Institut für Informatik und Computational Science
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In recent years, there has been a large amount of disparate work concerning the representation and reasoning with qualitative preferential information by means of approaches to nonmonotonic reasoning. Given the variety of underlying systems, assumptions, motivations, and intuitions, it is difficult to compare or relate one approach with another. Here, we present an overview and classification for approaches to dealing with preference. A set of criteria for classifying approaches is given, followed by a set of desiderata that an approach might be expected to satisfy. A comprehensive set of approaches is subsequently given and classified with respect to these sets of underlying principles
We present a new technique for uniquely identifying a single failing vector in an interval of test vectors. This technique is applicable to combinational circuits and for scan-BIST in sequential circuits with multiple scan chains. The proposed method relies on the linearity properties of the MISR and on the use of two test sequences, which are both applied to the circuit under test. The second test sequence is derived from the first in a straightforward manner and the same test pattern source is used for both test sequences. If an interval contains only a single failing vector, the algebraic analysis is guaranteed to identify it. We also show analytically that if an interval contains two failing vectors, the probability that this case is interpreted as one failing vector is very low. We present experimental results for the ISCAS benchmark circuits to demonstrate the use of the proposed method for identifying failing test vectors
We propose two methods that reduce the post-nonlinear blind source separation problem (PNL-BSS) to a linear BSS problem. The first method is based on the concept of maximal correlation: we apply the alternating conditional expectation (ACE) algorithm-a powerful technique from nonparametric statistics-to approximately invert the componentwise nonlinear functions. The second method is a Gaussianizing transformation, which is motivated by the fact that linearly mixed signals before nonlinear transformation are approximately Gaussian distributed. This heuristic, but simple and efficient procedure works as good as the ACE method. Using the framework provided by ACE, convergence can be proven. The optimal transformations obtained by ACE coincide with the sought-after inverse functions of the nonlinearitics. After equalizing the nonlinearities, temporal decorrelation separation (TDSEP) allows us to recover the source signals. Numerical simulations testing "ACE-TD" and "Gauss-TD" on realistic examples are performed with excellent results
Recently blind source separation (BSS) methods have been highly successful when applied to biomedical data. This paper reviews the concept of BSS and demonstrates its usefulness in the context of event-related MEG measurements. In a first experiment we apply BSS to artifact identification of raw MEG data and discuss how the quality of the resulting independent component projections can be evaluated. The second part of our study considers averaged data of event-related magnetic fields. Here, it is particularly important to monitor and thus avoid possible overfitting due to limited sample size. A stability assessment of the BSS decomposition allows to solve this task and an additional grouping of the BSS components reveals interesting structure, that could ultimately be used for gaining a better physiological modeling of the data
Noninvasive electroencephalogram (EEG) recordings provide for easy and safe access to human neocortical processes which can be exploited for a brain-computer interface (BCI). At present, however, the use of BCIs is severely limited by low bit-transfer rates. We systematically analyze and develop two recent concepts, both capable of enhancing the information gain from multichannel scalp EEG recordings: 1) the combination of classifiers, each specifically tailored for different physiological phenomena, e.g., slow cortical potential shifts, such as the premovement Bereitschaftspotential or differences in spatio-spectral distributions of brain activity (i.e., focal event-related desynchronizations) and 2) behavioral paradigms inducing the subjects to generate one out of several brain states (multiclass approach) which all bare a distinctive spatio-temporal signature well discriminable in the standard scalp EEG. We derive information-theoretic predictions and demonstrate their relevance in experimental data. We will show that a suitably arranged interaction between these concepts can significantly boost BCI performances
The power of a language L is the set of all powers of the words in L. In this paper, the following decision problem is investigated. Given a context-free language L, is the power of L context-free? We show that this problem is decidable for languages over unary alphabets, but it is undecidable whenever languages over alphabets with at least two letters are considered. (C) 2003 Elsevier B.V. All rights reserved
Independent component analysis (ICA) is a tool for statistical data analysis and signal processing that is able to decompose multivariate signals into their underlying source components. Although the classical ICA model is highly useful, there are many real-world applications that require powerful extensions of ICA. This thesis presents new methods that extend the functionality of ICA: (1) reliability and grouping of independent components with noise injection, (2) robust and overcomplete ICA with inlier detection, and (3) nonlinear ICA with kernel methods.
Usually, noise is considered to be destructive. We present a new method that constructively injects noise to assess the reliability and the grouping structure of empirical ICA component estimates. Our method can be viewed as a Monte-Carlo-style approximation of the curvature of some performance measure at the solution. Simulations show that the true root-mean-squared angle distances between the real sources and the source estimates can be approximated well by our method. In a toy experiment, we see that we are also able to reveal the underlying grouping structure of the extracted ICA components. Furthermore, an experiment with fetal ECG data demonstrates that our approach is useful for exploratory data analysis of real-world data. (C) 2003 Elsevier B.V. All rights reserved
In this paper, we show how an approach to belief revision and belief contraction can be axiomatized by means of quantified Boolean formulas. Specifically, we consider the approach of belief change scenarios, a general framework that has been introduced for expressing different forms of belief change. The essential idea is that for a belief change scenario (K, R, C), the set of formulas K, representing the knowledge base, is modified so that the sets of formulas R and C are respectively true in, and consistent with the result. By restricting the form of a belief change scenario, one obtains specific belief change operators including belief revision, contraction, update, and merging. For both the general approach and for specific operators, we give a quantified Boolean formula such that satisfying truth assignments to the free variables correspond to belief change extensions in the original approach. Hence, we reduce the problem of determining the results of a belief change operation to that of satisfiability. This approach has several benefits. First, it furnishes an axiomatic specification of belief change with respect to belief change scenarios. This then leads to further insight into the belief change framework. Second, this axiomatization allows us to identify strict complexity bounds for the considered reasoning tasks. Third, we have implemented these different forms of belief change by means of existing solvers for quantified Boolean formulas. As well, it appears that this approach may be straightforwardly applied to other specific approaches to belief change
We present a general approach for representing and reasoning with sets of defaults in default logic, focusing on reasoning about preferences among sets of defaults. First, we consider how to control the application of a set of defaults so that either all apply (if possible) or none do (if not). From this, an approach to dealing with preferences among sets of default rules is developed. We begin with an ordered default theory, consisting of a standard default theory, but with possible preferences on sets of rules. This theory is transformed into a second, standard default theory wherein the preferences are respected. The approach differs from other work, in that we obtain standard default theories and do not rely on prioritized versions of default logic. In practical terms this means we can immediately use existing default logic theorem provers for an implementation. Also, we directly generate just those extensions containing the most preferred applied rules; in contrast, most previous approaches generate all extensions, then select the most preferred. In a major application of the approach, we show how semimonotonic default theories can be encoded so that reasoning can be carried out at the object level. With this, we can reason about default extensions from within the framework of a standard default logic. Hence one can encode notions such as skeptical and credulous conclusions, and can reason about such conclusions within a single extension
Interest in developing a new method of man-to-machine communication-a brain-computer interface (BCI)-has grown steadily over the past few decades. BCIs create a new communication channel between the brain and an output device by bypassing conventional motor output pathways of nerves and muscles. These systems use signals recorded from the scalp, the surface of the cortex, or from inside the brain to enable users to control a variety of applications including simple word-processing software and orthotics. BCI technology could therefore provide a new communication and control option for individuals who cannot otherwise express their wishes to the outside world. Signal processing and classification methods are essential tools in the development of improved BCI technology. We organized the BCI Competition 2003 to evaluate the current state of the art of these tools. Four laboratories well versed in EEG-based BCI research provided six data sets in a documented format. We made these data sets (i.e., labeled training sets and unlabeled test sets) and their descriptions available on the Internet. The goal in the competition was to maximize the performance measure for the test labels. Researchers worldwide tested their algorithms and competed for the best classification results. This paper describes the six data sets and the results and function of the most successful algorithms
Motivation: Continued development of analytical techniques based on gas chromatography and mass spectrometry now facilitates the generation of larger sets of metabolite concentration data. An important step towards the understanding of metabolite dynamics is the recognition of stable states where metabolite concentrations exhibit a simple behaviour. Such states can be characterized through the identification of significant thresholds in the concentrations. But general techniques for finding discretization thresholds in continuous data prove to be practically insufficient for detecting states due to the weak conditional dependences in concentration data. Results: We introduce a method of recognizing states in the framework of decision tree induction. It is based upon a global analysis of decision forests where stability and quality are evaluated. It leads to the detection of thresholds that are both comprehensible and robust. Applied to metabolite concentration data, this method has led to the discovery of hidden states in the corresponding variables. Some of these reflect known properties of the biological experiments, and others point to putative new states
A well-known result by Stein (1956) shows that in particular situations, biased estimators can yield better parameter estimates than their generally preferred unbiased counterparts. This letter follows the same spirit, as we will stabilize the unbiased generalization error estimates by regularization and finally obtain more robust model selection criteria for learning. We trade a small bias against a larger variance reduction, which has the beneficial effect of being more precise on a single training set. We focus on the subspace information criterion (SIC), which is an unbiased estimator of the expected generalization error measured by the reproducing kernel Hilbert space norm. SIC can be applied to the kernel regression, and it was shown in earlier experiments that a small regularization of SIC has a stabilization effect. However, it remained open how to appropriately determine the degree of regularization in SIC. In this article, we derive an unbiased estimator of the expected squared error, between SIC and the expected generalization error and propose determining the degree of regularization of SIC such that the estimator of the expected squared error is minimized. Computer simulations with artificial and real data sets illustrate that the proposed method works effectively for improving the precision of SIC, especially in the high-noise-level cases. We furthermore compare the proposed method to the original SIC, the cross-validation, and an empirical Bayesian method in ridge parameter selection, with good results