We study the computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded degree can be learned in polynomial time and...
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We study the computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded degree can be learned in polynomial time and from a polynomial number of training examples, assuming that the data is generated by a network in this class. This result covers both parameter estimation for a known network structure and structurelearning. It implies as a corollary that we can learn factor graphs for both Bayesian networks and Markov networks of bounded degree, in polynomial time and sample complexity. Importantly, unlike standard maximum likelihood estimation algorithms, our method does not require inference in the underlying network, and so applies to networks where inference is intractable. We also show that the error of our learned model degrades gracefully when the generating distribution is not a member of the target class of networks. In addition to our main result, we show that the sample complexity of parameterlearning in graphical models has an O(1) dependence on the number of variables in the model when using the KL-divergence normalized by the number of variables as the performance criterion.(1)
This paper proposes an adaptive neuro-fuzzy system, HyFIS (Hybrid neural Fuzzy Inference System), for building and optimising fuzzy models. The proposed model introduces the learning power of neural networks to fuzzy ...
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This paper proposes an adaptive neuro-fuzzy system, HyFIS (Hybrid neural Fuzzy Inference System), for building and optimising fuzzy models. The proposed model introduces the learning power of neural networks to fuzzy logic systems and provides linguistic meaning to the connectionist architectures. Heuristic fuzzy logic rules and input-output fuzzy membership functions can be optimally tuned from training examples by a hybrid learning scheme comprised of two phases: rule generation phase from data;and rule tuning phase using error backpropagation learning scheme for a neural fuzzy system. To illustrate the performance and applicability of the proposed neuro-fuzzy hybrid model, extensive simulation studies of nonlinear complex dynamic systems are carried out. The proposed method can be applied to an on-line incremental adaptive learning for the prediction and control of nonlinear dynamical systems. Two benchmark case studies are used to demonstrate that the proposed HyFIS system is a superior neuro-fuzzy modelling technique. (C) 1999 Elsevier Science Ltd. All rights reserved.
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