Providing a very low critical probability pc means that certification occurs when the simulation ends after a large number of iterations m. We introduce `c the threshold associated to pc s.t. Table 5 shows that this approximation is excellent even for large pc. This shows that mis a little larger than mc = log(pc)/log(1 1/N). This section assumes that X = xo + σ X with X N(0n; In) and that h(x) = x>g τ with g Rn and kgk= 1 (w.l.o.g.).

Providing a very low critical probabilitypc means that certification occurs when the simulation ends after alarge number of iterationsm. On the other hand, the projection of X onto any other direction orthogonal tog remains normal distributed. For each couple of parameters(N,T)we make1000 runs and count the number of false positive(i.e. the number of times the algorithm wrongfully asserted thatp < pc). Combining the latter proposal withT we obtain again a proposal reversible w.r.t. Step4: Conclusionbyinduction Let l0 be any critical level such thatπ0(h(X) > l0) > 0. We consider the following induction hypothesisatiterationk: Hk On the event, Lk l0, The probability that the two particle systems are equal tends exponentiallyfastto1whent + .

Forouranalysis wedevise several concentration results forMarkovchains, including amaximal inequality for Markov chains, that may be of interest in their own right. As a byproduct of our analysis we also establish asymptotically optimal, finite-time guarantees for the case of multiple plays, and i.i.d.

In this paper, we develop a new change detection algorithm for detecting a change in the Markov kernel over a metric space in which the post-change kernel is unknown. Under the assumption that the pre- and post-change Markov kernel is geometrically ergodic, we derive an upper bound on the mean delay and a lower bound on the mean time between false alarms.

In this paper we define a probabilistic computational model which generalizes many noisy neural network models, including the recent work of Maass and Sontag [5]. We identify weak ergodicjty as the mechanism responsible for restriction of the computational power of probabilistic models to definite languages, independent of the characteristics of the noise: whether it is discrete or analog, or if it depends on the input or not, and independent of whether the variables are discrete or continuous. We give examples of weakly ergodic models including noisy computational systems with noise depending on the current state and inputs, aggregate models, and computational systems which update in continuous time. 1 Introduction Noisy neural networks were recently examined, e.g.

In this paper we define a probabilistic computational model which generalizes many noisy neural network models, including the recent work of Maass and Sontag [5]. We identify weak ergodicjty as the mechanism responsible for restriction of the computational power of probabilistic models to definite languages, independent of the characteristics of the noise: whether it is discrete or analog, or if it depends on the input or not, and independent of whether the variables are discrete or continuous. We give examples of weakly ergodic models including noisy computational systems with noise depending on the current state and inputs, aggregate models, and computational systems which update in continuous time. 1 Introduction Noisy neural networks were recently examined, e.g.

We consider recurrent analog neural nets where each gate is subject to Gaussian noise, or any other common noise distribution whose probability density function is nonzero on a large set.

We consider recurrent analog neural nets where each gate is subject to Gaussian noise, or any other common noise distribution whose probability density function is nonzero on a large set.

We consider recurrent analog neural nets where each gate is subject to Gaussian noise, or any other common noise distribution whose probability densityfunction is nonzero on a large set.