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Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…

This paper studies a Markov network model for unbalanced data, aiming to solve the problems of classification bias and insufficient minority class recognition ability of traditional machine learning models in environments with uneven class…

The accurate labeling of datasets is often both costly and time-consuming. Given an unlabeled dataset, programmatic weak supervision obtains probabilistic predictions for the labels by leveraging multiple weak labeling functions (LFs) that…

Intensive algorithmic efforts have been made to enable the rapid improvements of certificated robustness for complex ML models recently. However, current robustness certification methods are only able to certify under a limited perturbation…

There is a scalability gap between probabilistic and non-probabilistic verification. Probabilistic model checking tools are based either on explicit engines or on (Multi-Terminal) Binary Decision Diagrams. These structures are complemented…

We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…

We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is…

The embedding problem for Markov chains is a famous problem in probability theory and only partial results are available up till now. In this paper, we propose a variant of the embedding problem called the reversible embedding problem which…

In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump…

The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…

In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…

This paper proposes a new type of recurrence where we divide the Markov chains into intervals that start when the chain enters into a subset A, then sample another subset B far away from A and end when the chain again return to A. The…

We consider a two-node queue modeled as a two-dimensional random walk. In particular, we consider the case that one or both queues have finite buffers. We develop an approximation scheme based on the Markov reward approach to error bounds…

Methods for Bayesian simulation in the presence of computationally intractable likelihood functions are of growing interest. Termed likelihood-free samplers, standard simulation algorithms such as Markov chain Monte Carlo have been adapted…

We investigate the complexity of bilevel combinatorial optimization with uncertainty in the follower's objective, in a robust optimization approach. We show that the robust counterpart of the bilevel problem under interval uncertainty can…

Let $(M,d,\mu)$ be a uniformly discrete metric measure space satisfying space homogeneous volume doubling condition. We consider discrete time Markov chains on $M$ symmetric with respect to $\mu$ and whose one-step transition density is…

Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…

This paper develops a Bayesian computational platform at the interface between posterior sampling and optimization in models whose marginal likelihoods are difficult to evaluate. Inspired by adversarial optimization, namely Generative…

We study the algorithmic robustness of general finite Markov chains in terms of their stationary distributions to general, adversarial corruptions of the transition matrix. We show that for Markov chains admitting a spectral gap, variants…

If the state space of a homogeneous continuous-time Markov chain is too large, making inferences - here limited to determining marginal or limit expectations - becomes computationally infeasible. Fortunately, the state space of such a chain…