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A major challenge in cluster analysis is that the number of data clusters is mostly unknown and it must be estimated prior to clustering the observed data. In real-world applications, the observed data is often subject to heavy tailed noise and outliers which obscure the true underlying structure of the data. Consequently, estimating the number of clusters becomes challenging. To this end, we derive a robust cluster enumeration criterion by formulating the problem of estimating the number of clusters as maximization of the posterior probability of multivariate $t_\nu$ distributed candidate models. We utilize Bayes' theorem and asymptotic approximations to come up with a robust criterion that possesses a closed-form expression. Further, we refine the derivation and provide a robust cluster enumeration criterion for data sets with finite sample size. The robust criteria require an estimate of cluster parameters for each candidate model as an input. Hence, we propose a two-step cluster enumeration algorithm that uses the expectation maximization algorithm to partition the data and estimate cluster parameters prior to the calculation of one of the robust criteria. The performance of the proposed algorithm is tested and compared to existing cluster enumeration methods using numerical and real data experiments.

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses is revisited and it is shown that the partial derivatives of the corresponding cost function are closely related to the performance metrics of the underlying sequential test. Second, an implicit characterization of the least favorable distributions for a given testing policy is stated. By combining the results on optimal sequential tests and least favorable distributions, sufficient conditions for a sequential test to be minimax optimal under general distributional uncertainties are obtained. The cost function of the minimax optimal test is further identified as a generalized $f$-dissimilarity and the least favorable distributions as those that are most similar with respect to this dissimilarity. Numerical examples for minimax optimal sequential tests under different uncertainties illustrate the theoretical results., Comment: 43 pages, 5 figures, 2 tables

The accurate and low-cost localization of sensors using a wireless sensor network is critically required in a wide range of today's applications. We propose a novel, robust maximum likelihood-type method for distributed cooperative received signal strength-based localization in wireless sensor networks. To cope with mixed LoS/NLoS conditions, we model the measurements using a two-component Gaussian mixture model. The relevant channel parameters, including the reference path loss, the path loss exponent and the variance of the measurement error, for both LoS and NLoS conditions, are assumed to be unknown deterministic parameters and are adaptively estimated. Unlike existing algorithms, the proposed method naturally takes into account the (possible) asymmetry of links between nodes. The proposed approach has a communication overhead upper-bounded by a quadratic function of the number of nodes and computational complexity scaling linearly with it. The convergence of the proposed method is guaranteed for compatible network graphs and compatibility can be tested a priori by restating the problem as a graph coloring problem. Simulation results, carried out in comparison to a centralized benchmark algorithm, demonstrate the good overall performance and high robustness in mixed LoS/NLoS environments., Comment: 16 pages, 12 figures

Objective: In this paper, we demonstrate the applicability of radar for gait classification with application to home security, medical diagnosis, rehabilitation and assisted living. Aiming at identifying changes in gait patterns based on radar micro-Doppler signatures, this work is concerned with solving the intra motion category classification problem of gait recognition. Methods: New gait classification approaches utilizing physical features, subspace features and sum-of-harmonics modeling are presented and their performances are evaluated using experimental K-band radar data of four test subjects. Five different gait classes are considered for each person, including normal, pathological and assisted walks. Results: The proposed approaches are shown to outperform existing methods for radar-based gait recognition which utilize physical features from the cadence-velocity data representation domain as in this paper. The analyzed gait classes are correctly identified with an average accuracy of 93.8%, where a classification rate of 98.5% is achieved for a single gait class. When applied to new data of another individual a classification accuracy on the order of 80% can be expected. Conclusion: Radar micro-Doppler signatures and their Fourier transforms are well suited to capture changes in gait. Five different walking styles are recognized with high accuracy. Significance: Radar-based sensing of human gait is an emerging technology with multi-faceted applications in security and health care industries. We show that radar, as a contact-less sensing technology, can supplement existing gait diagnostic tools with respect to long-term monitoring and reproducibility of the examinations., Comment: 11 pages, 6 figures

This letter aims at deriving a Semiparametric Slepian-Bangs (SSB) formula for Complex Elliptically Symmetric (CES) distributed data vectors. The Semiparametric Cram\'{e}r-Rao Bound (SCRB), related to the proposed SSB formula, provides a lower bound on the Mean Square Error (MSE) of \textit{any} robust estimator of a parameter vector parameterizing the mean vector and the scatter matrix of the given CES-distributed vector in the presence of an unknown, nuisance, density generator., Comment: This letter has been merged with another letter and resubmitted as a full IEEE TSP paper

This letter aims at extending the Constrained Semiparametric Cramer-Rao Bound (CSCRB) for the joint estimation of mean vector and scatter matrix of Real Elliptically Symmetric (RES) distributions to Complex Elliptically Symmetric (CES) distributions. A closed form expression for the complex CSCRB (CCSCRB) is derived by exploiting the so-called \textit{Wirtinger} or $\mathbb{C}\mathbb{R}$-\textit{calculus}. Finally, the CCSCRB for the estimation of the complex mean vector and scatter matrix of a set of complex $t$-distributed random vectors is provided as an example of application., Comment: This letter has been merged with another letter and resubmitted as a full IEEE TSP paper

This paper has a twofold goal. The first aim is to provide a deeper understanding of the family of the Real Elliptically Symmetric (RES) distributions by investigating their intrinsic semiparametric nature. The second aim is to derive a semiparametric lower bound for the estimation of the parametric component of the model. The RES distributions represent a semiparametric model where the parametric part is given by the mean vector and by the scatter matrix while the non-parametric, infinite-dimensional, part is represented by the density generator. Since, in practical applications, we are often interested only in the estimation of the parametric component, the density generator can be considered as nuisance. The first part of the paper is dedicated to conveniently place the RES distributions in the framework of the semiparametric group models. The second part of the paper, building on the mathematical tools previously introduced, the Constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB) for the estimation of the mean vector and of the constrained scatter matrix of a RES distributed random vector is introduced. The CSCRB provides a lower bound on the Mean Squared Error (MSE) of any robust $M$-estimator of mean vector and scatter matrix when no a-priori information on the density generator is available. A closed form expression for the CSCRB is derived. Finally, in simulations, we assess the statistical efficiency of the Tyler's and Huber's scatter matrix $M$-estimators with respect to the CSCRB., Comment: This paper has been accepted for publication in IEEE Transactions on Signal Processing

Joint detection and estimation refers to deciding between two or more hypotheses and, depending on the test outcome, simultaneously estimating the unknown parameters of the underlying distribution. This problem is investigated in a sequential framework under mild assumptions on the underlying random process. We formulate an unconstrained sequential decision problem, whose cost function is the weighted sum of the expected run-length and the detection/estimation errors. Then, a strong connection between the derivatives of the cost function with respect to the weights, which can be interpreted as Lagrange multipliers, and the detection/estimation errors of the underlying scheme is shown. This property is used to characterize the solution of a closely related sequential decision problem, whose objective function is the expected run-length under constraints on the average detection/estimation errors. We show that the solution of the constrained problem coincides with the solution of the unconstrained problem with suitably chosen weights. These weights are characterized as the solution of a linear program, which can be solved using efficient off-the-shelf solvers. The theoretical results are illustrated with two example problems, for which optimal sequential schemes are designed numerically and whose performance is validated via Monte Carlo simulations., Comment: 35 pages, 2 figures, accepted for publication in Sequential Analysis

Tight bounds on the minimum mean square error for the additive Gaussian noise channel are derived, when the input distribution is constrained to be epsilon-close to a Gaussian reference distribution in terms of the Kullback--Leibler divergence. The distributions that attain the bounds are shown be Gaussian whose means are identical to that of the reference distribution and whose covariance matrices are defined implicitly via systems of matrix equations. The estimator that attains the upper bound is identified as a minimax optimal estimator that is robust against deviations from the assumed prior. The lower bound is shown to provide a potentially tighter alternative to the Cramer--Rao bound. Both properties are illustrated with numerical examples., Comment: 5 pages, 3 figures, accepted for publication in the proceedings of the IEEE Statistical Signal Processing Workshop 2018

The paper deals with minimax optimal statistical tests for two composite hypotheses, where each hypothesis is defined by a non-parametric uncertainty set of feasible distributions. It is shown that for every pair of uncertainty sets of the f-divergence ball type, a pair of uncertainty sets of the density band type can be constructed, which is equivalent in the sense that it admits the same pair of least favorable distributions. This result implies that robust tests under $f$-divergence ball uncertainty, which are typically only minimax optimal for the single sample case, are also fixed sample size minimax optimal with respect to the equivalent density band uncertainty sets., Comment: 5 pages, 1 figure, accepted for publication in the Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 2018

Advances in the field of inverse reinforcement learning (IRL) have led to sophisticated inference frameworks that relax the original modeling assumption of observing an agent behavior that reflects only a single intention. Instead of learning a global behavioral model, recent IRL methods divide the demonstration data into parts, to account for the fact that different trajectories may correspond to different intentions, e.g., because they were generated by different domain experts. In this work, we go one step further: using the intuitive concept of subgoals, we build upon the premise that even a single trajectory can be explained more efficiently locally within a certain context than globally, enabling a more compact representation of the observed behavior. Based on this assumption, we build an implicit intentional model of the agent's goals to forecast its behavior in unobserved situations. The result is an integrated Bayesian prediction framework that significantly outperforms existing IRL solutions and provides smooth policy estimates consistent with the expert's plan. Most notably, our framework naturally handles situations where the intentions of the agent change over time and classical IRL algorithms fail. In addition, due to its probabilistic nature, the model can be straightforwardly applied in active learning scenarios to guide the demonstration process of the expert., Comment: 45 pages, 14 figures; ### Version 3 ### published in the Journal of Machine Learning Research

This paper aims at providing a fresh look at semiparametric estimation theory and, in particular, at the Semiparametric Cram\'{e}r-Rao Bound (SCRB). Semiparametric models are characterized by a finite-dimensional parameter vector of interest and by an infinite-dimensional nuisance function that is often related to an unspecified functional form of the density of the noise underlying the observations. We summarize the main motivations and the intuitive concepts about semiparametric models. Then we provide a new look at the classical estimation theory based on a geometrical Hilbert space-based approach. Finally, the semiparametric version of the Cram\'{e}r-Rao Bound for the estimation of the finite-dimensional vector of the parameters of interest is provided., Comment: Submitted to EUSIPCO 2018

We consider the problem of sequential binary hypothesis testing with a distributed sensor network in a non-Gaussian noise environment. To this end, we present a general formulation of the Consensus + Innovations Sequential Probability Ratio Test (CISPRT). Furthermore, we introduce two different concepts for robustifying the CISPRT and propose four different algorithms, namely, the Least-Favorable-Density-CISPRT, the Median-CISPRT, the M-CISPRT, and the Myriad-CISPRT. Subsequently, we analyze their suitability for different binary hypothesis tests before verifying and evaluating their performance in a shift-in-mean and a shift-in-variance scenario., Comment: 13 pages, 5 figures

We derive a new Bayesian Information Criterion (BIC) by formulating the problem of estimating the number of clusters in an observed data set as maximization of the posterior probability of the candidate models. Given that some mild assumptions are satisfied, we provide a general BIC expression for a broad class of data distributions. This serves as a starting point when deriving the BIC for specific distributions. Along this line, we provide a closed-form BIC expression for multivariate Gaussian distributed variables. We show that incorporating the data structure of the clustering problem into the derivation of the BIC results in an expression whose penalty term is different from that of the original BIC. We propose a two-step cluster enumeration algorithm. First, a model-based unsupervised learning algorithm partitions the data according to a given set of candidate models. Subsequently, the number of clusters is determined as the one associated with the model for which the proposed BIC is maximal. The performance of the proposed two-step algorithm is tested using synthetic and real data sets., Comment: 14 pages, 7 figures

Distributed signal processing for wireless sensor networks enables that different devices cooperate to solve different signal processing tasks. A crucial first step is to answer the question: who observes what? Recently, several distributed algorithms have been proposed, which frame the signal/object labelling problem in terms of cluster analysis after extracting source-specific features, however, the number of clusters is assumed to be known. We propose a new method called Gravitational Clustering (GC) to adaptively estimate the time-varying number of clusters based on a set of feature vectors. The key idea is to exploit the physical principle of gravitational force between mass units: streaming-in feature vectors are considered as mass units of fixed position in the feature space, around which mobile mass units are injected at each time instant. The cluster enumeration exploits the fact that the highest attraction on the mobile mass units is exerted by regions with a high density of feature vectors, i.e., gravitational clusters. By sharing estimates among neighboring nodes via a diffusion-adaptation scheme, cooperative and distributed cluster enumeration is achieved. Numerical experiments concerning robustness against outliers, convergence and computational complexity are conducted. The application in a distributed cooperative multi-view camera network illustrates the applicability to real-world problems., Comment: 12 pages, 9 figures

Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted for. In past decades, the vast majority of robust linear regression estimators has focused on robustness against rowwise contamination. Even so called `high breakdown' estimators rely on the assumption that a majority of rows of the regression matrix is not affected by outliers. Only very recently, the first cellwise robust regression estimation methods have been developed. In this paper, we define robust oracle properties, which an estimator must have in order to perform robust model selection for under-determined, or ill-conditioned linear regression models that are contaminated by cellwise outliers in the regression matrix. We propose and analyze a robustly weighted and adaptive Lasso type regularization term which takes into account cellwise outliers for model selection. The proposed regularization term is integrated into the objective function of the MM-estimator, which yields the proposed MM-Robust Weighted Adaptive Lasso (MM-RWAL), for which we prove that at least the weak robust oracle properties hold. A performance comparison to existing robust Lasso estimators is provided using Monte Carlo experiments. Further, the MM-RWAL is applied to determine the temporal releases of the European Tracer Experiment (ETEX) at the source location. This ill-conditioned linear inverse problem contains cellwise and rowwise outliers and is sparse both in the regression matrix and the parameter vector. The proposed RWAL penalty is not limited to the MM-estimator but can easily be integrated into the objective function of other robust estimators.

In this paper, direction-of-arrival (DOA) estimation using non-coherent processing for partly calibrated arrays composed of multiple subarrays is considered. The subarrays are assumed to compute locally the sample covariance matrices of their measurements and communicate them to the processing center. A sufficient condition for the unique identifiability of the sources in the aforementioned non-coherent processing scheme is presented. We prove that, under mild conditions, with the non-coherent system of subarrays, it is possible to identify more sources than identifiable by each individual subarray. This property of non-coherent processing has not been investigated before. We derive the Maximum Likelihood estimator (MLE) for DOA estimation at the processing center using the sample covariance matrices received from the subarrays. Moreover, the Cramer-Rao Bound (CRB) for our measurement model is derived and is used to assess the presented DOA estimators. The behaviour of the CRB at high signal-to-noise ratio (SNR) is analyzed. In contrast to coherent processing, we prove that the CRB approaches zero at high SNR only if at least one subarray can identify the sources individually., Comment: 17 pages, 11 figures

The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality conditions as well as a bound on the optimality gap of feasible candidate solutions are derived. Based on these results, two numerical algorithms are proposed that iteratively solve the system of optimality conditions on a grid of discrete points. Both algorithms use a block coordinate descent strategy and terminate once the optimality gap falls below the desired tolerance. While the first algorithm is conceptually simpler and more efficient, it is not guaranteed to converge for objective functions that are not strictly convex. This shortcoming is overcome in the second algorithm, which uses an additional outer proximal iteration, and, which is proven to converge under mild assumptions. Two examples are given to demonstrate the theoretical usefulness of the optimality conditions as well as the high efficiency and accuracy of the proposed numerical algorithms., Comment: 13 pages, 5 figures, 2 tables, published in the IEEE Transactions on Signal Processing. In previous versions, the example in Section VI.B contained some mistakes and inaccuracies, which have been fixed in this version

A distributed multi-speaker voice activity detection (DM-VAD) method for wireless acoustic sensor networks (WASNs) is proposed. DM-VAD is required in many signal processing applications, e.g. distributed speech enhancement based on multi-channel Wiener filtering, but is non-existent up to date. The proposed method neither requires a fusion center nor prior knowledge about the node positions, microphone array orientations or the number of observed sources. It consists of two steps: (i) distributed source-specific energy signal unmixing (ii) energy signal based voice activity detection. Existing computationally efficient methods to extract source-specific energy signals from the mixed observations, e.g., multiplicative non-negative independent component analysis (MNICA) quickly loose performance with an increasing number of sources, and require a fusion center. To overcome these limitations, we introduce a distributed energy signal unmixing method based on a source-specific node clustering method to locate the nodes around each source. To determine the number of sources that are observed in the WASN, a source enumeration method that uses a Lasso penalized Poisson generalized linear model is developed. Each identified cluster estimates the energy signal of a single (dominant) source by applying a two-component MNICA. The VAD problem is transformed into a clustering task, by extracting features from the energy signals and applying K-means type clustering algorithms. All steps of the proposed method are evaluated using numerical experiments. A VAD accuracy of $> 85 \%$ is achieved for a challenging scenario where 20 nodes observe 7 sources in a simulated reverberant rectangular room.

Hyperspectral imaging is an important tool in remote sensing, allowing for accurate analysis of vast areas. Due to a low spatial resolution, a pixel of a hyperspectral image rarely represents a single material, but rather a mixture of different spectra. HSU aims at estimating the pure spectra present in the scene of interest, referred to as endmembers, and their fractions in each pixel, referred to as abundances. Today, many HSU algorithms have been proposed, based either on a geometrical or statistical model. While most methods assume that the number of endmembers present in the scene is known, there is only little work about estimating this number from the observed data. In this work, we propose a Bayesian nonparametric framework that jointly estimates the number of endmembers, the endmembers itself, and their abundances, by making use of the Indian Buffet Process as a prior for the endmembers. Simulation results and experiments on real data demonstrate the effectiveness of the proposed algorithm, yielding results comparable with state-of-the-art methods while being able to reliably infer the number of endmembers. In scenarios with strong noise, where other algorithms provide only poor results, the proposed approach tends to overestimate the number of endmembers slightly. The additional endmembers, however, often simply represent noisy replicas of present endmembers and could easily be merged in a post-processing step.

Learning from demonstrations has gained increasing interest in the recent past, enabling an agent to learn how to make decisions by observing an experienced teacher. While many approaches have been proposed to solve this problem, there is only little work that focuses on reasoning about the observed behavior. We assume that, in many practical problems, an agent makes its decision based on latent features, indicating a certain action. Therefore, we propose a generative model for the states and actions. Inference reveals the number of features, the features, and the policies, allowing us to learn and to analyze the underlying structure of the observed behavior. Further, our approach enables prediction of actions for new states. Simulations are used to assess the performance of the algorithm based upon this model. Moreover, the problem of learning a driver's behavior is investigated, demonstrating the performance of the proposed model in a real-world scenario.

We consider the problem of decentralized clustering and estimation over multi-task networks, where agents infer and track different models of interest. The agents do not know beforehand which model is generating their own data. They also do not know which agents in their neighborhood belong to the same cluster. We propose a decentralized clustering algorithm aimed at identifying and forming clusters of agents of similar objectives, and at guiding cooperation to enhance the inference performance. One key feature of the proposed technique is the integration of the learning and clustering tasks into a single strategy. We analyze the performance of the procedure and show that the error probabilities of types I and II decay exponentially to zero with the step-size parameter. While links between agents following different objectives are ignored in the clustering process, we nevertheless show how to exploit these links to relay critical information across the network for enhanced performance. Simulation results illustrate the performance of the proposed method in comparison to other useful techniques.

We present a sparse estimation and dictionary learning framework for compressed fiber sensing based on a probabilistic hierarchical sparse model. To handle severe dictionary coherence, selective shrinkage is achieved using a Weibull prior, which can be related to non-convex optimization with $p$-norm constraints for $0 < p < 1$. In addition, we leverage the specific dictionary structure to promote collective shrinkage based on a local similarity model. This is incorporated in form of a kernel function in the joint prior density of the sparse coefficients, thereby establishing a Markov random field-relation. Approximate inference is accomplished using a hybrid technique that combines Hamilton Monte Carlo and Gibbs sampling. To estimate the dictionary parameter, we pursue two strategies, relying on either a deterministic or a probabilistic model for the dictionary parameter. In the first strategy, the parameter is estimated based on alternating estimation. In the second strategy, it is jointly estimated along with the sparse coefficients. The performance is evaluated in comparison to an existing method in various scenarios using simulations and experimental data.

We propose a compressed sampling and dictionary learning framework for fiber-optic sensing using wavelength-tunable lasers. A redundant dictionary is generated from a model for the reflected sensor signal. Imperfect prior knowledge is considered in terms of uncertain local and global parameters. To estimate a sparse representation and the dictionary parameters, we present an alternating minimization algorithm that is equipped with a pre-processing routine to handle dictionary coherence. The support of the obtained sparse signal indicates the reflection delays, which can be used to measure impairments along the sensing fiber. The performance is evaluated by simulations and experimental data for a fiber sensor system with common core architecture., Comment: Accepted for publication in Journal of the Optical Society of America A [ \copyright\ 2017 Optical Society of America.]. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited

A new robust and statistically efficient estimator for ARMA models called the bounded influence propagation (BIP) {\tau}-estimator is proposed. The estimator incorporates an auxiliary model, which prevents the propagation of outliers. Strong consistency and asymptotic normality of the estimator for ARMA models that are driven by independently and identically distributed (iid) innovations with symmetric distributions are established. To analyze the infinitesimal effect of outliers on the estimator, the influence function is derived and computed explicitly for an AR(1) model with additive outliers. To obtain estimates for the AR(p) model, a robust Durbin-Levinson type and a forward-backward algorithm are proposed. An iterative algorithm to robustly obtain ARMA(p,q) parameter estimates is also presented. The problem of finding a robust initialization is addressed, which for orders p+q>2 is a non-trivial matter. Numerical experiments are conducted to compare the finite sample performance of the proposed estimator to existing robust methodologies for different types of outliers both in terms of average and of worst-case performance, as measured by the maximum bias curve. To illustrate the practical applicability of the proposed estimator, a real-data example of outlier cleaning for R-R interval plots derived from electrocardiographic (ECG) data is considered. The proposed estimator is not limited to biomedical applications, but is also useful in any real-world problem whose observations can be modeled as an ARMA process disturbed by outliers or impulsive noise.

Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the performance of popular estimators may deteriorate significantly. We have developed a new estimator that is both nearly optimal in the presence of Gaussian errors while being also robust against outliers. Furthermore, it obtains meaningful estimates when the problem is ill-posed through the inclusion of $\ell_1$ and $\ell_2$ regularizations. The computation of our estimate involves minimizing a non-convex objective function. Hence, we are not guaranteed to find the global minimum in a reasonable amount of time. Thus, we propose two algorithms that converge to a good local minimum in a reasonable (and adjustable) amount of time, as an approximation of the global minimum. We also analyze how the introduction of the regularization term affects the statistical properties of our estimator. We confirm high robustness against outliers and asymptotic efficiency for Gaussian distributions by deriving measures of robustness such as the influence function, sensitivity curve, bias, asymptotic variance, and mean square error. We verify the theoretical results using numerical experiments and show that the proposed estimator outperforms recently proposed methods, especially for increasing amounts of outlier contamination. Python code for all of the algorithms are available online in the spirit of reproducible research.

Learning from demonstration (LfD) is the process of building behavioral models of a task from demonstrations provided by an expert. These models can be used e.g. for system control by generalizing the expert demonstrations to previously unencountered situations. Most LfD methods, however, make strong assumptions about the expert behavior, e.g. they assume the existence of a deterministic optimal ground truth policy or require direct monitoring of the expert's controls, which limits their practical use as part of a general system identification framework. In this work, we consider the LfD problem in a more general setting where we allow for arbitrary stochastic expert policies, without reasoning about the optimality of the demonstrations. Following a Bayesian methodology, we model the full posterior distribution of possible expert controllers that explain the provided demonstration data. Moreover, we show that our methodology can be applied in a nonparametric context to infer the complexity of the state representation used by the expert, and to learn task-appropriate partitionings of the system state space., Comment: 17 pages, 8 figures; ### Version 4 ### to appear in IEEE Transactions on Pattern Analysis and Machine Intelligence

Inverse reinforcement learning (IRL) has become a useful tool for learning behavioral models from demonstration data. However, IRL remains mostly unexplored for multi-agent systems. In this paper, we show how the principle of IRL can be extended to homogeneous large-scale problems, inspired by the collective swarming behavior of natural systems. In particular, we make the following contributions to the field: 1) We introduce the swarMDP framework, a sub-class of decentralized partially observable Markov decision processes endowed with a swarm characterization. 2) Exploiting the inherent homogeneity of this framework, we reduce the resulting multi-agent IRL problem to a single-agent one by proving that the agent-specific value functions in this model coincide. 3) To solve the corresponding control problem, we propose a novel heterogeneous learning scheme that is particularly tailored to the swarm setting. Results on two example systems demonstrate that our framework is able to produce meaningful local reward models from which we can replicate the observed global system dynamics., Comment: 9 pages, 8 figures; ### Version 2 ### version accepted at AAMAS 2017

Glucometers present an important self-monitoring tool for diabetes patients and therefore must exhibit high accu- racy as well as good usability features. Based on an invasive, photometric measurement principle that drastically reduces the volume of the blood sample needed from the patient, we present a framework that is capable of dealing with small blood samples, while maintaining the required accuracy. The framework consists of two major parts: 1) image segmentation; and 2) convergence detection. Step 1) is based on iterative mode-seeking methods to estimate the intensity value of the region of interest. We present several variations of these methods and give theoretical proofs of their convergence. Our approach is able to deal with changes in the number and position of clusters without any prior knowledge. Furthermore, we propose a method based on sparse approximation to decrease the computational load, while maintaining accuracy. Step 2) is achieved by employing temporal tracking and prediction, herewith decreasing the measurement time, and, thus, improving usability. Our framework is validated on several real data sets with different characteristics. We show that we are able to estimate the underlying glucose concentration from much smaller blood samples than is currently state-of-the- art with sufficient accuracy according to the most recent ISO standards and reduce measurement time significantly compared to state-of-the-art methods.