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- W2255026220 abstract "We first consider system classification as a learning problem and study a class realized by continuous-time linear control systems. The difficulty of learning is characterized by the Vapnik-Chervonenkis (VC) dimension of the class of such mappings with binary output classifications. We provide upper and lower bounds for the VC-dimension in terms of the system dimensions and constants related to controls. Also, pseudo-dimension bounds are given for studying the input-output behavior without classification. For systems with bounded controls and parameters, fat-shattering bounds are proved in terms of the dimension of the parameter set and the Lipschitz constant associated to the systems. A control application motivates the problem of learning with side information in which each random sample x gives rise to a translate s(x), where s is a known side information mapping. Both x and s(x) are classified for training, but the aim is to classify correctly only a future unseen x-sample. The learning utilizes non-i.i.d. data and the training and evaluation spaces are different. First we consider a simple problem pointing to phenomena that hold more generally: we calculate exact learning rates for a fixed algorithm for learning an interval on the unit circle under the uniform distribution and reflection as side information. Typically, learning rates with side information correspond to traditional learning with twice as large a sample, but this may fail for some targets. In general, the advantage of side information depends on the distribution, learning algorithm and due to non-i.i.d. data there is an interaction between the target and the side information mapping. We incorporate side information in the analysis of uniform convergence of empirical probabilities. Two convergence bounds are analyzed and the exponential improvement in the convergence rate is indicated. As a new technique the bound utilizing Hoeffding's inequality is studied in the large deviations setting. The best improvement doubles the sample size in a bound for consistent algorithms and the sample size is multiplied by 4 in a general convergence bound. However, there are cases in which the exponential improvement due to side information fails." @default.
- W2255026220 created "2016-06-24" @default.
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- W2255026220 date "1999-01-01" @default.
- W2255026220 modified "2023-09-28" @default.
- W2255026220 title "Learning theory techniques in control theory" @default.
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