5 papers
Minimax estimation of the pseudo-spectral gap of continuous Markov chains, with applications to empirical concentration bounds
Vahe Karagulyan, Mikołaj Kasprzak, Pierre Alquier
We study the minimax estimation of the pseudo-spectral gap of a Markov chain from the observation of a single trajectory. Extending earlier works on finite-state space cha…
Empirical PAC-Bayes Bounds for Markov Chains
Vahe Karagulyan, Pierre Alquier
The core of generalization theory was developed for independent observations. Some PAC and PAC-Bayes bounds are available for data that exhibit a temporal dependence. However, ther…
Adaptive Mean Estimation in the Hidden Markov sub-Gaussian Mixture Model
Vahe Karagulyan, Mohamed Ndaoud
We investigate the problem of center estimation in the high dimensional binary sub-Gaussian Mixture Model with Hidden Markov structure on the labels. We first study the limitations…
Asymptotic estimates for double-coverings
Grigori A. Karagulyan, Vahe G. Karagulyan
A collection of finite sets is said to be a double-covering if each is included in exactly two sets of the collection. For fix…
On generalized lacunary series
Grigori A. Karagulyan, Vahe G. Karagulyan
Given lacunary sequence of integers, , , we define a new sequence formed by all possible -wise sums …