Related papers: On Algorithmic Robustness of Corrupted Markov Chai…

In the search engine of Google, the PageRank algorithm plays a crucial role in ranking the search results. The algorithm quantifies the importance of each web page based on the link structure of the web. We first provide an overview of the…

Despite its prevalence, probabilistic bisimilarity suffers from a lack of robustness under minuscule perturbations of the transition probabilities. This can lead to discontinuities in the probabilistic bisimilarity distance function,…

Modal regression, a widely used regression protocol, has been extensively investigated in statistical and machine learning communities due to its robustness to outliers and heavy-tailed noises. Understanding modal regression's theoretical…

Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…

A lumping of a Markov chain is a coordinate-wise projection of the chain. We characterise the entropy rate preservation of a lumping of an aperiodic and irreducible Markov chain on a finite state space by the random growth rate of the…

The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in…

We study the design of computationally efficient algorithms with provable guarantees, that are robust to adversarial (test time) perturbations. While there has been an proliferation of recent work on this topic due to its connections to…

We consider the computational task of sampling a bit string $x$ from a distribution $\pi(x)=|\langle x|\psi\rangle|^2$, where $\psi$ is the unique ground state of a local Hamiltonian $H$. Our main result describes a direct link between the…

We discuss a definition of robust dominant eigenvector of a family of stochastic matrices. Our focus is on application to ranking problems, where the proposed approach can be seen as a robust alternative to the standard PageRank technique.…

Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…

Probabilistic model checking is a useful technique for specifying and verifying properties of stochastic systems including randomized protocols and reinforcement learning models. Existing methods rely on the assumed structure and…

The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is…

Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…

Machine learning models have demonstrated remarkable success across diverse domains but remain vulnerable to adversarial attacks. Empirical defense mechanisms often fail, as new attacks constantly emerge, rendering existing defenses…

We consider the problem of reconstructing a rank-one matrix from a revealed subset of its entries when some of the revealed entries are corrupted with perturbations that are unknown and can be arbitrarily large. It is not known which…

Thanks to their extensive capacity, over-parameterized neural networks exhibit superior predictive capabilities and generalization. However, having a large parameter space is considered one of the main suspects of the neural networks'…

Dynamics in biological networks are in general robust against several perturbations. We investigate a coupled map network as a model motivated by gene regulatory networks and design systems which are robust against phenotypic perturbations…

A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures…

Despite their numerous successes, there are many scenarios where adversarial risk metrics do not provide an appropriate measure of robustness. For example, test-time perturbations may occur in a probabilistic manner rather than being…

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…