Related papers: A coupling approach to random circle maps expandin…
For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of $n$ variables $K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on coupling and decay of…
The evolution of random undirected graphs by the clustering attachment (CA) both without node and edge deletion and with uniform node or edge deletion is investigated. Theoretical results are obtained for the CA without node and edge…
We prove existence of (at most denumerable many) absolutely continuous invariant probability measures for random one-dimensional dynamical systems with asymptotic expansion. If the rate of expansion (Lyapunov exponents) is bounded away from…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
Yurinskii's coupling is a popular theoretical tool for non-asymptotic distributional analysis in mathematical statistics and applied probability, offering a Gaussian strong approximation with an explicit error bound under easily verifiable…
Takens constructed a residual subset of the state space consisting of initial points with historic behaviour for expanding maps on the circle. We prove that this statistical property of expanding maps on the circle is preserved under small…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
We study the property of global-local mixing for full-branched expanding maps of either the half-line or the interval, with one indifferent fixed point. Global-local mixing expresses the decorrelation of global vs local observables w.r.t.…
The couplings between the Ising model and its graphical representations, the random-cluster, random current and loop $\mathrm{O}(1)$ models, are put on common footing through a generalization of the Swendsen-Wang-Edwards-Sokal coupling. A…
A common approach to aggregate classification estimates in an ensemble of decision trees is to either use voting or to average the probabilities for each class. The latter takes uncertainty into account, but not the reliability of the…
On a compact group the Haar probability measure plays the role of uniform distribution. The entropy and rate distortion theory for this uniform distribution is studied. New results and simplified proofs on convergence of convolutions on…
We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the…
Symmetry-aware methods for machine learning, such as data augmentation and equivariant architectures, encourage correct model behavior on all transformations (e.g. rotations or permutations) of the original dataset. These methods can…
Ensembling is now recognized as an effective approach for increasing the predictive performance and calibration of deep networks. We introduce a new approach, Parameter Ensembling by Perturbation (PEP), that constructs an ensemble of…
The phenomena of synchronization and nontrivial collective behavior are studied in a model of coupled chaotic maps with random global coupling. The mean field of the system is coupled to a fraction of elements randomly chosen at any given…
We consider piecewise expanding maps of the interval with finitely many branches of monotonicity and show that they are generically combinatorially stable, i.e., the number of ergodic attractors and their corresponding mixing periods do not…
We study the long-term behavior of the iteration of a random map consisting of Lipschitz transformations on a compact metric space, independently and randomly selected according to a fixed probability measure. Such a random map is said to…
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…
For a Coupled Map Lattice with a specific strong coupling emulating Stavskaya's probabilistic cellular automata, we prove the existence of a phase transition using a Peierls argument, and exponential convergence to the invariant measures…