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Digital product passports (DPPs) are an emerging technology and are considered as enablers of sustainable and circular value chains as they support sustainable product management (SPM) by gathering and containing product life cycle data. However, some life cycle data are considered sensitive by stakeholders, resulting in a reluctance to share such data. This contribution provides a concept illustrating how data science and machine learning approaches enable electric vehicle battery (EVB) value chain stakeholders to carry out confidentiality-preserving data exchange via a DPP. This, in turn, can support overcoming data sharing reluctances, consequently facilitating sustainability data management on a DPP for an EVB. The concept development comprised a literature review to identify data needs for sustainable EVB management, data management challenges, and potential data science approaches for data management support. Furthermore, three explorative focus group workshops and follow-up consultations with data scientists were conducted to discuss identified data sciences approaches. This work complements the emerging literature on digitalization and SPM by exploring the specific potential of data science, and machine learning approaches enabling sustainability data management and reducing data sharing reluctance. Furthermore, practical relevance is given, as this concept may provide practitioners with new impulses regarding DPP development and implementation. Version of record

The information-theoretic framework promises to explain the predictive power of neural networks. In particular, the information plane analysis, which measures mutual information (MI) between input and representation as well as representation and output, should give rich insights into the training process. This approach, however, was shown to strongly depend on the choice of estimator of the MI. The problem is amplified for deterministic networks if the MI between input and representation is infinite. Thus, the estimated values are defined by the different approaches for estimation, but do not adequately represent the training process from an information-theoretic perspective. In this work, we show that dropout with continuously distributed noise ensures that MI is finite. We demonstrate in a range of experiments that this enables a meaningful information plane analysis for a class of dropout neural networks that is widely used in practice., Comment: Published as a conference paper at ICLR2023

Learning invariant representations that remain useful for a downstream task is still a key challenge in machine learning. We investigate a set of related information funnels and bottleneck problems that claim to learn invariant representations from the data. We also propose a new element to this family of information-theoretic objectives: The Conditional Privacy Funnel with Side Information, which we investigate in fully and semi-supervised settings. Given the generally intractable objectives, we derive tractable approximations using amortized variational inference parameterized by neural networks and study the intrinsic trade-offs of these objectives. We describe empirically the proposed approach and show that with a few labels it is possible to learn fair classifiers and generate useful representations approximately invariant to unwanted sources of variation. Furthermore, we provide insights about the applicability of these methods in real-world scenarios with ordinary tabular datasets when the data is scarce., 28 pages

In this paper, we frame homogeneous-feature multi-task learning (MTL) as a hierarchical representation learning problem, with one task-agnostic and multiple task-specific latent representations. Drawing inspiration from the information bottleneck principle and assuming an additive independent noise model between the task-agnostic and task-specific latent representations, we limit the information contained in each task-specific representation. It is shown that our resulting representations yield competitive performance for several MTL benchmarks. Furthermore, for certain setups, we show that the trained parameters of the additive noise model are closely related to the similarity of different tasks. This indicates that our approach yields a task-agnostic representation that is disentangled in the sense that its individual dimensions may be interpretable from a task-specific perspective., Accepted by the 2022 International Joint Conference on Neural Networks (IJCNN 2022)

This paper empirically studies commonly observed training difficulties of Physics-Informed Neural Networks (PINNs) on dynamical systems. Our results indicate that fixed points which are inherent to these systems play a key role in the optimization of the in PINNs embedded physics loss function. We observe that the loss landscape exhibits local optima that are shaped by the presence of fixed points. We find that these local optima contribute to the complexity of the physics loss optimization which can explain common training difficulties and resulting nonphysical predictions. Under certain settings, e.g., initial conditions close to fixed points or long simulations times, we show that those optima can even become better than that of the desired solution., 22 pages

We survey information-theoretic approaches to the reduction of Markov chains. Our survey is structured in two parts: The first part considers Markov chain coarse graining, which focuses on projecting the Markov chain to a process on a smaller state space that is informative}about certain quantities of interest. The second part considers Markov chain model reduction, which focuses on replacing the original Markov model by a simplified one that yields similar behavior as the original Markov model. We discuss the practical relevance of both approaches in the field of knowledge discovery and data mining by formulating problems of unsupervised machine learning as reduction problems of Markov chains. Finally, we briefly discuss the concept of lumpability, the phenomenon when a coarse graining yields a reduced Markov model., Comment: 16 pages, 3 figures; survey paper

Recently a new type of deep learning method has emerged, called physics-informed neural networks. Despite their success in solving problems that are governed by partial differential equations, physics-informed neural networks are often difficult to train. Frequently reported convergence issues are still poorly understood and complicate the inference of correct system dynamics. In this paper, we shed light on the training process of physics-informed neural networks. By trading between data- and physics-based constraints in the network training, we study the Pareto front in multi-objective optimization problems. We use the diffusion equation and Navier-Stokes equations in various test environments to analyze the effects of system parameters on the shape of the Pareto front. Additionally, we assess the effectiveness of state-of-the-art adaptive activation functions and adaptive loss weighting methods. Our results demonstrate the prominent role of system parameters in the multi-objective optimization and contribute to understanding convergence properties of physics-informed neural networks., 17 pages, 11 figures

Drive towards improved performance of machine learning models has led to the creation of complex features representing a database of condensed matter systems. The complex features, however, do not offer an intuitive explanation on which physical attributes do improve the performance. The effect of the database on the performance of the trained model is often neglected. In this work we seek to understand in depth the effect that the choice of features and the properties of the database have on a machine learning application. In our experiments, we consider the complex phase space of carbon as a test case, for which we use a set of simple, human understandable and cheaply computable features for the aim of predicting the total energy of the crystal structure. Our study shows that (i) the performance of the machine learning model varies depending on the set of features and the database, (ii) is not transferable to every structure in the phase space and (iii) depends on how well structures are represented in the database., 18 pages, 11 figures

Centrality measures derived from character networks can be used to detect the main characters in a play. For example, previous research has shown that characters with high network centrality typically perform the majority of speech acts and appear in most of the scenes. However, one can extract character networks from plays in various ways. Close reading may omit minor characters like attendants or servants, while distant reading (e.g., parsing an XML file) may include aggregate characters like "All", "Both Lords", or similar. Furthermore, the networks may display either implicit or explicit connections, depending on whether we connect characters because they appear in the same scene or because they are directly addressing each other, respectively. Thus, as adding more characters or connections to the network affects centralities and other network measures, the interpretation of both qualitative and quantitative aspects of character networks depends on the extraction method. In this work we are concerned with the specific question whether details of the textual source and the extraction method, such as adding minor or aggregate characters, make main characters less "central". Answering this question will allow us to better assess the validity of automated literary network analysis.

Distance-based classification is among the most competitive classification methods for time series data. The most critical component of distance-based classification is the selected distance function. Past research has proposed various different distance metrics or measures dedicated to particular aspects of real-world time series data, yet there is an important aspect that has not been considered so far: Robustness against arbitrary data contamination. In this work, we propose a novel distance metric that is robust against arbitrarily "bad" contamination and has a worst-case computational complexity of $\mathcal{O}(n\log n)$. We formally argue why our proposed metric is robust, and demonstrate in an empirical evaluation that the metric yields competitive classification accuracy when applied in k-Nearest Neighbor time series classification., MileTS Workshop at KDD'19

This paper presents a hybrid model for the prediction of magnetostriction in power transformers by leveraging the strengths of a data-driven approach and a physics-based model. Specifically, a non-linear physics-based model for magnetostriction as a function of the magnetic field is employed, the parameters of which are estimated as linear combinations of electrical coil measurements and coil dimensions. The model is validated in a practical scenario with coil data from two different suppliers, showing that the proposed approach captures the different magnetostrictive properties of the two suppliers and provides an estimation of magnetostriction in agreement with the measurement system in place. It is argued that the combination of a non-linear physics-based model with few parameters and a linear data-driven model to estimate these parameters is attractive both in terms of model accuracy and because it allows training the data-driven part with comparably small datasets.

We propose a semi-supervised generative model, SeGMA, which learns a joint probability distribution of data and their classes and which is implemented in a typical Wasserstein auto-encoder framework. We choose a mixture of Gaussians as a target distribution in latent space, which provides a natural splitting of data into clusters. To connect Gaussian components with correct classes, we use a small amount of labeled data and a Gaussian classifier induced by the target distribution. SeGMA is optimized efficiently due to the use of Cramer-Wold distance as a maximum mean discrepancy penalty, which yields a closed-form expression for a mixture of spherical Gaussian components and thus obviates the need of sampling. While SeGMA preserves all properties of its semi-supervised predecessors and achieves at least as good generative performance on standard benchmark data sets, it presents additional features: (a) interpolation between any pair of points in the latent space produces realistically-looking samples; (b) combining the interpolation property with disentangled class and style variables, SeGMA is able to perform a continuous style transfer from one class to another; (c) it is possible to change the intensity of class characteristics in a data point by moving the latent representation of the data point away from specific Gaussian components.

The development of automated tools for data analysis is a growing need in semiconductor manufacturing. For this purpose, especially wafer test data carry a high potential as they allow the expert to draw conclusions on both product performance, as well as production process deviations. The latter are assumed to be identifiable by spatial patterns on wafermaps. The target of this work is to propose a system that judges the similarities between wafermaps regarding the depicted process pattern in an automated way. For this purpose, we propose a similarity measure to perform a pairwise comparison of wafermaps based on extracted, high-dimensional features.

International Zurich Seminar on Information and Communication (IZS 2018). Proceedings

This short note presents results about the symmetric Jensen-Shannon divergence between two discrete mixture distributions $p_1$ and $p_2$. Specifically, for $i=1,2$, $p_i$ is the mixture of a common distribution $q$ and a distribution $\tilde{p}_i$ with mixture proportion $\lambda_i$. In general, $\tilde{p}_1\neq \tilde{p}_2$ and $\lambda_1\neq\lambda_2$. We provide experimental and theoretical insight to the behavior of the symmetric Jensen-Shannon divergence between $p_1$ and $p_2$ as the mixture proportions or the divergence between $\tilde{p}_1$ and $\tilde{p}_2$ change. We also provide insight into scenarios where the supports of the distributions $\tilde{p}_1$, $\tilde{p}_2$, and $q$ do not coincide., Comment: four-page tech note

In this paper, we investigate mutual information as a cost function for clustering, and show in which cases hard, i.e., deterministic, clusters are optimal. Using convexity properties of mutual information, we show that certain formulations of the information bottleneck problem are solved by hard clusters. Similarly, hard clusters are optimal for the information-theoretic co-clustering problem that deals with simultaneous clustering of two dependent data sets. If both data sets have to be clustered using the same cluster assignment, hard clusters are not optimal in general. We point at interesting and practically relevant special cases of this so-called pairwise clustering problem, for which we can either prove or have evidence that hard clusters are optimal. Our results thus show that one can relax the otherwise combinatorial hard clustering problem to a real-valued optimization problem with the same global optimum.

The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which is an appropriate measure, e.g., in the context of data compression. Properties of the optimal approximation are derived and bounds on the approximation error are presented, which are asymptotically tight. It is shown that $M$-type approximations that minimize either $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, or $\mathbb{D}(\mathbf{p}\Vert\mathbf{t})$, or the variational distance $\Vert\mathbf{p}-\mathbf{t}\Vert_1$ can all be found by using specific instances of the same general greedy algorithm., Comment: 5 pages

We consider the problem of reducing a first-order Markov chain on a large alphabet to a higher-order Markov chain on a small alphabet. We present information-theoretic cost functions that are related to predictability and lumpability, show relations between these cost functions, and discuss heuristics to minimize them. Our experiments suggest that the generalization to higher orders is useful for model reduction in reliability analysis and natural language processing.

An alternative parametric description for discrete random variables, called muculants, is proposed. In contrast to cumulants, muculants are based on the Fourier series expansion, rather than on the Taylor series expansion, of the logarithm of the characteristic function. We utilize results from cepstral theory to derive elementary properties of muculants, some of which demonstrate behavior superior to those of cumulants. For example, muculants and cumulants are both additive. While the existence of cumulants is linked to how often the characteristic function is differentiable, all muculants exist if the characteristic function satisfies a Paley-Wiener condition. Moreover, the muculant sequence and, if the random variable has finite expectation, the reconstruction of the characteristic function from its muculants converge. We furthermore develop a connection between muculants and cumulants and present the muculants of selected discrete random variables. Specifically, it is shown that the Poisson distribution is the only distribution where only the first two muculants are nonzero., 5 pages

This work investigates the information loss in a decimation system, i.e., in a downsampler preceded by an anti-aliasing filter. It is shown that, without a specific signal model in mind, the anti-aliasing filter cannot reduce information loss, while, e.g., for a simple signal-plus-noise model it can. For the Gaussian case, the optimal anti-aliasing filter is shown to coincide with the one obtained from energetic considerations. For a non-Gaussian signal corrupted by Gaussian noise, the Gaussian assumption yields an upper bound on the information loss, justifying filter design principles based on second-order statistics from an information-theoretic point-of-view., Comment: 12 pages; a shorter version of this paper was published at the 2014 International Zurich Seminar on Communications

In this work the information loss in deterministic, memoryless systems is investigated by evaluating the conditional entropy of the input random variable given the output random variable. It is shown that for a large class of systems the information loss is finite, even if the input is continuously distributed. Based on this finiteness, the problem of perfectly reconstructing the input is addressed and Fano-type bounds between the information loss and the reconstruction error probability are derived. For systems with infinite information loss a relative measure is defined and shown to be tightly related to R\'{e}nyi information dimension. Employing another Fano-type argument, the reconstruction error probability is bounded by the relative information loss from below. In view of developing a system theory from an information-theoretic point-of-view, the theoretical results are illustrated by a few example systems, among them a multi-channel autocorrelation receiver., Comment: 23 pages, 12 figures; submitted

In this work we present results about the rate of (relative) information loss induced by passing a real-valued, stationary stochastic process through a memoryless system. We show that for a special class of systems the information loss rate is closely related to the difference of differential entropy rates of the input and output processes. It is further shown that the rate of (relative) information loss is bounded from above by the (relative) information loss the system induces on a random variable distributed according to the process's marginal distribution. As a side result, in this work we present sufficient conditions such that for a continuous-valued Markovian input process also the output process possesses the Markov property., Comment: 9 pages, 4 figures; submitted to a conference

We introduce a relative variant of information loss to characterize the behavior of deterministic input-output systems. We show that the relative loss is closely related to Renyi's information dimension. We provide an upper bound for continuous input random variables and an exact result for a class of functions (comprising quantizers) with infinite absolute information loss. A connection between relative information loss and reconstruction error is investigated., 6 pages; submitted to a conference

In this work we give a concise definition of information loss from a system-theoretic point of view. Based on this definition, we analyze the information loss in static input-output systems subject to a continuous-valued input. For a certain class of multiple-input, multiple-output systems the information loss is quantified. An interpretation of this loss is accompanied by upper bounds which are simple to evaluate. Finally, a class of systems is identified for which the information loss is necessarily infinite. Quantizers and limiters are shown to belong to this class., 7 pages, 6 figures; submitted to a conference

Community detection is an essential tool for analyzing the organization of complex social, biological and information networks. Among the numerous community detection algorithms proposed so far, Infomap is a prominent and well-established framework. In this thesis, we propose a novel method for community detection inspired by Infomap. Whereas Infomap approaches community detection analytically by minimizing the average description length of a random walk on a network, our method minimizes dissimilarity, measured using Kullback-Leibler divergence, between a graph-induced and a synthetic random walker to arrive at a partition into communities. Hence, we call our method synthesizing Infomap. Specifically, we focus on commu- nity detection in undirected networks with non-overlapping communities and two-level hierarchies. In this work, we provide a formalization and a rigorous derivation of the synthesizing Infomap objective function. By applying synthesizing Infomap on a set of toy graphs we explore its properties and qualitative behavior. Our experiments on artificially generated benchmark networks show that synthesizing Infomap outperforms original Infomap in terms of adjusted mutual information on networks with weak community structure. Both methods perform equally well on a selection of real-world networks, indi- cating that synthesizing Infomap produces reasonable results on real-world networks as well. The promising results of synthesizing Infomap encour- age further evaluation on real-world networks, as well as extensions to multilevel hierarchies and overlapping community structures.