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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
PLATON
(2019)
Lesson planning is both an important and demanding task—especially as part of teacher training. This paper presents the requirements for a lesson planning system and evaluates existing systems regarding these requirements. One major drawback of existing software tools is that most are limited to a text- or form-based representation of the lesson designs. In this article, a new approach with a graphical, time-based representation with (automatic) analyses methods is proposed and the system architecture and domain model are described in detail. The approach is implemented in an interactive, web-based prototype called PLATON, which additionally supports the management of lessons in units as well as the modelling of teacher and student-generated resources. The prototype was evaluated in a study with 61 prospective teachers (bachelor’s and master’s preservice teachers as well as teacher trainees in post-university teacher training) in Berlin, Germany, with a focus on usability. The results show that this approach proofed usable for lesson planning and offers positive effects for the perception of time and self-reflection.
And/Or reasoning graphs for determining prime implicants in multi-level combinational networks
(1997)
Background: The biological interpretation of large-scale gene expression data is one of the paramount challenges in current bioinformatics. In particular, placing the results in the context of other available functional genomics data, such as existing bio-ontologies, has already provided substantial improvement for detecting and categorizing genes of interest. One common approach is to look for functional annotations that are significantly enriched within a group or cluster of genes, as compared to a reference group. Results: In this work, we suggest the information-theoretic concept of mutual information to investigate the relationship between groups of genes, as given by data-driven clustering, and their respective functional categories. Drawing upon related approaches (Gibbons and Roth, Genome Research 12: 1574-1581, 2002), we seek to quantify to what extent individual attributes are sufficient to characterize a given group or cluster of genes. Conclusion: We show that the mutual information provides a systematic framework to assess the relationship between groups or clusters of genes and their functional annotations in a quantitative way. Within this framework, the mutual information allows us to address and incorporate several important issues, such as the interdependence of functional annotations and combinatorial combinations of attributes. It thus supplements and extends the conventional search for overrepresented attributes within a group or cluster of genes. In particular taking combinations of attributes into account, the mutual information opens the way to uncover specific functional descriptions of a group of genes or clustering result. All datasets and functional annotations used in this study are publicly available. All scripts used in the analysis are provided as additional files.
The use of neural networks is considered as the state of the art in the field of image classification. A large number of different networks are available for this purpose, which, appropriately trained, permit a high level of classification accuracy. Typically, these networks are applied to uncompressed image data, since a corresponding training was also carried out using image data of similar high quality. However, if image data contains image errors, the classification accuracy deteriorates drastically. This applies in particular to coding artifacts which occur due to image and video compression. Typical application scenarios for video compression are narrowband transmission channels for which video coding is required but a subsequent classification is to be carried out on the receiver side. In this paper we present a special H.264/Advanced Video Codec (AVC) based video codec that allows certain regions of a picture to be coded with near constant picture quality in order to allow a reliable classification using neural networks, whereas the remaining image will be coded using constant bit rate. We have combined this feature with the ability to run with lowest latency properties, which is usually also required in remote control applications scenarios. The codec has been implemented as a fully hardwired High Definition video capable hardware architecture which is suitable for Field Programmable Gate Arrays.