arXiv subjects

Kevin O'Connor

Publications and source records attributed to Kevin O'Connor.

6 recordsLinked to original sources

arXiv2024

Sampling low-fidelity outputs for estimation of high-fidelity density and its tails

In a multifidelity setting, data are available under the same conditions from two (or more) sources, e.g. computer codes, one being lower-fidelity but computationally cheaper, and the other higher-fidelity and more expensive. This work studies for which low-fidelity outputs, one should obtain high-fidelity outputs, if the goal is to estimate the probability density function of the latter, especially when it comes to the distribution tails and extremes. It is suggested to approach this problem from the perspective of the importance sampling of low-fidelity outputs according to some proposal distribution, combined with special considerations for the distribution tails based on extreme value theory. The notion of an optimal proposal distribution is introduced and investigated, in both theory and simulations. The approach is motivated and illustrated with an application to estimate the probability density function of record extremes of ship motions, obtained through two computer codes of different fidelities.

stat.ME↗

arXiv2024

Alignment and Comparison of Directed Networks via Transition Couplings of Random Walks

We describe and study a transport based procedure called NetOTC (network optimal transition coupling) for the comparison and alignment of two networks. The networks of interest may be directed or undirected, weighted or unweighted, and may have distinct vertex sets of different sizes. Given two networks and a cost function relating their vertices, NetOTC finds a transition coupling of their associated random walks having minimum expected cost. The minimizing cost quantifies the difference between the networks, while the optimal transport plan itself provides alignments of both the vertices and the edges of the two networks. Coupling of the full random walks, rather than their marginal distributions, ensures that NetOTC captures local and global information about the networks, and preserves edges. NetOTC has no free parameters, and does not rely on randomization. We investigate a number of theoretical properties of NetOTC and present experiments establishing its empirical performance.

cs.LG↗

arXiv2022

Nanoscale Thermal Imaging of VO$_2$ via Poole-Frenkel Conduction

We present a method for nanoscale thermal imaging of insulating thin films using atomic force microscopy (AFM), and we demonstrate its utility on VO$_2$. We sweep the applied voltage $V$ to a conducting AFM tip in contact mode and measure the local current $I$ through the film. By fitting the $IV$ curves to a Poole-Frenkel conduction model at low $V$, we calculate the local temperature with spatial resolution better than 50 nm using only fundamental constants and known film properties. Our thermometry technique enables local temperature measurement of \textit{any} insulating film dominated by the Poole-Frenkel conduction mechanism, and can be extended to insulators that display other conduction mechanisms.

cond-mat.str-el↗

arXiv2021

Estimation of Stationary Optimal Transport Plans

We study optimal transport for stationary stochastic processes taking values in finite spaces. In order to reflect the stationarity of the underlying processes, we restrict attention to stationary couplings, also known as joinings. The resulting optimal joining problem captures differences in the long run average behavior of the processes of interest. We introduce estimators of both optimal joinings and the optimal joining cost, and we establish consistency of the estimators under mild conditions. Furthermore, under stronger mixing assumptions we establish finite-sample error rates for the estimated optimal joining cost that extend the best known results in the iid case. Finally, we extend the consistency and rate analysis to an entropy-penalized version of the optimal joining problem.

math.ST↗

arXiv2021

Optimal Transport for Stationary Markov Chains via Policy Iteration

We study the optimal transport problem for pairs of stationary finite-state Markov chains, with an emphasis on the computation of optimal transition couplings. Transition couplings are a constrained family of transport plans that capture the dynamics of Markov chains. Solutions of the optimal transition coupling (OTC) problem correspond to alignments of the two chains that minimize long-term average cost. We establish a connection between the OTC problem and Markov decision processes, and show that solutions of the OTC problem can be obtained via an adaptation of policy iteration. For settings with large state spaces, we develop a fast approximate algorithm based on an entropy-regularized version of the OTC problem, and provide bounds on its per-iteration complexity. We establish a stability result for both the regularized and unregularized algorithms, from which a statistical consistency result follows as a corollary. We validate our theoretical results empirically through a simulation study, demonstrating that the approximate algorithm exhibits faster overall runtime with low error. Finally, we extend the setting and application of our methods to hidden Markov models, and illustrate the potential use of the proposed algorithms in practice with an application to computer-generated music.

math.OC↗

arXiv2019

Exchangeable Generative Models with Flow Scans

In this work, we develop a new approach to generative density estimation for exchangeable, non-i.i.d. data. The proposed framework, FlowScan, combines invertible flow transformations with a sorted scan to flexibly model the data while preserving exchangeability. Unlike most existing methods, FlowScan exploits the intradependencies within sets to learn both global and local structure. FlowScan represents the first approach that is able to apply sequential methods to exchangeable density estimation without resorting to averaging over all possible permutations. We achieve new state-of-the-art performance on point cloud and image set modeling.

cs.LG↗