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Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only…

Graph convolutional networks (GCNs) are \emph{discriminative models} that directly model the class posterior $p(y|\mathbf{x})$ for semi-supervised classification of graph data. While being effective, as a representation learning approach,…

Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…

Flow-based generative models provide strong unconditional priors for inverse problems, but guiding their dynamics for conditional generation remains challenging. Recent work casts training-free conditional generation in flow models as an…

In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established…

Chance constrained optimal power flow (CC-OPF) formulations have been proposed to minimize operational costs while controlling the risk arising from uncertainties like renewable generation and load consumption. To solve CC-OPF, we often…

We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the implicit bias of unregularized non-convex gradient flow as convex regularization of an…

Optimal power flow (OPF) over power transmission networks poses challenging large-scale nonlinear optimization problems, which involve a large number of quadratic equality and indefinite quadratic inequality constraints. These…

This article develops a strengthened convex quadratic convex (QC) relaxation of the AC Optimal Power Flow (AC-OPF) problem and presents an optimization-based bound-tightening (OBBT) algorithm to compute tight, feasible bounds on the voltage…

In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…

Normalizing flows are exact-likelihood generative neural networks which approximately transform samples from a simple prior distribution to samples of the probability distribution of interest. Recent work showed that such generative models…

Predicting potential and counterfactual outcomes from observational data is central to individualized decision-making, particularly in clinical settings where treatment choices must be tailored to each patient rather than guided solely by…

Finding a transformation between two unknown probability distributions from finite samples is crucial for modeling complex data distributions and performing tasks such as sample generation, domain adaptation and statistical inference. One…

The uncertainty of multiple power loads and renewable energy generations (PLREG) in power systems increases the complexity of power flow analysis for decision-makers. The chance-constrained method can be applied to model the optimization…

We consider the problem of transforming samples from one continuous source distribution into samples from another target distribution. We demonstrate with optimal transport theory that when the source distribution can be easily sampled from…

Conformal prediction (CP) constructs uncertainty sets for model outputs with finite-sample coverage guarantees. A candidate output is included in the prediction set if its non-conformity score is not considered extreme relative to the…

The chance constrained optimal power flow (CC-OPF) essentially finds the low-cost generation dispatch scheme ensuring operational constraints are met with a specified probability, termed the security level. While the security level is a…

Flow-based generative models have highly desirable properties like exact log-likelihood evaluation and exact latent-variable inference, however they are still in their infancy and have not received as much attention as alternative…

Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data…

Optimal Transport (OT) is being widely used in various fields such as machine learning and computer vision, as it is a powerful tool for measuring the similarity between probability distributions and histograms. In previous studies, OT has…