P. Bartlett, P. Fischer, and K.U. Ho#gen. Exploiting random walks for learning. In Proceedings of the Seventh Annual Conference on Computational Learning Theory, pages 318--327, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....memoryless case and to enter the world of dynamical systems. Our contribution should be thought of as an attempt to bridge the existing gap between learning theory and the theory of identification of dynamical systems. For other approaches to addressing dependency we refer the reader to [7] and [8]. 2 Problem Description Consider a single input, single output system with input u t 2 U and output y t 2 Y , where U and Y are totally bounded subsets of R. We assume that y t is conditionally independent of u t 1 ; y Gamma1 and y t 1 given u (throughout, u r : u r ; u r 1 ; ....

P. L. Bartlett, P. Fischer and K-U. Hoffgen, "Exploiting random walks for learning, " COLT94, 1994.

....other (in time sense) the learner obtains a model which is closed to i.i.d. In this paper we estimate the sample sizes which would make this approximation possible and in particular to show that the required sample sizes are polynomial. This approach has been used by Bartlett, Fischer and Hoffgen [4] specifically for uniform random walks on a binary cube. The PAC learning for a Markov chain with countably infinite state space is more complicated. Such a Markov chain does not necessarily have a steady state distribution. And even if a steady state distribution exists and Markov chain is ....

....ffl and confidence ffi when X t is a Markov chain. 2. Observe that the sample size required for PAC learning depends linearly on log jX j. Thus fast learning is possible even if the state space is exponentially large (for example is a binary cube) 3. Theorem 1 is a generalization of Theorem 3. 3 [4] to arbitrary finite state Markov chains. The proof is based on establishing an analogue of Lemmas 3.1, 3.2 [4] However, unlike [4] we do not assume that the Markov chain is in steady state. We now refine Theorem 1 for reversible Markov chains. As we mentioned above, for reversible Markov chains ....

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P. Bartlett, P. Fischer, and K. Hoffgen. Exploiting random walks for learning. Proc. 7th ACM Conf. on Computational Learning Theory, 1994.

....m ) is an outcome of this process, where x i is distributed according to j (i) i = 0, m. To exhibit the potentiality of our method, we measure the sample complexity of learning to classify correctly the next labelled example rather than referring to a fixed testing distribution (see, e.g. [2, 4]) 8 . Now the advantage of the strong separation between P and M in the notion of (P,M) learnability is highly evident. Suppose we are in the error free case. In Definition 1 set Q to the distribution of x m and P to the distribution of the next point x m 1 . The sample complexity of the ....

.... x 1 , x d and initial distribution j (0) ek d 1 , ek d 1 , 1 ek ) 9 . Set P to the distribution j (m 1) j (0) P m 1 . 7 Vectors are intended as row vectors. 8 The reader should note the difference between our model and the bounded mistake rate model of [4]. We are clearly making a distinction between training and testing phases: at the end of training a testing phase begins and the hypothesis produced cannot be updated anymore. 9 Note that j (0) is quite near the limit j ( ek (1 ek) d 1) ek (1 ek) d 1) 1 (1 ek) ....

P.L. BARTLETT, P. FISCHER, K. HÖFFGEN, Exploiting Random Walks for Learning, in: Proc. of the 7th Workshop on Comput. Learning Th., (Morgan Kaufmann, New Brunswick, NJ, 1994) 318-327.

....memoryless case and to enter the world of dynamical systems. Our contribution should be thought of as an attempt to bridge the existing gap between learning theory and the theory of identification of dynamical systems. For other approaches to addressing dependency we refer the reader to [7] and [8]. 2 Problem Description Consider a single input, single output system with input u t 2 U and output y t 2 Y , where U and Y are totally bounded subsets of R. We assume that y t is conditionally independent of u 1 t 1 ; y t Gamma1 Gamma1 and y 1 t 1 given u t Gamma1 (throughout, u s ....

P. L. Bartlett, P. Fischer and K-U. Hoffgen, "Exploiting random walks for learning, " COLT94, 1994.

....labels to be subject to noise. There are many other possible models for classi cation whichwe do not consider here. These include models which assume that there exists a target function belonging to a particular class of functions [41, 66] relax the assumption of independently generated examples [1, 7], allow for drift in the generating distribution [4, 8, 33] and relax the assumption that there is a xed relationship between measurements and class labels [6, 12, 39] Typically, the measurement space X is taken to be some subset of # . For the sake of simplicity,we will almost exclusively ....

P.L.Bartlett,P.Fischer, and K. Hogen. Exploiting random walks for learning. In Proceedings of the 7th Annual ACM Workshop on Computational Learning Theory, pages 318-327. ACM Press, 1994.

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P. Bartlett, P. Fischer, and K.U. Ho#gen. Exploiting random walks for learning. In Proceedings of the Seventh Annual Conference on Computational Learning Theory, pages 318--327, 1994.

No context found.

P. Bartlett, P. Fischer, and K.-U. Ho#gen. Exploiting random walks for learning. In Proc. 7th Ann. Workshop on Comp. Learning Theory, pages 318--327, 1994.

No context found.

P. Bartlett, P. Fischer, and K. Ho#gen. Exploiting random walks for learning. Proc. 7th ACM Conf. on Computational Learning Theory, 1994.

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