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12
A tail inequality for suprema of unbounded empirical processes with applications to Markov chains
, 2008
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Concentration inequalities for dependent random variables via the martingale method
 ANNALS OF PROBABILITY
, 2008
"... The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, bounds are obtained on martingale differences associate ..."
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Cited by 31 (4 self)
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The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, bounds are obtained on martingale differences associated with the random sequences, which may be of independent interest. As applications of the main result, concentration inequalities are also derived for inhomogeneous Markov chains and hidden Markov chains, and an extremal property associated with their martingale difference bounds is established. This work complements and generalizes certain concentration inequalities obtained by Marton and Samson, while also providing different proofs of some known results.
Large deviation asymptotics and control variates for simulating large functions
, 2005
"... Consider the normalized partial sums of a realvalued function F of a Markov chain, φn: = n −1 n−1 F(Φ(k)), n ≥ 1. k=0 The chain {Φ(k) : k ≥ 0} takes values in a general state space X, with transition kernel P, and it is assumed that the Lyapunov drift condition holds: PV ≤ V −W +bIC where V: X → (0 ..."
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Cited by 18 (6 self)
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Consider the normalized partial sums of a realvalued function F of a Markov chain, φn: = n −1 n−1 F(Φ(k)), n ≥ 1. k=0 The chain {Φ(k) : k ≥ 0} takes values in a general state space X, with transition kernel P, and it is assumed that the Lyapunov drift condition holds: PV ≤ V −W +bIC where V: X → (0, ∞), W: X → [1, ∞), the set C is small, and W dominates F. Under these assumptions, the following conclusions are obtained: (i) It is known that this drift condition is equivalent to the existence of a unique invariant distribution π satisfying π(W) < ∞, and the Law of Large Numbers holds for any function F dominated by W: φn → φ: = π(F), a.s., n → ∞. (ii) The lower error probability defined by P{φn ≤ c}, for c < φ, n ≥ 1, satisfies a large deviation limit theorem when the function F satisfies a monotonicity condition. Under additional minor conditions an exact large deviations expansion is obtained. (iii) If W is nearmonotone then controlvariates are constructed based on the Lyapunov function V, providing a pair of estimators that together satisfy nontrivial large asymptotics for the lower and upper error probabilities. In an application to simulation of queues it is shown that exact large deviation asymptotics are possible even when the estimator does not satisfy a Central Limit Theorem.
Modeling the
 DOCSIS 1.1/2.0 MAC Protocol”, ICCCN03
, 2003
"... universal data compression; enumerative coding; tree models; Markov sources; method of types Efficient enumerative coding for tree sources is, in general, surprisingly intricate a simple uniform encoding of type classes, which is asymptotically optimal in expectation for many classical models such ..."
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Cited by 11 (2 self)
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universal data compression; enumerative coding; tree models; Markov sources; method of types Efficient enumerative coding for tree sources is, in general, surprisingly intricate a simple uniform encoding of type classes, which is asymptotically optimal in expectation for many classical models such as FSMs, turns out not to be so in this case. We describe an efficiently computable enumerative code that is universal in the family of tree models in the sense that, for a string emitted by an unknown source whose model is supported on a known tree, the expected normalized code length of the encoding approaches the entropy rate of the source with a convergence rate (K/2)(log n)/n, where K is the number of free parameters of the model family. Based on recent results characterizing type classes of context trees, the code consists of the index of the sequence in the tree type class, and an efficient description of the class itself using a nonuniform encoding of selected string counts. The results are extended to a twiceuniversal setting, where the tree underlying the source model is unknown.
Simulationbased uniform value function estimates of discounted and averagereward MDPs
 SIAM Journal on Control and Optimization
, 2004
"... Abstract — The value function of a Markov decision problem assigns to each policy its expected discounted reward. This expected reward can be estimated as the empirical average of the reward over many independent simulation runs. We derive bounds on the number of runs needed for the convergence of t ..."
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Cited by 9 (1 self)
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Abstract — The value function of a Markov decision problem assigns to each policy its expected discounted reward. This expected reward can be estimated as the empirical average of the reward over many independent simulation runs. We derive bounds on the number of runs needed for the convergence of the empirical average to the expected reward uniformly for a class of policies, in terms of the VC or pseudo dimension of the policy class. Uniform convergence results are also obtained for the average reward case. They can be extended to partially observed MDPs and Markov games. The results can be viewed as an extension of the probably approximately correct (PAC) learning theory for partially observable MDPs (POMDPs) and Markov games. I.
Finding the best mismatched detector for channel coding
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Online pairing of voip conversations
 The VLDB Journal
"... This paper answers the following question; given a multiplicity of evolving 1way conversations, can a machine or an algorithm discern the conversational pairs in an online fashion, without understanding the content of the communications? Our analysis indicates that this is possible, and can be achi ..."
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This paper answers the following question; given a multiplicity of evolving 1way conversations, can a machine or an algorithm discern the conversational pairs in an online fashion, without understanding the content of the communications? Our analysis indicates that this is possible, and can be achieved just by exploiting the temporal dynamics inherent in a conversation. We also show that our findings are applicable for anonymous and encrypted conversations over VoIP networks. We achieve this by exploiting the aperiodic interdeparture time of VoIP packets, hence trivializing each VoIP stream into a binary timeseries, indicating the voice activity of each stream. We propose effective techniques that progressively pair conversing parties with high accuracy and in a limited amount of time. Our findings are verified empirically on a dataset consisting of 1000 conversations. We obtain very high pairing accuracy that reaches 97 % after 5 minutes of voice conversations. Using a modeling approach we also demonstrate analytically that our result can be extended over an unlimited number of conversations.
WorstCase LargeDeviations Asymptotics with Application to Queueing and Information Theory∗
, 2007
"... An i.i.d. process X is considered on a compact metric space X. Its marginal distribution π is unknown, but is assumed to lie in a moment class of the form, P = {π: 〈π, fi 〉 = ci, i = 1,..., n}, where {fi} are realvalued, continuous functions on X, and {ci} are constants. The following conclusions ..."
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An i.i.d. process X is considered on a compact metric space X. Its marginal distribution π is unknown, but is assumed to lie in a moment class of the form, P = {π: 〈π, fi 〉 = ci, i = 1,..., n}, where {fi} are realvalued, continuous functions on X, and {ci} are constants. The following conclusions are obtained: (i) For any probability distribution µ on X, Sanov’s ratefunction for the empirical distributions of X is equal to the KullbackLeibler divergence D(µ ‖ π). The worstcase ratefunction is identified as L(µ): = inf pi∈P D(µ ‖ π) = sup λ∈R(f,c) µ, log(λTf) where f = (1, f1,..., fn) T, and R(f, c) ⊂ Rn+1 is a compact, convex set. (ii) A stochastic approximation algorithm for computing L is introduced based based on samples of the process X. (iii) A solution to the worstcase onedimensional largedeviations problem is obtained through properties of extremal distributions, generalizing Markov’s canonical distributions. (iv) Applications to robust hypotheses testing and to the theory of buffer overflows in queues are also developed.
unknown title
, 2005
"... www.elsevier.com/locate/spa Worstcase largedeviation asymptotics with application to queueing and information theory ✩ Charuhas Pandit a, Sean Meyn b,∗ ..."
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www.elsevier.com/locate/spa Worstcase largedeviation asymptotics with application to queueing and information theory ✩ Charuhas Pandit a, Sean Meyn b,∗