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Register a new userSupplementary Material for CDC Submission No. 1461
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Added by
Yue Ju
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In this paper, we focus on the influences of the condition number of the regression matrix upon the comparison between two hyper-parameter estimation methods: the empirical Bayes (EB) and the Steins unbiased estimator with respect to the mean square error (MSE) related to output prediction (SUREy). We firstly show that the greatest power of the condition number of the regression matrix of SUREy cost function convergence rate upper bound is always one larger than that of EB cost function convergence rate upper bound. Meanwhile, EB and SUREy hyper-parameter estimators are both proved to be asymptotically normally distributed under suitable conditions. In addition, one ridge regression case is further investigated to show that when the condition number of the regression matrix goes to infinity, the asymptotic variance of SUREy estimator tends to be larger than that of EB estimator.
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In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding bound is an immediate consequence of the theory. Moreover, we propose a rigorous and efficient method for probability estimation, which is an adaptive Monte Carlo estimation method based on truncated inverse binomial sampling. Our proposed method of probability estimation can be orders of magnitude more efficient as compared to existing methods in literature and widely used software.
In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the absolute value of the prediction error. The proposed scheme is based on a probabilistic scaling methodology in which the number of required randomized samples is independent of the complexity of the prediction model. The methodology is extended to address the case in which the probabilistic uncertain quantification is required to be valid for every member of a finite family of predictors. We illustrate the results of the paper by means of a numerical example.
This paper introduces a new technique for learning probabilistic models of mass and friction distributions of unknown objects, and performing robust sliding actions by using the learned models. The proposed method is executed in two consecutive phases. In the exploration phase, a table-top object is poked by a robot from different angles. The observed motions of the object are compared against simulated motions with various hypothesized mass and friction models. The simulation-to-reality gap is then differentiated with respect to the unknown mass and friction parameters, and the analytically computed gradient is used to optimize those parameters. Since it is difficult to disentangle the mass from the friction coefficients in low-data and quasi-static motion regimes, our approach retains a set of locally optimal pairs of mass and friction models. A probability distribution on the models is computed based on the relative accuracy of each pair of models. In the exploitation phase, a probabilistic planner is used to select a goal configuration and waypoints that are stable with a high confidence. The proposed technique is evaluated on real objects and using a real manipulator. The results show that this technique can not only identify accurately mass and friction coefficients of non-uniform heterogeneous objects, but can also be used to successfully slide an unknown object to the edge of a table and pick it up from there, without any human assistance or feedback.
This report includes the original manuscript (pp. 2-40) and the supplementary material (pp. 41-48) of Passive Mechanical Realizations of Bicubic Impedances with No More Than Five Elements for Inerter-Based Control Design.
In this supplementary material, we investigate further the impurity-induced freezing mechanism in a doped system of 3D weakly coupled ladders resembling Bi(Cu$_{1-x}$Zn$_x$)$_2$ZnPO$_6$ using large scale Quantum Monte Carlo simulations.
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