相关论文: Stationary Algorithmic Probability
In this paper we study subsequences of random numbers. In Kamae (1973), selection functions that depend only on coordinates are studied, and their necessary and sufficient condition for the selected sequences to be normal numbers is given.…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
Our model is a constrained homogeneous random walk in a nonnegative orthant Z_+^d. The convergence to stationarity for such a random walk can often be checked by constructing a Lyapunov function. The same Lyapunov function can also be used…
We present some hardness results on finding the optimal policy for the static formulation of distributionally robust Markov decision processes. We construct problem instances such that when the considered policy class is Markovian and…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
We consider refined versions of Markov chains related to juggling introduced by Warrington. We further generalize the construction to juggling with arbitrary heights as well as infinitely many balls, which are expressed more succinctly in…
We show that there exists a universal quantum Turing machine (UQTM) that can simulate every other QTM until the other QTM has halted and then halt itself with probability one. This extends work by Bernstein and Vazirani who have shown that…
Natural selection explains how life has evolved over millions of years from more primitive forms. The speed at which this happens, however, has sometimes defied formal explanations when based on random (uniformly distributed) mutations.…
Sequential probability assignment and universal compression go hand in hand. We propose sequential probability assignment for non-binary (and large alphabet) sequences with empirical distributions whose parameters are known to be bounded…
In this paper, we present a novel iterative Monte Carlo method for approximating the stationary probability of a single state of a positive recurrent Markov chain. We utilize the characterization that the stationary probability of a state…
A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures…
Given a chain complex with the only modification that each cell of the complex has a probability distribution assigned. We will call this complex - a random complex and what should be understood in practice, is that we have a classical…
The main subject of the paper is everywhere complex sequences. An everywhere complex sequence is a sequence that does not contain substrings of Kolmogorov complexity less than $\alpha n-O(1)$ where $n$ is the length of substring and…
Rue and Held (2005) proposed a method for efficiently computing the Gaussian likelihood for stationary Markov random field models, when the data locations fall on a complete regular grid, and the model has no additive error term. The…
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…
A fundamental algorithm for selecting ranks from a finite subset of an ordered set is Radix Selection. This algorithm requires the data to be given as strings of symbols over an ordered alphabet, e.g., binary expansions of real numbers. Its…
We consider the value 1 problem for probabilistic automata over finite words: it asks whether a given probabilistic automaton accepts words with probability arbitrarily close to 1. This problem is known to be undecidable. However, different…
This is a chapter for the forthcoming New Handbook of Mathematical Psychology, to be published by Cambridge University Press. A systematic theory of random variables and joint distributions under varying conditions is presented. This is a…
It is well known that normality can be described as incompressibility via finite automata. Still the statement and the proof of this result as given by Becher and Heiber (2013) in terms of "lossless finite-state compressors" do not follow…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…