no code implementations • 16 Feb 2023 • Geoffrey Wolfer, Shun Watanabe
We consider the problem of testing the identity of a reversible Markov chain against a reference from a single trajectory of observations.
no code implementations • 13 Oct 2022 • Geoffrey Wolfer, Pierre Alquier
An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness features of the kernel.
no code implementations • 20 May 2021 • Sela Fried, Geoffrey Wolfer
Given access to a single long trajectory generated by an unknown irreducible Markov chain $M$, we simulate an $\alpha$-lazy version of $M$ which is ergodic.
no code implementations • 13 May 2021 • Sela Fried, Geoffrey Wolfer
In this work we relax the symmetry assumption and show that it is possible to perform identity testing under the much weaker assumption of reversibility, provided that the stationary distributions of the reference and of the unknown Markov chains are close under a distance notion related to the separation distance.
no code implementations • 14 Dec 2019 • Geoffrey Wolfer
This allows us to derive instance-dependent rates for estimating the matrix with respect to the induced uniform norm, and some of its mixing properties.
no code implementations • 1 Feb 2019 • Geoffrey Wolfer, Aryeh Kontorovich
Furthermore, even if an eigenvalue perturbation analysis with better dependence on $d$ were available, in the non-reversible case the connection between the spectral gap and the mixing time is not nearly as straightforward as in the reversible case.
no code implementations • 31 Jan 2019 • Geoffrey Wolfer, Aryeh Kontorovich
We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or $\varepsilon$-far from a given reference chain.
no code implementations • 13 Sep 2018 • Geoffrey Wolfer, Aryeh Kontorovich
We investigate the statistical complexity of estimating the parameters of a discrete-state Markov chain kernel from a single long sequence of state observations.
