Related papers: On Algorithmic Robustness of Corrupted Markov Chai…
Upper bounds are derived on the total variation distance between the invariant distributions of two stochastic matrices differing on a subset W of rows. Such bounds depend on three parameters: the mixing time and the minimal expected…
We recall the classical formulation of PageRank as the stationary distribution of a singularly perturbed irreducible Markov chain that is not irreducible when the perturbation parameter goes to zero. Specifically, we use the Markov chain…
Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…
Markov Chain Monte Carlo (MCMC) is a flexible approach to approximate sampling from intractable probability distributions, with a rich theoretical foundation and comprising a wealth of exemplar algorithms. While the qualitative correctness…
Synthetic corruptions gathered into a benchmark are frequently used to measure neural network robustness to distribution shifts. However, robustness to synthetic corruption benchmarks is not always predictive of robustness to distribution…
We argue that the vulnerability of model parameters is of crucial value to the study of model robustness and generalization but little research has been devoted to understanding this matter. In this work, we propose an indicator to measure…
The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…
The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the…
Numerous modern optimization and machine learning algorithms rely on subgradient information being trustworthy and hence, they may fail to converge when such information is corrupted. In this paper, we consider the setting where subgradient…
There is a tension between robustness and efficiency when designing Markov chain Monte Carlo (MCMC) sampling algorithms. Here we focus on robustness with respect to tuning parameters, showing that more sophisticated algorithms tend to be…
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
Perturbation analysis of Markov chains provides bounds on the effect that a change in a Markov transition matrix has on the corresponding stationary distribution. This paper compares and analyzes bounds found in the literature for finite…
In this paper, we first extend the celebrated PageRank modification to a higher-order Markov chain. Although this system has attractive theoretical properties, it is computationally intractable for many interesting problems. We next study a…
We study the stability with respect to perturbations and the accuracy of numerical algorithms for computing solutions to the multilinear PageRank problem $\mathbf{x} = (1-\alpha)\mathbf{v} + \alpha \mathcal{P} \mathbf{x}^2$. Our results…
We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary…
We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated…
In today's era of big data, robust least-squares regression becomes a more challenging problem when considering the adversarial corruption along with explosive growth of datasets. Traditional robust methods can handle the noise but suffer…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
This paper is a survey of various proofs of the so called {\em fundamental theorem of Markov chains}: every ergodic Markov chain has a unique positive stationary distribution and the chain attains this distribution in the limit independent…
With the increasing scale of communication networks, the likelihood of failures grows as well. Since these networks form a critical backbone of our digital society, it is important that they rely on robust routing algorithms which ensure…