We use neural networks as control variates with geometric integration techniques.
problem Analytic integration of neural network approximations for variance reduction.
method Integration domain subdivision using computational geometry for MLPs with continuous piecewise linear activation functions.
result Neural networks can be used as control variates with geometric integration methods.
NCV uses neural networks to improve Monte Carlo integration.
problem Improving variance reduction in parametric Monte Carlo integration.
method NCV combines a normalizing flow and a neural network to approximate the integrand and solve the integral equation, with a neural importance sampler to estimate the difference.
result NCV achieves state-of-the-art performance in light transport simulation with reduced noise and negligible bias.
Paper relaxes optimal transport using convex functions for data science.
problem Optimal transport problem on finite spaces.
method Relaxation via strictly convex functions (Kullback-Leibler divergence, Bregman divergences). Gradient descent iterative process.
result Mathematical foundations and iterative process for the relaxed optimal transport problem.
Measuring sentence similarity is a classic topic in natural language processing. Light-weighted similarities are still of particular practical significance even when deep learning models have succeeded in many other tasks. Some light-weighted similarities with more theoretical insights have been demonstrated to be even…
Generates samples conditioned on labels using optimal transport.
problem Estimating conditional distributions for specific labels.
method Wasserstein geodesic generator based on optimal transport theory.
result Learned conditional distributions and optimal transport maps.
We review a numerical technique, referred to as the Transport-based Mesh-free Method (TMM), and we discuss its applications to mathematical finance. We recently introduced this method from a numerical standpoint and investigated the accuracy of integration formulas based on the Monte-Carlo methodology: quantitative err…
New emulator bridges simulators using conditional optimal transport.
problem Bridging simulators with minimal distortion.
method Flow-based approach to learn likelihood transport, COT-FM for optimal matching.
result Emulator accurately captures full correction between simulators.
Accelerates pulsar light curve inference with learned representations and optimization.
problem Computational expense of Markov chain Monte Carlo methods for posterior inference.
method Combining U-Net latent representations with local simulator-guided optimization.
result 120x reduction in inference time (24 hours to 12 minutes) with accuracy preserved.
Study Hilbert's projective metric for bounded growth functions leading to Sinkhorn's algorithm convergence.
problem Optimal transport in unbounded settings with heavy-tailed distributions.
method Hilbert's projective metric for integrable functions of bounded growth, kernel integral operators as contractions.
result Exponential convergence of Sinkhorn's algorithm for light-tailed marginal distributions.
The paper uses optimal transport to calibrate stochastic simulations.
problem Improper fidelity of stochastic simulators in scientific applications.
method Optimal transport theory applied to neural network corrections.
result Calibrated stochastic simulations improve fidelity to reality.
Novel proof shows continuity of optimal transport feasible set mapping.
problem Continuity of feasible set mapping in optimal transport problems.
method Presented a novel and shorter proof of continuity.
result Established continuity of the feasible set mapping.
This short article revisits some of the ideas introduced in arXiv:1701.07875 and arXiv:1705.07642 in a simple setup. This sheds some lights on the connexions between Variational Autoencoders (VAE), Generative Adversarial Networks (GAN) and Minimum Kantorovitch Estimators (MKE).
Cooperative communication plays a central role in theories of human cognition, language, development, culture, and human-robot interaction. Prior models of cooperative communication are algorithmic in nature and do not shed light on why cooperation may yield effective belief transmission and what limitations may arise …
Extends geostatistical simulation method to handle multiple variables and large grids.
problem Scalability and handling of multiple variables in geostatistical simulation.
method Uses Sinkhorn optimal transport with sparse matcher and FFT-MA Gaussian backbone.
result MST-Direct reproduces joint distribution with zero histogram error and accurately preserves spatial correlation.
Intelligent Transportation Systems (ITSs) are envisioned to play a critical role in improving traffic flow and reducing congestion, which is a pervasive issue impacting urban areas around the globe. Rapidly advancing vehicular communication and edge cloud computation technologies provide key enablers for smart traffic …
The feature map obtained from the denoising autoencoder (DAE) is investigated by determining transportation dynamics of the DAE, which is a cornerstone for deep learning. Despite the rapid development in its application, deep neural networks remain analytically unexplained, because the feature maps are nested and param…
Solves open problem on simple surfaces with novel twistor correspondence.
problem Existence of nontrivial holomorphic vector bundles on simple surfaces.
method Novel twistor correspondence, Nash-Moser inverse function theorem, and microlocal analysis.
result Simple surface twistor space supports no nontrivial holomorphic vector bundles.
We analyze errors in filtering algorithms using optimal transport.
problem Estimation errors in optimal transport-based filtering algorithms.
method Systematic analysis of estimation errors for conditional Brenier maps.
result Demonstrates effectiveness and practical potential of the optimal transport filtering algorithm.
Paper uses DeePC to improve urban traffic lights, reducing congestion and emissions.
problem Urban traffic congestion in expanding cities.
method Behavioral system theory, data-driven control, DeePC algorithm.
result DeePC outperforms existing traffic control methods in travel time and CO2 emissions.
Existing inefficient traffic light control causes numerous problems, such as long delay and waste of energy. To improve efficiency, taking real-time traffic information as an input and dynamically adjusting the traffic light duration accordingly is a must. In terms of how to dynamically adjust traffic signals' duration…
Bayesian calibration improves ABMs for predicting travel patterns.
problem Calibrating ABMs for accurate travel pattern predictions.
method Gaussian Process emulator with deep learning dimensionality reduction for high-dimensional, non-stationary data.
result Improved accuracy in predicting travel patterns using traffic flow data.
In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of …
Novel algorithm solves optimal transport using evolving probability distributions and convolution.
problem Sample-based optimal transport problem.
method Adversarial formulation with convolution of adaptive kernel and evolving measure.
result Algorithm robust to dimensionality and produces complex maps.
This work introduces benchmarks for evaluating nanophotonic structures in design simulations.
problem Design and understanding of nanophotonic structures for various applications.
method Development of frameworks and benchmarks for evaluating nanophotonic structures in parametric design problems.
result Strategic use of evaluation fidelity in enhancing structure designs.
A new method for averaging probability distributions based on optimal weak mass transport.
problem Averaging probability distributions in a geometric way.
method Weak barycenters based on optimal weak mass transport.
result Extracts common geometric information shared by all input distributions.
New methods target conditional demographic parity using optimal transport distances.
problem Auditing and enforcing conditional demographic parity (CDP) in models with complex conditioning variables.
method Developed novel measures of conditional demographic disparity (CDD) based on optimal transport distances and regularization-based approaches.
result Validated methods airbit{} and airlp{} effectively target CDP in real-world datasets with continuous model outputs.
Optimal transport calibrates machine learning models for particle physics simulations.
problem Discrepancies between simulation and experimental data limit machine learning effectiveness.
method A model calibration approach based on optimal transport applied to high-dimensional simulations.
result Calibrated high-dimensional representations enable proper calibration of various downstream quantities.
Estimates conditional Brenier maps using entropic optimal transport.
problem Non-parametric estimation of conditional Brenier maps.
method Entropic optimal transport for scalable non-parametric estimation.
result Entropic optimal transport maps asymptotically converge to conditional Brenier maps.
Develops active learning for scale-bridging simulations.
problem Quantitative predictions in nanoporous media and inertial confinement fusion.
method Active learning approach to optimize fine-scale simulations for coarse-scale hydrodynamics.
result Optimizes use of fine-scale simulations for coarse-scale predictions.
Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry originates from coordinate-invariant properties of statistical inference. Their con…
Structural and topological information play a key role in modeling flow and transport through fractured rock in the subsurface. Discrete fracture network (DFN) computational suites such as dfnWorks are designed to simulate flow and transport in such porous media. Flow and transport calculations reveal that a small back…
New framework for conditional risk minimization using optimal transport.
problem High-stakes decisions with side information, especially economic conditions.
method Universal framework based on union-ball formulation in optimal transport.
result Offers interpretability, tractability, and scalability for various risk functionals.
A new framework for generative modeling using value-driven transport.
problem Developing efficient methods for generative modeling.
method A discrete-time stochastic control formulation of measure transport, formulated as a linear program with dual variables corresponding to the optimal value function.
result Well-trained VDT policies lead to straight transport paths that can be simulated quickly and robustly.
We present a technique for efficiently synthesizing images of atmospheric clouds using a combination of Monte Carlo integration and neural networks. The intricacies of Lorenz-Mie scattering and the high albedo of cloud-forming aerosols make rendering of clouds---e.g. the characteristic silverlining and the "whiteness" …
Models of spatial firm competition assume that customers are distributed in space and transportation costs are associated with their purchases of products from a small number of firms that are also placed at definite locations. It has been long known that the competition equilibrium is not guaranteed to exist if the mo…
We explore the use of deep learning and deep reinforcement learning for optimization problems in transportation. Many transportation system analysis tasks are formulated as an optimization problem - such as optimal control problems in intelligent transportation systems and long term urban planning. Often transportation…
In this paper we outline methodology to efficiently simulate (jump) diffusion bridge sample paths without discretisation error. We achieve this by considering the simulation of conditioned (jump) diffusion bridge sample paths in light of recent work developing a mathematical framework for simulating finite dimensional …
New algorithm reduces variance in Monte Carlo simulations using deep neural networks and policy gradients.
problem Reducing variance in Monte Carlo simulations for estimating function values.
method Optimal correlation search using deep neural networks and policy gradients.
result Optimal correlation function reduces variance by approximating and calibrating policy.
Developed a cost and revenue model for HEMS to estimate breakeven transport volumes under different reimbursement and labor cost assumptions.
problem Estimating breakeven transport volumes for HEMS under varying reimbursement and labor cost assumptions.
method Developed a two-part model: cost framework and actuarial revenue model using healthcare encounter data and payer reimbursement rates.
result Estimated breakeven transport volumes under different reimbursement and labor cost assumptions.
Researchers analyze inverse optimal transport, deriving theoretical and empirical insights.
problem Understanding the inverse problem of inferring cost matrices from optimal couplings.
method Formalized and analyzed using entropy-regularized optimal transport, with theoretical and empirical contributions.
result Characterization of the manifold of cross-ratio equivalent costs and derivation of an MCMC sampler.
New method uses nested optimal transport for financial time series evaluation.
problem Lack of consensus metric for evaluating generative models in finance.
method Nested optimal transport distance for time-causal tasks, with a parallelizable algorithm.
result Substantial speedups and robustness to financial tasks.
This study identifies RwD crash patterns on rural two-lane highways under different lighting conditions.
problem Insufficient investigation of RwD crashes under varying lighting conditions.
method Data mining using association rules mining (ARM) on crash database.
result Interesting crash patterns and risk factors identified under different lighting conditions.
FEAT estimates free energy using adaptive transports.
problem Estimating free energy across scientific domains.
method Uses learned transports and stochastic interpolants.
result Provides consistent, minimum-variance estimators.
Survey of deep RL in intelligent transportation systems.
problem Optimizing traffic signals and autonomous driving using deep RL.
method Comprehensive review of deep RL applications in traffic control and autonomous driving.
result Summarizes existing works in deep RL-based transportation applications.
Study uses OT to simulate markets, revealing power-law returns are driven by informational effect.
problem Reproduce power-law returns in financial markets using realistic simulations.
method Constructed artificial markets, used optimal transport (OT) to measure similarity, incrementally introduced behavioral components.
result Informational effect of prices is dominant in reproducing power-law returns, and multiple components interact synergistically.
New method uses transport maps for efficient Bayesian inference.
problem Efficiently perform sequential Bayesian inference of static model parameters.
method Estimation of structured transport maps to extract conditional distributions.
result Gradient-based characterization of posterior density for online parameter estimation.
Paper investigates optimal transport map estimation in infinite-dimensional spaces.
problem Estimating optimal transport maps in infinite-dimensional spaces is challenging.
method Characterizes γ-smoothness for optimal transport maps and develops a polynomial-rate estimator. result Shows polynomial-order minimax risk for optimal transport map estimation.
Agent-based simulation assesses tradable credit schemes for congestion reduction.
problem Simplistic modeling of TCS impacts in transportation research.
method Agent- and activity-based simulation framework within SimMobility.
result TCS stabilizes network and market performance over time, reducing congestion.