1,139 research outputs found

    Blind Multilinear Identification

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    We discuss a technique that allows blind recovery of signals or blind identification of mixtures in instances where such recovery or identification were previously thought to be impossible: (i) closely located or highly correlated sources in antenna array processing, (ii) highly correlated spreading codes in CDMA radio communication, (iii) nearly dependent spectra in fluorescent spectroscopy. This has important implications --- in the case of antenna array processing, it allows for joint localization and extraction of multiple sources from the measurement of a noisy mixture recorded on multiple sensors in an entirely deterministic manner. In the case of CDMA, it allows the possibility of having a number of users larger than the spreading gain. In the case of fluorescent spectroscopy, it allows for detection of nearly identical chemical constituents. The proposed technique involves the solution of a bounded coherence low-rank multilinear approximation problem. We show that bounded coherence allows us to establish existence and uniqueness of the recovered solution. We will provide some statistical motivation for the approximation problem and discuss greedy approximation bounds. To provide the theoretical underpinnings for this technique, we develop a corresponding theory of sparse separable decompositions of functions, including notions of rank and nuclear norm that specialize to the usual ones for matrices and operators but apply to also hypermatrices and tensors.Comment: 20 pages, to appear in IEEE Transactions on Information Theor

    Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors

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    Meaningful quantification of data and structural uncertainties in conceptual rainfall-runoff modeling is a major scientific and engineering challenge. This paper focuses on the total predictive uncertainty and its decomposition into input and structural components under different inference scenarios. Several Bayesian inference schemes are investigated, differing in the treatment of rainfall and structural uncertainties, and in the precision of the priors describing rainfall uncertainty. Compared with traditional lumped additive error approaches, the quantification of the total predictive uncertainty in the runoff is improved when rainfall and/or structural errors are characterized explicitly. However, the decomposition of the total uncertainty into individual sources is more challenging. In particular, poor identifiability may arise when the inference scheme represents rainfall and structural errors using separate probabilistic models. The inference becomes ill‐posed unless sufficiently precise prior knowledge of data uncertainty is supplied; this ill‐posedness can often be detected from the behavior of the Monte Carlo sampling algorithm. Moreover, the priors on the data quality must also be sufficiently accurate if the inference is to be reliable and support meaningful uncertainty decomposition. Our findings highlight the inherent limitations of inferring inaccurate hydrologic models using rainfall‐runoff data with large unknown errors. Bayesian total error analysis can overcome these problems using independent prior information. The need for deriving independent descriptions of the uncertainties in the input and output data is clearly demonstrated.Benjamin Renard, Dmitri Kavetski, George Kuczera, Mark Thyer, and Stewart W. Frank

    Distinguishing Cause and Effect via Second Order Exponential Models

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    We propose a method to infer causal structures containing both discrete and continuous variables. The idea is to select causal hypotheses for which the conditional density of every variable, given its causes, becomes smooth. We define a family of smooth densities and conditional densities by second order exponential models, i.e., by maximizing conditional entropy subject to first and second statistical moments. If some of the variables take only values in proper subsets of R^n, these conditionals can induce different families of joint distributions even for Markov-equivalent graphs. We consider the case of one binary and one real-valued variable where the method can distinguish between cause and effect. Using this example, we describe that sometimes a causal hypothesis must be rejected because P(effect|cause) and P(cause) share algorithmic information (which is untypical if they are chosen independently). This way, our method is in the same spirit as faithfulness-based causal inference because it also rejects non-generic mutual adjustments among DAG-parameters.Comment: 36 pages, 8 figure

    Identifikation von Schadstoffeinleitungen und angepasstes Design eines Monitoringnetzwerkes in Ästuaren

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    In the last decades there have been thousands of accidental pollution spills as well as intentional illegal discharges into surface waters all over the world. The identification of pollution source parameters (e.g. the source location) has often proven difficult and heavily depends on measured pollutant concentration data collected after the incident. This thesis investigates how an adapted monitoring design can improve the identification of source parameters after a spill incident, especially in the case of estuaries. Initially, the effect of the spatial and temporal monitoring design on parameter identifiability is analyzed based on a synthetic unidirectional (river) as well as a bidirectional (estuary) test case is carried out. While the transport processes in the river could be represented by an analytical solution of the 2D advection-dispersion-reaction equation, to take into account the tidal dynamics in the estuary, a numerical transport model had to be set up with the Delft3D software suite. The results of the analysis indicate that parameter dependencies exist between different source parameters, which can weaken the identifiability of the individual parameters. However, an appropriate monitoring design can improve parameter identifiability and consequently lead to more reliable parameter estimates. To identify the source parameters after potential pollution incidents, two optimization approaches were selected in this work, which were initially applied to the synthetic bidirectional test case. Both approaches achieved very good results for both perfect and noise perturbed monitoring data. Subsequently, both optimization approaches were transferred to a real-world estuary, the Thi Vai Estuary, located in South Vietnam. To simulate pollution scenarios, a 2D hydrodynamic transport model was set up in Delft3D and calibrated based on monitoring data collected in the EWATEC-COAST research project. The synthetically generated monitoring data of an optimized monitoring network were then used to identify several theoretical spill incidents in the Thi Vai Estuary. Both optimization approaches performed generally well and could correctly identify the source parameters in 80% of the considered scenarios.In den letzten Jahrzehnten kam es weltweit immer wieder zu zahlreichen UnfĂ€llen und illegalen Einleitungen, bei denen Schadstoffe in OberflĂ€chengewĂ€sser eingeleitet wurden. Die Identifikation der Einleitungsparameter (u.a. des Ortes) stellt hierbei eine große Herausforderung dar und hĂ€ngt stark von den gesammelten Konzentrationsdaten ab, die nach dem Schadstoffeintrag erhoben wurden. Daher bestand das Hauptziel der Dissertation darin, die Identifikation der Einleitungsparameter im Falle eines Schadstoffeintrags durch ein angepasstes Monitoringdesign insbesondere in Ästuaren zu verbessern. ZunĂ€chst wurde, aufbauend auf einen synthetischen Fluss- und Ästuarabschnitt, der Einfluss des rĂ€umlichen und zeitlichen Monitoringdesigns auf die Identifizierbarkeit der Einleitungsparameter analysiert. WĂ€hrend die Transportprozesse im Fluss durch eine analytische Lösung der 2D Advektions-Dispersions-Reaktions-Gleichung abgebildet werden konnten, musste fĂŒr das Ästuar zur BerĂŒcksichtigung des Tideeinflusses ein numerisches Transportmodell mit der Software Delft3D aufgebaut werden. Die Ergebnisse der Analyse zeigen, dass zwischen bestimmten Einleitungsparametern Interaktionen bestehen, die die Identifizierbarkeit der einzelnen Parameter schwĂ€chen. Ein angepasstes Monitoringdesign kann die Identifizierbarkeit allerdings verbessern und folglich zu einer zuverlĂ€ssigeren ParameterschĂ€tzung fĂŒhren. Zur Identifikation der Einleitungsparameter nach potentiellen SchadstoffeintrĂ€gen wurden in dieser Arbeit zwei verschiedene OptimierungsansĂ€tze ausgewĂ€hlt, die zunĂ€chst auf den synthetischen Ästuarabschnitt angewandt wurden. Hier konnten durch beide AnsĂ€tze sowohl fĂŒr perfekte als auch fehlerbehaftete Messdaten sehr gute Ergebnisse erzielt werden. Anschließend wurden beide OptimierungsansĂ€tze auf einen realen Ästuar, den Thi Vai Ästuar in SĂŒdvietnam ĂŒbertragen. Zur Simulation verschiedener Einleitungsszenarien wurde ein 2D hydrodynamisches Transportmodell in Delft3D aufgebaut und mit Messdaten, die im Forschungsprojekt EWATEC-COAST erhoben wurden, kalibriert. Die synthetisch generierten Monitoringdaten eines optimalen Monitoringnetzwerkes dienten anschließend zur Identifikation mehrerer theoretischer Einleitungsszenarien. Beide OptimierungsansĂ€tze zeigten gute Ergebnisse und konnten die Einleitungsparameter in 80% der betrachteten Szenarien korrekt bestimmen
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