arXiv subjects

Khai Nguyen

Publications and source records attributed to Khai Nguyen.

At least 19 recordsLinked to original sources

arXiv2026

Generalized Bayesian Clustering with Regression for Unaligned Longitudinal Binary Data

We propose a generalized Bayesian clustering with regression model for unaligned longitudinal binary outcomes, motivated by seizure diary data from the Human Epilepsy Project. Seizure diaries are sparse, irregularly observed, and vary enormously across patients. A single fully-specified generative model tends to be either misspecified or computationally inefficient. We address the challenge by two strategies. We set up a regression by way of clustering as model-based clustering using a mixture model. For the latter, we take a generalized Bayesian perspective which replaces the full likelihood with a loss-based update using a generalized likelihood. We combine a trajectory similarity loss and a regression loss, so that clustering is informed by both trajectory similarity and the prediction of outcomes The trajectory similarity loss is constructed by representing each trajectory as an (empirical) distribution of subsequences, called reads, and then is defined based on the sliced Wasserstein distance between these empirical distributions. This loss allows alignment-free comparison of sequences that are irregularly observed or temporally misaligned, and it scales quasi-linearly in trajectory length. The regression loss is the negative log-likelihood of a probit regression. A prior on the cluster-specific parameters is defined by way of a Dirichlet process prior on the mixing measure.

stat.ME↗

arXiv2026

Distributional Determinantal Point Process for Repulsive Clustering of Distributions

We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process whose atoms are probability distributions rather than points in a real space. The dDPP is constructed via an L-ensemble with a sliced Wasserstein (SW) kernel between distributions. We show its validity as a well-defined point process. In the discrete setting, we derive concentration results for plug-in estimators of the L-ensemble, the correlation kernel, and their determinants given i.i.d. samples from the distributional atoms. Leveraging this framework, we propose a distribution-valued random partition model by way of a repulsive generalized Bayesian mixture model. The model places a dDPP prior over the atoms of the mixing measure and defines a generalized likelihood based on SW distance. To summarize posterior inference, we develop a decision-theoretic approach to report a point estimate of the mixing measure as a Bayes rule under a hierarchical optimal transport utility function. The latter is a natural choice given that the mixing measure is itself a distribution over distributions. We use the proposed framework for inference with single-cell gene expression data and human epilepsy data, producing interpretable and well-separated clusters that reflect meaningful structure in the data.

stat.ME↗

arXiv2026

On regularity of finite-maturity American put options in the Heston model

This paper studies the regularity of finite-maturity American value functions in the Heston model. Although the Heston operator is degenerate when the volatility is zero, we are able to establish C^{1,2} regularity of the American value functions in the exercise domain and the smooth-fit principle, using PDE techniques.

q-fin.MF↗

arXiv2026

Sliced-Regularized Optimal Transport

We propose a new regularized optimal transport (OT) formulation, termed sliced-regularized optimal transport (SROT). Unlike entropic OT (EOT), which regularizes the transport plan toward an independent coupling, SROT regularizes it toward a smoothened sliced OT (SOT) plan. To the best of our knowledge, SROT is the first approach to leverage a version of SOT plan as a reference to improve classical OT. We provide a formal definition of SROT, derive its dual formulation, and provide a post-Bayesian interpretation of SROT. We then develop a Sinkhorn-style algorithm for efficient computation, retaining the same scalability advantages as EOT. By incorporating a scalable SOT plan as a prior, SROT yields more accurate approximations of the exact OT plan than EOT under the same level of regularization. Moreover, the resulting transport plan improves upon the reference SOT plan itself. We further introduce the corresponding OT divergence induced by SROT, named SROT divergence, and analyze its topological and computational properties. Finally, we validate our approach through experiments on synthetic datasets and color transfer tasks, demonstrating that SROT is better than both EOT and SOT in approximating exact OT. Additional experiments on gradient flows further highlight the advantages of SROT divergence.

stat.ML↗

arXiv2026

Amortized Optimal Transport from Sliced Potentials

We propose a novel amortized optimization method for predicting optimal transport (OT) plans across multiple pairs of measures by leveraging Kantorovich potentials derived from sliced OT. We introduce two amortization strategies: regression-based amortization (RA-OT) and objective-based amortization (OA-OT). In RA-OT, we formulate a functional regression model that treats Kantorovich potentials from the original OT problem as responses and those obtained from sliced OT as predictors, and estimate these models via least-squares methods. In OA-OT, we estimate the parameters of the functional model by optimizing the Kantorovich dual objective. In both approaches, the predicted OT plan is subsequently recovered from the estimated potentials. As amortized OT methods, both RA-OT and OA-OT enable efficient solutions to repeated OT problems across different measure pairs by reusing information learned from prior instances to rapidly approximate new solutions. Moreover, by exploiting the structure provided by sliced OT, the proposed models are more parsimonious, independent of specific structures of the measures, such as the number of atoms in the discrete case, while achieving high accuracy. We demonstrate the effectiveness of our approaches on tasks including MNIST digit transport, color transfer, supply-demand transportation on spherical data, and mini-batch OT conditional flow matching.

stat.ML↗

arXiv2026

Coexistence of CHSH Nonlocality and KCBS Contextuality in a Single Quantum State

Contextuality and nonlocality are distinct manifestations at the foundation of quantum mechanics, yet their coexistence within a single quantum state remains subtle. In a hybrid CHSH--KCBS scenario involving the entanglment of a qubit and a qutrit, the qutrit supports the KCBS contextuality test, and the CHSH nonlocality arises from correlations between the qubit and qutrit. Here, we derive the analytical closed-form expressions for both inequalities and also simulate this physics on a quantum circuit. We show that contextuality is governed solely by a population parameter $p_2$, associated with the occupation of the qutrit subsystem in the $|2\rangle$ level, which plays a distinguished role in the KCBS structure. In contrast, nonlocality depends irreducibly on coherence, involving both amplitudes and phases encoded in parameters $(X_i, Y_i)$. This separation of physical resources reveals parameter regimes that optimize KCBS violation while suppress CHSH violation, and vice versa. As a result, the optimal regions do not overlap, and coexistence is restricted to a narrow intermediate regime in parameter space.

quant-ph↗

arXiv2026

Vertical Consensus Inference for High-Dimensional Random Partition

We review recently proposed Bayesian approaches for clustering high-dimensional data. After identifying the main limitations of available approaches, we introduce an alternative framework based on vertical consensus inference (VCI) to mitigate the curse of dimensionality in high-dimensional Bayesian clustering. VCI builds on the idea of consensus Monte Carlo by dividing the data into multiple shards (smaller subsets of variables), performing posterior inference on each shard, and then combining the shard-level posteriors to obtain a consensus posterior. The key distinction is that VCI splits the data vertically, producing vertical shards that retain the same number of observations but have lower dimensionality. We use an entropic regularized Wasserstein barycenter to define a consensus posterior. The shard-specific barycenter weights are constructed to favor shards that provide meaningful partitions, distinct from a trivial single cluster or all singleton clusters, favoring balanced cluster sizes and precise shard-specific posterior random partitions. We show that VCI can be interpreted as a variational approximation to the posterior under a hierarchical model with a generalized Bayes prior. For relatively low-dimensional problems, experiments suggest that VCI closely approximates inference based on clustering the entire multivariate data. For high-dimensional data and in the presence of many noninformative dimensions, VCI introduces a new framework for model-based and principled inference on random partitions. Although our focus here is on random partitions, VCI can be applied to any dimension-independent parameters and serves as a bridge to emerging areas in statistics such as consensus Monte Carlo, optimal transport, variational inference, and generalized Bayes.

stat.ME↗

arXiv2026

Cheap Thrills: Effective Amortized Optimization Using Inexpensive Labels

To scale optimization and simulation, prior work has explored training machine-learning surrogates that map problem parameters to solutions inexpensively at inference time. Unfortunately, commonly used approaches, including supervised and self-supervised learning with either soft or hard feasibility enforcement, face inherent challenges such as reliance on expensive high-quality labels or difficult optimization landscapes. To address their trade-offs, we propose a novel framework that collects "cheap" imperfect labels, performs supervised model pretraining with a merit loss-based termination scheme, and finally refines the model through self-supervised learning to improve final performance. Empirical validation across challenging domains -- including nonconvex constrained optimization, power-grid operation, and stiff dynamical systems -- shows that this three-stage strategy yields faster convergence; improved accuracy, feasibility, and optimality; and up to 59x reductions in total offline computational cost. We further analyze why and when our framework improves surrogate model training, finding that (i) merit loss is an informative signal and (ii) only small numbers of cheap, inexact labels are needed to place the model in a favorable regime for self-supervised learning.

cs.LG↗

arXiv2026

Bayesian Multiple Multivariate Density-Density Regression

We propose the first approach for multiple multivariate density-density regression (MDDR), making it possible to consider the regression of a multivariate density-valued response on multiple multivariate density-valued predictors. The core idea is to define a fitted distribution using a sliced Wasserstein barycenter (SWB) of push-forwards of the predictors and to quantify deviations from the observed response using the sliced Wasserstein (SW) distance. Regression functions, which map predictors' supports to the response support, and barycenter weights are inferred within a generalized Bayes framework, enabling principled uncertainty quantification without requiring a fully specified likelihood. The inference process can be seen as an instance of an inverse SWB problem. We establish theoretical guarantees, including the stability of the SWB under perturbations of marginals and barycenter weights, sample complexity of the generalized likelihood, and posterior consistency. For practical inference, we introduce a differentiable approximation of the SWB and a smooth reparameterization to handle the simplex constraint on barycenter weights, allowing efficient gradient-based MCMC sampling. We demonstrate MDDR in an application to inference for population-scale single-cell data. Posterior analysis under the MDDR model in this example includes inference on communication between multiple source/sender cell types and a target/receiver cell type. The proposed approach provides accurate fits, reliable predictions, and interpretable posterior estimates of barycenter weights, which can be used to construct sparse cell-cell communication networks.

stat.ME↗

arXiv2025

CarbonEdge: Leveraging Mesoscale Spatial Carbon-Intensity Variations for Low Carbon Edge Computing

The proliferation of latency-critical and compute-intensive edge applications is driving increases in computing demand and carbon emissions at the edge. To better understand carbon emissions at the edge, we analyze granular carbon intensity traces at intermediate "mesoscales," such as within a single US state or among neighboring countries in Europe, and observe significant variations in carbon intensity at these spatial scales. Importantly, our analysis shows that carbon intensity variations, which are known to occur at large continental scales (e.g., cloud regions), also occur at much finer spatial scales, making it feasible to exploit geographic workload shifting in the edge computing context. Motivated by these findings, we propose \proposedsystem, a carbon-aware framework for edge computing that optimizes the placement of edge workloads across mesoscale edge data centers to reduce carbon emissions while meeting latency SLOs. We implement CarbonEdge and evaluate it on a real edge computing testbed and through large-scale simulations for multiple edge workloads and settings. Our experimental results on a real testbed demonstrate that CarbonEdge can reduce emissions by up to 78.7\% for a regional edge deployment in central Europe. Moreover, our CDN-scale experiments show potential savings of 49.5\% and 67.8\% in the US and Europe, respectively, while limiting the one-way latency increase to less than 5.5 ms.

cs.DC↗

arXiv2025

An Introduction to Sliced Optimal Transport

Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables fast and scalable computation of distances, barycenters, and kernels for probability measures, while retaining rich geometric structure. This paper provides a comprehensive review of SOT, covering its mathematical foundations, methodological advances, computational methods, and applications. We discuss key concepts of OT and one-dimensional OT, the role of tools from integral geometry such as Radon transform in projecting measures, and statistical techniques for estimating sliced distances. The paper further explores recent methodological advances, including non-linear projections, improved Monte Carlo approximations, statistical estimation techniques for one-dimensional optimal transport, weighted slicing techniques, and transportation plan estimation methods. Variational problems, such as minimum sliced Wasserstein estimation, barycenters, gradient flows, kernel constructions, and embeddings are examined alongside extensions to unbalanced, partial, multi-marginal, and Gromov-Wasserstein settings. Applications span machine learning, statistics, computer graphics and computer visions, highlighting SOT's versatility as a practical computational tool. This work will be of interest to researchers and practitioners in machine learning, data sciences, and computational disciplines seeking efficient alternatives to classical OT.

stat.ML↗

arXiv2025

Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distances

We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced Wasserstein (SW) distances. Specifically, we leverage both standard SW distances, which provide lower bounds, and lifted SW distances, which provide upper bounds, as predictors of the true Wasserstein distance. To ensure parsimony, we introduce two linear models: an unconstrained model with a closed-form least-squares solution, and a constrained model that uses only half as many parameters. We show that accurate models can be learned from a small number of distribution pairs. Once estimated, the model can predict the Wasserstein distance for any pair of distributions via a linear combination of SW distances, making it highly efficient. Empirically, we validate our approach on diverse tasks, including Gaussian mixtures, point-cloud classification, and Wasserstein-space visualizations for 3D point clouds. Across various datasets such as MNIST point clouds, ShapeNetV2, MERFISH Cell Niches, and scRNA-seq, our method consistently provides a better approximation of Wasserstein distance than the state-of-the-art Wasserstein embedding model, Wasserstein Wormhole, particularly in low-data regimes. Finally, we demonstrate that our estimator can also accelerate Wormhole training, yielding \textit{RG-Wormhole}.

stat.ML↗

arXiv2025

Bayesian Multivariate Density-Density Regression

We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing in spaces of differing dimensions. We utilize a generalized Bayes framework, circumventing the need for a fully specified likelihood by employing the sliced Wasserstein distance to measure the discrepancy between fitted and observed distributions. This choice not only handles high-dimensional data and varying sample sizes efficiently but also facilitates a Metropolis-adjusted Langevin algorithm (MALA) for posterior inference. Furthermore, we establish the posterior consistency of our generalized Bayesian approach, ensuring that the posterior distribution concentrates around the true parameters as the sample size increases. Through simulations and application to a population-scale single-cell dataset, we show that Bayesian DDR provides robust fits, superior predictive performance compared to traditional methods, and valuable insights into complex biological interactions.

stat.ME↗

arXiv2025

TinyMPC: Model-Predictive Control on Resource-Constrained Microcontrollers

Model-predictive control (MPC) is a powerful tool for controlling highly dynamic robotic systems subject to complex constraints. However, MPC is computationally demanding, and is often impractical to implement on small, resource-constrained robotic platforms. We present TinyMPC, a high-speed MPC solver with a low memory footprint targeting the microcontrollers common on small robots. Our approach is based on the alternating direction method of multipliers (ADMM) and leverages the structure of the MPC problem for efficiency. We demonstrate TinyMPC's effectiveness by benchmarking against the state-of-the-art solver OSQP, achieving nearly an order of magnitude speed increase, as well as through hardware experiments on a 27 gram quadrotor, demonstrating high-speed trajectory tracking and dynamic obstacle avoidance. TinyMPC is publicly available at https://tinympc.org.

cs.RO↗

arXiv2025

Model Tensor Planning

Sampling-based model predictive control (MPC) offers strong performance in nonlinear and contact-rich robotic tasks, yet often suffers from poor exploration due to locally greedy sampling schemes. We propose \emph{Model Tensor Planning} (MTP), a novel sampling-based MPC framework that introduces high-entropy control trajectory generation through structured tensor sampling. By sampling over randomized multipartite graphs and interpolating control trajectories with B-splines and Akima splines, MTP ensures smooth and globally diverse control candidates. We further propose a simple $β$-mixing strategy that blends local exploitative and global exploratory samples within the modified Cross-Entropy Method (CEM) update, balancing control refinement and exploration. Theoretically, we show that MTP achieves asymptotic path coverage and maximum entropy in the control trajectory space in the limit of infinite tensor depth and width. Our implementation is fully vectorized using JAX and compatible with MuJoCo XLA, supporting \emph{Just-in-time} (JIT) compilation and batched rollouts for real-time control with online domain randomization. Through experiments on various challenging robotic tasks, ranging from dexterous in-hand manipulation to humanoid locomotion, we demonstrate that MTP outperforms standard MPC and evolutionary strategy baselines in task success and control robustness. Design and sensitivity ablations confirm the effectiveness of MTP tensor sampling structure, spline interpolation choices, and mixing strategy. Altogether, MTP offers a scalable framework for robust exploration in model-based planning and control.

cs.RO↗

arXiv2025

Secrecy Offloading Analysis of UAV-assisted NOMA-MEC Incorporating WPT in IoT Networks

This article studies the efficiency of secrecy data offloading for an unmanned aerial vehicle (UAV)-assisted nonorthogonal multiple access (NOMA)-integrated mobile-edge computing (MEC) incorporating wireless power transfer (WPT) within an Internet of Things (IoT) network. Specifically, this study assumes an UAV to function in dual roles: as a mobile computation platform and as an aerial power-supply station, offering substantial advantages for resource-constrained edge devices (EDs) in mitigating interference from an passive eavesdropper. To assess the system's secrecy offloading efficacy, the secrecy successful computation probability (SSCP) closed-formed formulation under Nakagami-m fading channel is derived. The theoretical results are conducted with a variety of parameters, thereby validating the precision of our analysis.

cs.IT↗

arXiv2025

TD-GRPC: Temporal Difference Learning with Group Relative Policy Constraint for Humanoid Locomotion

Robot learning in high-dimensional control settings, such as humanoid locomotion, presents persistent challenges for reinforcement learning (RL) algorithms due to unstable dynamics, complex contact interactions, and sensitivity to distributional shifts during training. Model-based methods, \textit{e.g.}, Temporal-Difference Model Predictive Control (TD-MPC), have demonstrated promising results by combining short-horizon planning with value-based learning, enabling efficient solutions for basic locomotion tasks. However, these approaches remain ineffective in addressing policy mismatch and instability introduced by off-policy updates. Thus, in this work, we introduce Temporal-Difference Group Relative Policy Constraint (TD-GRPC), an extension of the TD-MPC framework that unifies Group Relative Policy Optimization (GRPO) with explicit Policy Constraints (PC). TD-GRPC applies a trust-region constraint in the latent policy space to maintain consistency between the planning priors and learned rollouts, while leveraging group-relative ranking to assess and preserve the physical feasibility of candidate trajectories. Unlike prior methods, TD-GRPC achieves robust motions without modifying the underlying planner, enabling flexible planning and policy learning. We validate our method across a locomotion task suite ranging from basic walking to highly dynamic movements on the 26-DoF Unitree H1-2 humanoid robot. Through simulation results, TD-GRPC demonstrates its improvements in stability and policy robustness with sampling efficiency while training for complex humanoid control tasks.

cs.RO↗

arXiv2025

Lightspeed Geometric Dataset Distance via Sliced Optimal Transport

We introduce sliced optimal transport dataset distance (s-OTDD), a model-agnostic, embedding-agnostic approach for dataset comparison that requires no training, is robust to variations in the number of classes, and can handle disjoint label sets. The core innovation is Moment Transform Projection (MTP), which maps a label, represented as a distribution over features, to a real number. Using MTP, we derive a data point projection that transforms datasets into one-dimensional distributions. The s-OTDD is defined as the expected Wasserstein distance between the projected distributions, with respect to random projection parameters. Leveraging the closed form solution of one-dimensional optimal transport, s-OTDD achieves (near-)linear computational complexity in the number of data points and feature dimensions and is independent of the number of classes. With its geometrically meaningful projection, s-OTDD strongly correlates with the optimal transport dataset distance while being more efficient than existing dataset discrepancy measures. Moreover, it correlates well with the performance gap in transfer learning and classification accuracy in data augmentation.

cs.LG↗