Related papers: Running Markov chain without Markov basis
Sequential scaling is a prominent inference-time scaling paradigm, yet its performance improvements are typically modest and not well understood, largely due to the prevalence of heuristic, non-principled approaches that obscure clear…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
This paper presents a simple algorithm to check whether reachability probabilities in parametric Markov chains are monotonic in (some of) the parameters. The idea is to construct - only using the graph structure of the Markov chain and…
We consider the problem of constructing exact goodness-of-fit tests for discrete exponential family models. This classical problem remains practically unsolved for many types of structured or sparse data, as it rests on a computationally…
Markov chains have been widely employed as a fundamental model in the studies of probabilistic and stochastic communicating and concurrent systems. It is well-understood that decomposition techniques play a key role in reachability analysis…
Multistage stochastic optimization problems are oftentimes formulated informally in a pathwise way. These are correct in a discrete setting and suitable when addressing computational challenges, for example. But the pathwise problem…
Parametric Markov chains occur quite naturally in various applications: they can be used for a conservative analysis of probabilistic systems (no matter how the parameter is chosen, the system works to specification); they can be used to…
Lanczos-based methods have become standard tools for tasks involving matrix functions. Progress on these algorithms has been driven by several largely disjoint communities, resulting many innovative and important advancements which would…
Minimum-weight perfect matching (MWPM) has been been the primary classical algorithm for error correction in the surface code, since it is of low runtime complexity and achieves relatively low logical error rates [Phys. Rev. Lett. 108,…
Classical distribution testing assumes access to i.i.d. samples from the distribution that is being tested. We initiate the study of Markov chain testing, assuming access to a single trajectory of a Markov Chain. In particular, we observe a…
We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden…
Dating from the work of Neuts in the 1980s, the field of matrix-analytic methods has been developed to analyse discrete or continuous-time Markov chains with a two-dimensional state space in which the increment of a level variable is…
Quantitative model checkers for Markov Decision Processes typically use finite-precision arithmetic. If all the coefficients in the process are rational numbers, then the model checking results are rational, and so they can be computed…
Markov Chain Monte Carlo (MCMC) method is a widely used algorithm design scheme with many applications. To make efficient use of this method, the key step is to prove that the Markov chain is rapid mixing. Canonical paths is one of the two…
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…
Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…
We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…
In recent years probabilistic model checking has become an important area of research because of the diffusion of computational systems of stochastic nature. Despite its great success, standard probabilistic model checking suffers the…
This paper presents a novel framework for enhancing the quantum resistance of NTRUEncrypt using Markov Chain Monte Carlo (MCMC) methods. We establish formal bounds on sampling efficiency and provide security reductions to lattice problems,…
In this work, two algorithms are developed related to lattice codes. In the first one, an extended complete Gr\"obner basis is computed for the label code of a lattice. This basis supports all term orderings associated with a total degree…