The recent success of multicast applications such as Internet teleconferencing illustrates the tremendous potential of applications built upon wide-area multicast communication services. A critical issue for such multicast applications and the higher layer protocols required to support them is the manner in which packet losses occur within the multicast network. In this paper we present and analyze packet loss data collected on multicast-capable hosts at 17 geographically distinct locations in Europe and the US and connected via the MBone. We experimentally and quantitatively examine the spatial and temporal correlation in packet loss among participants in a multicast session. Our results show that there is some spatial correlation in loss among the multicast sites. However, the shared loss in the backbone of the MBone is, for the most part, low. We find a fairly significant amount of of burst loss (consecutive losses) at most sites. In every dataset, at least one receiver experienced ...

The method of types is one of the key technical tools in Shannon Theory, and this tool is valuable also in other fields. In this paper, some key applications will be presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method, and a wide selection of further applications will be surveyed. These range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems. While the method of types is suitable primarily for discrete memoryless models, its extensions to certain models with memory will also be discussed. Index Terms---Arbitrarily varying channels, choice of decoder, counting approach, error exponents, extended type concepts, hypothesis testing, large deviations, multiuser problems, universal coding. I.

. The Bayesian Information Criterion (BIC) estimates the order of a Markov chain (with finite alphabet A) from observation of a sample path x 1 ; x 2 ; : : : ; x n , as that value k = k that minimizes the sum of the negative logarithm of the k-th order maximum likelihood and the penalty term jAj k (jAj\Gamma1) 2 log n: We show that k equals the correct order of the chain, eventually almost surely as n ! 1, thereby strengthening earlier consistency results that assumed an apriori bound on the order. A key tool is a strong ratio-typicality result for Markov sample paths. We also show that the Bayesian estimator or minimum description length estimator, of which the BIC estimator is an approximation, fails to be consistent for the uniformly distributed i.i.d. process. AMS 1991 subject classification: Primary 62F12, 62M05; Secondary 62F13, 60J10 Key words and phrases: Bayesian Information Criterion, order estimation, ratiotypicality, Markov chains. 1 Supported in part by a joint N...

We consider the estimation of the order, i.e., the number of hidden states, of a special class of discrete-time finite-alphabet hidden Markov sources. This class can be characterized in terms of equivalent renewal processes. No a priori bound is assumed on the maximum permissible order. An order estimator based on renewal types is constructed, and is shown to be strongly consistent by computing the precise asymptotics of the probability of estimation error. The probability of underestimation of the true order decays exponentially in the number of observations while the probability of overestimation goes to zero sufficiently fast. It is further shown that this estimator has the best possible error exponent in a large class of estimators. Our results are also valid for the general class of binary independent-renewal processes with finite mean renewal times.

The problem of learning forest-structured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu tree through adaptive thresholding is proposed. It is shown that this algorithm is both structurally consistent and risk consistent and the error probability of structure learning decays faster than any polynomial in the number of samples under fixed model size. For the high-dimensional scenario where the size of the model d and the number of edges k scale with the number of samples n, sufficient conditions on (n,d,k) are given for the algorithm to satisfy structural and risk consistencies. In addition, the extremal structures for learning are identified; we prove that the independent (resp. tree) model is the hardest (resp. easiest) to learn using the proposed algorithm in terms of error rates for structure learning.

We are studying long term sequence prediction (forecasting). We approach this by investigating criteria for choosing a compact useful state representation. The state is supposed to summarize useful information from the history. We want a method that is asymptotically consistent in the sense it will provably eventually only choose between alternatives that satisfy an optimality property related to the used criterion. We extend our work to the case where there is side information that one can take advantage of and, furthermore, we briefly discuss the active setting where an agent takes actions to achieve desirable outcomes.

Abstract. In this paper we obtain exponential upper bounds for the rate of convergence of a version of the algorithm Context, when the underlying tree is not necessarily bounded. The algorithm Context is a well-known tool to estimate the context tree of a Variable Length Markov Chain. As a consequence of the exponential bounds we obtain a strong consistency result. We generalize in this way several previous results in the field. 1.

Abstract. Most treatments of the model selection problem are either restricted to special situations (lag selection in AR, MA or ARMA models, regression selection, selection of a model out of a nested sequence) or to special selection methods (selection through testing or penalization). Our aim is to provide some basic tools for the analysis of model selection as a statistical decision problem, independently of the situation and of the method used. In order to achieve this objective, we embed model selection in the theoretical decision framework offered by modern Decision Theory. This allows us to obtain simple conditions under which pairwise comparison of models and penalization of objective functions arise naturally from preferences defined on the collection of statistical models under scrutiny. As a major application of our framework, we derive necessary and sufficient conditions for an information criterion to satisfy in the case of independent and identically distributed realizations in order to deliver almost surely the “true ” model out of a class of J models. “In probability ” versions of the previous results are also discussed. At last, some

Some upper bounds for the rate of convergence of penalized likelihood context tree estimators

inequalities for empirical unbounded context trees