Study shows boundedness of klt singularities in 3D or with bounded Kollár components.
problem Boundedness of klt singularities in algebraic geometry.
method Analysis of Kollár components and local volumes.
result Minimal log discrepancies of Kollár components are bounded in dimension 3.
TMDA aligns subdomain data distribution discrepancies across domains using manifold representations.
problem Transfer learning challenges due to domain divergence.
method TMDA uses low-dimensional manifolds to represent subdomains and aligns local data distribution discrepancies across domains using M3D.
result TMDA is a promising method for various transfer learning tasks.
Study confirms boundedness of certain singularities in log Fano geometry.
problem Boundedness of log Fano cone singularities and minimal log discrepancies.
method Analyzing local volumes and minimal log discrepancies of Kollár components.
result Boundedness of K-semistable log Fano cone singularities confirmed in dimension three.
New partition designs reduce star discrepancy in high-dimensional sampling.
problem Improving the expected star discrepancy in high-dimensional sampling.
method Developed non-equal volume partitions to achieve lower expected star discrepancy.
result Explicit upper bounds for expected star discrepancy under non-equal volume partitions.
EVI-MMD approximates target distributions via MMD minimization with adaptive kernel.
problem Approximating target distributions using kernel discrepancy methods.
method EVI-MMD uses Maximum Mean Discrepancy (MMD) to minimize kernel discrepancy, solving ODEs with implicit Euler scheme and L-BFGS optimization.
result EVI-MMD with adaptive bandwidth selection significantly improves performance in sampling problems.
We propose a framework for synthesis of geological images based on an exemplar image. We synthesize new realizations such that the discrepancy in the patch distribution between the realizations and the exemplar image is minimized. Such discrepancy is quantified using a kernel method for two-sample test called maximum m…
Stein discrepancy improves UDA performance in low-data scenarios.
problem Improving model performance on unlabeled target domains with limited data.
method Proposes a novel UDA framework using Stein discrepancy, an asymmetric measure that depends on the target distribution through its score function.
result Consistently outperforms prior UDA approaches under limited target data across multiple benchmarks.
Private algorithms adapt from public to private domains with minimal labeled data.
problem Adapting from a public source domain to a private target domain with few labeled data.
method Differentially private discrepancy minimization algorithms based on Frank-Wolfe and Mirror-Descent methods.
result Effective adaptation with strong generalization and privacy guarantees.
Supervised learning results typically rely on assumptions of i.i.d. data. Unfortunately, those assumptions are commonly violated in practice. In this work, we tackle such problem by focusing on domain generalization: a formalization where the data generating process at test time may yield samples from never-before-seen…
Active learning algorithms propose which unlabeled objects should be queried for their labels to improve a predictive model the most. We study active learners that minimize generalization bounds and uncover relationships between these bounds that lead to an improved approach to active learning. In particular we show th…
We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model's log-density. We estimate the Stein discrepancy between the data density p(x) and the model density q(x) defined by a vector function of the data. We paramete…
The paper proposes a method to produce well-calibrated predictions in regression tasks using maximum mean discrepancy.
problem The need for accurate uncertainty quantification in machine learning predictions.
method The method uses maximum mean discrepancy to minimize the kernel embedding measure and calibrate predictions.
result The method produces well-calibrated and sharp prediction intervals, outperforming state-of-the-art methods.
New knots found with Seifert genus not matching minimal genus Seifert surfaces.
problem Discrepancy between Seifert genus and minimal genus Seifert surfaces.
method Constructed knots with specific genus and handle numbers to demonstrate the discrepancy.
result Found knots where Seifert genus is not realized by minimal genus Seifert surfaces.
We propose a notion of distance between two parametrized planar curves, called their discrepancy, and defined intuitively as the minimal amount of deformation needed to deform the source curve into the target curve. A precise definition of discrepancy is given as follows. A curve of transformations in the special Eucli…
We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel).…
A new ensemble filter uses transport maps and MMD optimization for high-dimensional data assimilation.
problem High-dimensional data assimilation challenges in ensemble filtering.
method Optimized Maximum Mean Discrepancy (MMD) for transport map construction.
result Significant improvement in robustness and posterior approximation.
Proposes TFDF to learn transferable and discriminative features for unsupervised domain adaptation.
problem Difficult to induce supervised classifier without labeled data in unsupervised domain adaptation.
method TFDF optimizes transferability and discriminability by aligning distributions and minimizing class confusion.
result TFDF achieves better performance on real-world datasets compared to existing methods.
New method optimizes non-linear functionals over probability measures.
problem Optimizing non-linear functionals defined over probability measures.
method N-particle underdamped Langevin algorithm with spacetime discretization.
result Converges globally in total variation distance.
A new metric detects non-Markovian states in partially observable environments.
problem Learning state representations in partially observable environments.
method Introducing the λ-discrepancy metric to detect non-Markovian states. result The λ-discrepancy is zero for Markov processes and non-zero for partially observable environments. Generative adversarial networks (GANs) generate data based on minimizing a divergence between two distributions. The choice of that divergence is therefore critical. We argue that the divergence must take into account the hypothesis set and the loss function used in a subsequent learning task, where the data generated …
Recent unsupervised approaches to domain adaptation primarily focus on minimizing the gap between the source and the target domains through refining the feature generator, in order to learn a better alignment between the two domains. This minimization can be achieved via a domain classifier to detect target-domain feat…
CFR-Pro enhances treatment effect estimation by incorporating local proximity.
problem Treatment selection bias in HTE estimation from observational data.
method Proximity-enhanced CounterFactual Regression (CFR-Pro) with pair-wise proximity regularizer and subspace projector.
result Significantly outperforms competitors in HTE estimation accuracy.
New autoencoder improves latent space learning by optimizing sliced Gromov-Wasserstein discrepancies.
problem Improving inner discrepancy between prior and posterior distributions in autoencoders.
method Proposed spherical sliced fused Gromov Wasserstein (SSFG) and variants (MSSFG, PSSFG) to find important directions.
result New autoencoders achieve favorable performance in latent manifold learning, image generation, and reconstruction.
Biases in observational data of treatments pose a major challenge to estimating expected treatment outcomes in different populations. An important technique that accounts for these biases is reweighting samples to minimize the discrepancy between treatment groups. We present a novel reweighting approach that uses bi-le…
Optimizes MMD learning for generative models with theoretical guarantees.
problem Theoretical guarantees for optimizing non-convex MMD objectives.
method Analyzes MMD optimization landscape for specific distributions.
result Gradient-based methods globally minimize MMD objective for certain distributions.
New algorithms minimize MMD to approximate probability measures efficiently.
problem Approximating probability measures by representative point sets.
method Sequential greedy minimization of maximum mean discrepancy (MMD) over candidate sets, with mini-batch variants.
result Consistency of proposed algorithms and mini-batch variants established.
New model learns better policies from expert demonstrations with higher efficiency.
problem Learning accurate policies from expert demonstrations with high efficiency.
method Generative adversarial imitation learning (GAIL) model that learns f-divergence automatically. result Learns better policies with higher data efficiency in physics-based control tasks.
In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily draw samples. Recently discrete approximation by particles has attracted attention …
A new method for Gaussian filtering using gradient flows and Wasserstein metrics.
problem Approximating Gaussian and mixture-of-Gaussians filtering for complex systems.
method Variational approximation via gradient-flow representation on Wasserstein metric space.
result Competitive performance in posterior representation and parameter estimation for systems with multiplicative noise and multi-modal distributions.
A new method trains deep neural networks for open set domain adaptation without negative open set difference.
problem Training deep neural networks for open set domain adaptation without negative open set difference.
method Proposes a new upper bound of target-domain risk, including source-domain risk, ε-open set difference (Δε), distributional discrepancy, and constant. Uses gradient descent for source-domain risk and Δε, and adversarial training for distributional discrepancy. Trains DNNs via minimizing the new upper bound. result Shows state-of-the-art performance on benchmark datasets.
Though machine learning algorithms excel at minimizing the average loss over a population, this might lead to large discrepancies between the losses across groups within the population. To capture this inequality, we introduce and study a notion we call maximum weighted loss discrepancy (MWLD), the maximum (weighted) d…
New limits of minimal surface systems have surprising large interior parts.
problem Minimal surface system limits with large interior vertical and non-minimal portions.
method Construction of limits with smallest possible dimension and codimension.
result Limits of minimal surface systems can have surprising large interior parts.
Optimizes kernel discrepancies by selecting subsets efficiently.
problem Improving kernel discrepancies for QMC methods.
method Introduces a novel subset selection algorithm for kernel discrepancies.
result Efficiently generates low-discrepancy samples from various distributions.
MMD-B-Fair learns fair representations by minimizing MMD test power.
problem Learning fair representations of data while preserving target attributes.
method Kernel two-sample testing and block testing schemes.
result Minimizing MMD test power allows hiding sensitive attribute information.
Motivated by applications in hyperspectral imaging we investigate methods for approximating a high-dimensional non-negative matrix Y by a product of two lower-dimensional, non-negative matrices K and X. This so-called non-negative matrix factorization is based…
New algorithm tunes SGMCMC hyperparameters for scalable Bayesian inference.
problem Tuning hyperparameters for SGMCMC is challenging due to lack of principled methods.
method Proposes a bandit-based algorithm using Stein discrepancies to tune hyperparameters.
result The method effectively tunes SGMCMC hyperparameters for various applications.
New discrepancy function compares discrete probability measures considering space geometry.
problem Comparing discrete probability measures in a geometrically meaningful way.
method Proposes the Fourier Discrepancy Function, proving convexity, differentiability, and providing gradient formula.
result Proves the Fourier Discrepancy is convex, twice differentiable, and provides an explicit gradient formula.
This paper introduces localized discrepancy theories for unsupervised domain adaptation.
problem Improving generalization bounds for unsupervised domain adaptation.
method Localized discrepancies defined on the hypothesis space after localization, leading to smaller and asymmetric values.
result Improved generalization bounds and sample complexity reduction.
Paper presents variational estimates for EBLVMs without structural assumptions.
problem Challenges in learning and evaluating EBLVMs due to intractable true posteriors and partition functions.
method Variational estimates of the score function and its gradient (VaES and VaGES) in a general EBLVM.
result The estimates can be applied to KSD and SM-based methods to learn EBLVMs and estimate Fisher divergence.
Transfer learning has been demonstrated to be successful and essential in diverse applications, which transfers knowledge from related but different source domains to the target domain. Online transfer learning(OTL) is a more challenging problem where the target data arrive in an online manner. Most OTL methods combine…
We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a relational way. It estimates observed graphs as GW barycenters constructed by a se…
The article introduces practical estimators for kernel discrepancies.
problem Estimating kernel discrepancies accurately and efficiently.
method Presented various estimators for MMD, HSIC, and KSD, including V-statistics, U-statistics, and incomplete U-statistics. Stressed the importance of kernel bandwidth and introduced adaptive estimators.
result Adaptive estimators combining multiple estimators with various kernels address the problem of kernel selection.
Partial model averaging improves Federated Learning performance.
problem Periodic model averaging causes significant model discrepancy in Federated Learning.
method Proposes a partial model averaging framework that encourages local models to stay close to each other.
result Partial averaging achieves up to 2.2% higher validation accuracy than full averaging.
New method improves neural spike train models by minimizing divergence directly, leading to better performance.
problem Poor performance and divergence issues in spike train models using maximum likelihood estimation.
method Directly minimize maximum mean discrepancy using spike train kernels and stochastic optimization.
result The proposed method generates well-behaved models with better control over feature trade-offs.
In unsupervised domain adaptation, it is widely known that the target domain error can be provably reduced by having a shared input representation that makes the source and target domains indistinguishable from each other. Very recently it has been studied that not just matching the marginal input distributions, but th…
New methods for Bayesian inference using mean shift particle systems.
problem Approximating expectations with unnormalized densities in Bayesian inference.
method Mean shift interacting particle systems that minimize maximum mean discrepancy (MMD).
result Mean shift interacting particle systems converge quickly and capture complex distributions.
The paper analyzes greedy algorithms for MMD minimization, showing their efficiency and approximation error.
problem Minimizing Maximum Mean Discrepancy (MMD) for probability measure quantization.
method Iterative algorithms including kernel herding, greedy MMD minimization, and Sequential Bayesian Quadrature (SBQ).
result The greedy algorithms have a lower approximation error than SBQ, but are significantly faster.
MPMC generates low-discrepancy points using graph neural networks.
problem Generating efficient low-discrepancy point sets.
method Leveraging Graph Neural Networks to model geometric properties.
result Achieves state-of-the-art performance in generating low-discrepancy points.