail. On a lower level, this tutorial helps ML engineers to choose suitable methods for the application at hand. The book also offers a higher-level view on the implementation of ML methods which is typically required to manage a team of ML engineers and data scientists.

Henrik Ambos, Nguyen Tran, Alexander Jung

We apply the network Lasso to solve binary classification and clustering problems for network-structured data. To this end, we generalize ordinary logistic regression to non-Euclidean data with an intrinsic network structure. The resulting "logistic network Lasso" amounts to solving a non-smooth convex regularized empirical risk minimization. The risk is measured using the logistic loss incurred over a small set of labeled nodes. For the regularization, we propose to use the total variation of the classifier requiring it to conform to the underlying network structure. A scalable implementation of the learning method is obtained using an inexact variant of the alternating direction methods of multipliers which results in a scalable learning algorithm

Alexander Jung

This paper investigates the computational complexity of sparse label propagation which has been proposed recently for processing network structured data. Sparse label propagation amounts to a convex optimization problem and might be considered as an extension of basis pursuit from sparse vectors to network structured datasets. Using a standard first-order oracle model, we characterize the number of iterations for sparse label propagation to achieve a prescribed accuracy. In particular, we derive an upper bound on the number of iterations required to achieve a certain accuracy and show that this upper bound is sharp for datasets having a chain structure (e.g., time series).

Buse Gul Atli, Alexander Jung

Many current approaches to the design of intrusion detection systems apply feature selection in a static, non-adaptive fashion. These methods often neglect the dynamic nature of network data which requires to use adaptive feature selection techniques. In this paper, we present a simple technique based on incremental learning of support vector machines in order to rank the features in real time within a streaming model for network data. Some illustrative numerical experiments with two popular benchmark datasets show that our approach allows to adapt to the changes in normal network behaviour and novel attack patterns which have not been experienced before.

Nguyen Tran, Saeed Basirian, Alexander Jung

A recently proposed learning algorithm for massive network-structured data sets (big data over networks) is the network Lasso (nLasso), which extends the well- known Lasso estimator from sparse models to network-structured datasets. Efficient implementations of the nLasso have been presented using modern convex optimization methods. In this paper, we provide sufficient conditions on the network structure and available label information such that nLasso accurately learns a vector-valued graph signal (representing label information) from the information provided by the labels of a few data points.

Markku Hinkka, Teemu Lehto, Keijo Heljanko et al.

We consider the problem of classifying business process instances based on structural features derived from event logs. The main motivation is to provide machine learning based techniques with quick response times for interactive computer assisted root cause analysis. In particular, we create structural features from process mining such as activity and transition occurrence counts, and ordering of activities to be evaluated as potential features for classification. We show that adding such structural features increases the amount of information thus potentially increasing classification accuracy. However, there is an inherent trade-off as using too many features leads to too long run-times for machine learning classification models. One way to improve the machine learning algorithms' run-time is to only select a small number of features by a feature selection algorithm. However, the run-time required by the feature selection algorithm must also be taken into account. Also, the classification accuracy should not suffer too much from the feature selection. The main contributions of this paper are as follows: First, we propose and compare six different feature selection algorithms by means of an experimental setup comparing their classification accuracy and achievable response times. Second, we discuss the potential use of feature selection results for computer assisted root cause analysis as well as the properties of different types of structural features in the context of feature selection.

Alexandru Mara, Alexander Jung

The network Lasso is a recently proposed convex optimization method for machine learning from massive network structured datasets, i.e., big data over networks. It is a variant of the well-known least absolute shrinkage and selection operator (Lasso), which is underlying many methods in learning and signal processing involving sparse models. Highly scalable implementations of the network Lasso can be obtained by state-of-the art proximal methods, e.g., the alternating direction method of multipliers (ADMM). By generalizing the concept of the compatibility condition put forward by van de Geer and Buehlmann as a powerful tool for the analysis of plain Lasso, we derive a sufficient condition, i.e., the network compatibility condition, on the underlying network topology such that network Lasso accurately learns a clustered underlying graph signal. This network compatibility condition relates the location of the sampled nodes with the clustering structure of the network. In particular, the NCC informs the choice of which nodes to sample, or in machine learning terms, which data points provide most information if labeled.

Alexander Jung

Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in machine learning for massive data sets (big data). In particular, stochastic gradient methods are considered the de- facto standard for training deep neural networks. Studying gradient methods within the realm of fixed-point theory provides us with powerful tools to analyze their convergence properties. In particular, gradient methods using inexact or noisy gradients, such as stochastic gradient descent, can be studied conveniently using well-known results on inexact fixed-point iterations. Moreover, as we demonstrate in this paper, the fixed-point approach allows an elegant derivation of accelerations for basic gradient methods. In particular, we will show how gradient descent can be accelerated by a fixed-point preserving transformation of an operator associated with the objective function.

Alexander Jung, Madelon Hulsebos

We present a novel condition, which we term the net- work nullspace property, which ensures accurate recovery of graph signals representing massive network-structured datasets from few signal values. The network nullspace property couples the cluster structure of the underlying network-structure with the geometry of the sampling set. Our results can be used to design efficient sampling strategies based on the network topology.

Saeed Basirian, Alexander Jung

It has been shown recently that graph signals with small total variation can be accurately recovered from only few samples if the sampling set satisfies a certain condition, referred to as the network nullspace property. Based on this recovery condition, we propose a sampling strategy for smooth graph signals based on random walks. Numerical experiments demonstrate the effectiveness of this approach for graph signals obtained from a synthetic random graph model as well as a real-world dataset.

Alexander Jung, Nguyen Tran Quang, Alexandru Mara

The "least absolute shrinkage and selection operator" (Lasso) method has been adapted recently for networkstructured datasets. In particular, this network Lasso method allows to learn graph signals from a small number of noisy signal samples by using the total variation of a graph signal for regularization. While efficient and scalable implementations of the network Lasso are available, only little is known about the conditions on the underlying network structure which ensure network Lasso to be accurate. By leveraging concepts of compressed sensing, we address this gap and derive precise conditions on the underlying network topology and sampling set which guarantee the network Lasso for a particular loss function to deliver an accurate estimate of the entire underlying graph signal. We also quantify the error incurred by network Lasso in terms of two constants which reflect the connectivity of the sampled nodes.

Nguyen Q. Tran, Oleksii Abramenko, Alexander Jung

We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different covariance matrices. This model contains as special cases the standard setting of i.i.d. samples as well as the case of samples forming a stationary or underspread (non-stationary) processes. More generally, our model applies to any process model for which an efficient decorrelation can be obtained. By analyzing a particular model selection method, we derive a sufficient condition on the required sample size for accurate graphical model selection based on non-stationary data.

Alexander Jung, Alfred O. Hero, Alexandru Mara et al.

This work proposes a novel method for semi-supervised learning from partially labeled massive network-structured datasets, i.e., big data over networks. We model the underlying hypothesis, which relates data points to labels, as a graph signal, defined over some graph (network) structure intrinsic to the dataset. Following the key principle of supervised learning, i.e., similar inputs yield similar outputs, we require the graph signals induced by labels to have small total variation. Accordingly, we formulate the problem of learning the labels of data points as a non-smooth convex optimization problem which amounts to balancing between the empirical loss, i.e., the discrepancy with some partially available label information, and the smoothness quantified by the total variation of the learned graph signal. We solve this optimization problem by appealing to a recently proposed preconditioned variant of the popular primal-dual method by Pock and Chambolle, which results in a sparse label propagation algorithm. This learning algorithm allows for a highly scalable implementation as message passing over the underlying data graph. By applying concepts of compressed sensing to the learning problem, we are also able to provide a transparent sufficient condition on the underlying network structure such that accurate learning of the labels is possible. We also present an implementation of the message passing formulation allows for a highly scalable implementation in big data frameworks.

Alexander Jung, Alfred O. Hero, Alexandru Mara et al.

We propose a scalable method for semi-supervised (transductive) learning from massive network-structured datasets. Our approach to semi-supervised learning is based on representing the underlying hypothesis as a graph signal with small total variation. Requiring a small total variation of the graph signal representing the underlying hypothesis corresponds to the central smoothness assumption that forms the basis for semi-supervised learning, i.e., input points forming clusters have similar output values or labels. We formulate the learning problem as a nonsmooth convex optimization problem which we solve by appealing to Nesterovs optimal first-order method for nonsmooth optimization. We also provide a message passing formulation of the learning method which allows for a highly scalable implementation in big data frameworks.

Nguyen Tran Quang, Alexander Jung

We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process samples are assumed uncorrelated over time and having a time-varying marginal distribution. The selection method is based on testing conditional variances obtained for small subsets of process components. This allows to cope with the high-dimensional regime, where the sample size can be (drastically) smaller than the process dimension. We characterize the required sample size such that the proposed selection method is successful with high probability.

Alexander Jung, Yonina C. Eldar, Norbert Görtz

We consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common underlying dictionary. In particular, we derive lower bounds on the minimum achievable worst case mean squared error (MSE), regardless of computational complexity of the dictionary learning (DL) schemes. By casting DL as a classical (or frequentist) estimation problem, the lower bounds on the worst case MSE are derived by following an established information-theoretic approach to minimax estimation. The main conceptual contribution of this paper is the adaption of the information-theoretic approach to minimax estimation for the DL problem in order to derive lower bounds on the worst case MSE of any DL scheme. We derive three different lower bounds applying to different generative models for the observed signals. The first bound applies to a wide range of models, it only requires the existence of a covariance matrix of the (unknown) underlying coefficient vector. By specializing this bound to the case of sparse coefficient distributions, and assuming the true dictionary satisfies the restricted isometry property, we obtain a lower bound on the worst case MSE of DL schemes in terms of a signal to noise ratio (SNR). The third bound applies to a more restrictive subclass of coefficient distributions by requiring the non-zero coefficients to be Gaussian. While, compared with the previous two bounds, the applicability of this final bound is the most limited it is the tightest of the three bounds in the low SNR regime.

Alexander Jung, Gabor Hannak, Norbert Görtz

We propose a novel graphical model selection (GMS) scheme for high-dimensional stationary time series or discrete time process. The method is based on a natural generalization of the graphical LASSO (gLASSO), introduced originally for GMS based on i.i.d. samples, and estimates the conditional independence graph (CIG) of a time series from a finite length observation. The gLASSO for time series is defined as the solution of an l1-regularized maximum (approximate) likelihood problem. We solve this optimization problem using the alternating direction method of multipliers (ADMM). Our approach is nonparametric as we do not assume a finite dimensional (e.g., an autoregressive) parametric model for the observed process. Instead, we require the process to be sufficiently smooth in the spectral domain. For Gaussian processes, we characterize the performance of our method theoretically by deriving an upper bound on the probability that our algorithm fails to correctly identify the CIG. Numerical experiments demonstrate the ability of our method to recover the correct CIG from a limited amount of samples.

Alexander Jung

We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a parametric process model (such as, e.g., an autoregressive model) for the observed random process. Instead, we only require certain smoothness properties (in the Fourier domain) of the process. The proposed inference scheme works even for sample sizes much smaller than the number of scalar process components if the true underlying CIG is sufficiently sparse. A theoretical performance analysis provides conditions which guarantee that the probability of the proposed inference method to deliver a wrong CIG is below a prescribed value. These conditions imply lower bounds on the sample size such that the new method is consistent asymptotically. Some numerical experiments validate our theoretical performance analysis and demonstrate superior performance of our scheme compared to an existing (parametric) approach in case of model mismatch.

Alexander Jung, Yonina C. Eldar, Norbert Görtz

We consider the problem of dictionary learning under the assumption that the observed signals can be represented as sparse linear combinations of the columns of a single large dictionary matrix. In particular, we analyze the minimax risk of the dictionary learning problem which governs the mean squared error (MSE) performance of any learning scheme, regardless of its computational complexity. By following an established information-theoretic method based on Fanos inequality, we derive a lower bound on the minimax risk for a given dictionary learning problem. This lower bound yields a characterization of the sample-complexity, i.e., a lower bound on the required number of observations such that consistent dictionary learning schemes exist. Our bounds may be compared with the performance of a given learning scheme, allowing to characterize how far the method is from optimal performance.

Alexander Jung, Reinhard Heckel, Helmut Bölcskei et al.

We propose a method for inferring the conditional indepen- dence graph (CIG) of a high-dimensional discrete-time Gaus- sian vector random process from finite-length observations. Our approach does not rely on a parametric model (such as, e.g., an autoregressive model) for the vector random process; rather, it only assumes certain spectral smoothness proper- ties. The proposed inference scheme is compressive in that it works for sample sizes that are (much) smaller than the number of scalar process components. We provide analytical conditions for our method to correctly identify the CIG with high probability.