相关论文: An impossibility result for process discrimination

We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. As a corollary we obtain that uniformly recurrent morphic…

Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…

We give sufficient conditions on the rates of two asymmetric exclusion processes such that the existence of a blocking invariant measure for the first implies the existence of such a measure for the second. The main tool is a coupling…

The asymmetric switch process is a binary stochastic process that alternates between the values one and minus one, where the distributions of the time in these states may differ. Two versions of the process are considered: a non-stationary…

Binary classification is a fundamental task in machine learning, with applications spanning various scientific domains. Whether scientists are conducting fundamental research or refining practical applications, they typically assess and…

In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…

Finding the most probable explanation for observed variables in a Bayesian network is a notoriously intractable problem, particularly if there are hidden variables in the network. In this paper we examine the complexity of a related…

In our problem, we are given access to a number of sequences of nonnegative i.i.d. random variables, whose realizations are observed sequentially. All sequences are of the same finite length. The goal is to pick one element from each…

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…

The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process $X_0,X_1,...X_n$ has been considered by many authors from different points of view. It has long been known through…

Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…

We study the complexity of approximations to the normalized information distance. We introduce a hierarchy of computable approximations by considering the number of oscillations. This is a function version of the difference hierarchy for…

We construct long sequences of braids that are descending with respect to the standard order of braids (``Dehornoy order''), and we deduce that, contrary to all usual algebraic properties of braids, certain simple combinatorial statements…

Let us consider a pair signal-observation ((xn,yn),n 0) where the unobserved signal (xn) is a Markov chain and the observed component is such that, given the whole sequence (xn), the random variables (yn) are independent and the conditional…

Correlations for the Bell gedankenexperiment are constructed using probabilities given by quantum mechanics, and nonlocal information. They satisfy Bell's inequality and exhibit spatial non stationarity in angle. Correlations for three…

Consider Dyson's Hermitian Brownian motion model after a finite time S, where the process is started at N equidistant points on the real line. These N points after time S form a determinantal process and has a limit as N tends to infinity.…

We prove several results concerning classifications, based on successive observations $(X_1,..., X_n)$ of an unknown stationary and ergodic process, for membership in a given class of processes, such as the class of all finite order Markov…

We propose a natural, bivariate, generalization of the nonsingular similarity relations considered by T. Fine. We also provide an enumeration formulae and a generating tree for those relations. The latter allow us to give a new bijection…

We revisit the problem of statistical sequence matching initiated by Unnikrishnan (TIT 2015) and derive theoretical performance guarantees for sequential tests that have bounded expected stopping times. Specifically, in this problem, one is…

The well known prefer-one, prefer-opposite, and prefer-same binary de Bruijn sequences are all constructed using simple preference rules. We apply the technique of preference functions of span one to define q-ary sequences that generalize…