COMBO optimizes Bayesian Optimization for combinatorial search spaces.
problem Optimizing objectives on combinatorial search spaces with high-order interactions.
method COMBO uses a combinatorial graph and ARD diffusion kernel with Horseshoe prior for efficient modeling and variable selection.
result COMBO outperforms state-of-the-art methods consistently across various benchmarks.
Bayesian optimisation improves with fully-Bayesian treatment of hyperparameters.
problem Overconfident model predictions in BO due to ignoring hyperparameter uncertainty.
method Investigate FBBO using three approximate inference schemes compared to maximum likelihood approach.
result FBBO using EI with an ARD kernel leads to best performance in noise-free setting.
Study uses LCA to identify ARDS sub-phenotypes improving predictive models.
problem Complex and heterogeneous nature of ARDS makes early recognition difficult.
method Applied latent class analysis to identify sub-groups, then built predictive models.
result Significantly improved prediction performance for two sub-phenotypes of ARDS.
RFFNet scales kernel methods to large datasets by learning kernel relevance.
problem Scaling kernel methods to large datasets while maintaining interpretability.
method Designs random Fourier features for ARD kernels and uses first-order stochastic optimization for learning kernel relevances.
result RFFNet achieves low prediction error and identifies relevant features, leading to more interpretable solutions.
New kernel interprets 3D anisotropic data with rotations and improved predictions.
problem Capturing rotated anisotropy in 3D spatial fields.
method Introduces a Lie-algebraic kernel with three principal length-scales and an explicit rotation.
result Posterior recovers rotated anisotropy and improves prediction over axis-aligned kernels.
Financial markets are notoriously complex environments, presenting vast amounts of noisy, yet potentially informative data. We consider the problem of forecasting financial time series from a wide range of information sources using online Gaussian Processes with Automatic Relevance Determination (ARD) kernels. We measu…
Adaptive sparseness enhances robust regression using MCC and ARD.
problem Developing a robust regression method with adaptive sparseness.
method Integrating MCC with ARD in a Bayesian framework using variational Bayesian inference.
result MCC-ARD regression outperforms existing methods in prediction and feature selection.
This paper improves robustness in small neural networks through distillation.
problem Vulnerability of small neural networks to adversarial attacks.
method Adversarially Robust Distillation (ARD) to transfer robustness from teacher to student networks.
result ARD produces small models with superior robust accuracy compared to adversarially trained networks.
This paper uses Bayesian ARD to automatically determine utility functions for discrete choice models.
problem Challenging and time-consuming task in identifying optimal utility function specifications.
method Bayesian framework and automatic relevance determination (ARD) for data-driven utility function specification.
result The proposed DCM-ARD model accurately recovers true utility function specifications and outperforms previous methods.
Deep state space model forecasts time series with uncertainty.
problem Probabilistic forecasting for risk management.
method Parameterized deep networks for non-linear models, recurrent neural nets for dependency, ARD network for exogenous variables.
result Accurate and sharp probabilistic forecasts with realistic uncertainty growth.
Two adaptive kernel selection methods improve the accuracy of Kernelized Diffusion Maps.
problem Selecting an appropriate kernel for Kernelized Diffusion Maps.
method Two complementary approaches: variational outer loop and unsupervised cross-validation.
result Both methods improve the quality and stability of the recovered eigenfunctions.
Conditional diffusion models can approximate target distributions well with Gaussian-mixture reverse kernels.
problem Approximating target distributions in conditional diffusion models.
method Using finite Gaussian mixtures with ReLU-network logits as reverse kernels, reducing the problem to static conditional density approximation.
result The resulting neural reverse-kernel class is dense in conditional KL divergence under exact terminal matching.
Study RKHS on manifolds, linking Sobolev and diffusion spaces.
problem Characterizing RKHS on manifolds and their properties.
method Analyzing Sobolev and diffusion spaces on Riemannian manifolds.
result Sobolev spaces are RKHS under certain conditions, and diffusion spaces are introduced.
The paper analyzes methods for sparse Bayesian regression in nonlinear system identification.
problem Learning sparse models in Bayesian regression with nonlinear applications.
method Two classes of methods: regularization and thresholding based, built on automatic relevance determination (ARD).
result Analytical demonstration of favorable performance with sparse solutions in linear problems.
This research explores how different discrete diffusion kernels affect graph generation quality.
problem The impact of different discrete diffusion kernels on graph generation quality.
method Developed a family of discrete diffusion kernels that converge to different Bernoulli priors.
result The quality of generated graphs is sensitive to the prior used, challenging previous intuitions.
We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer's law. The algorithm promotes solutions that are sparse in the pixel/voxel-differences domain by introduci…
A new method for efficient diffusion geometry computation from data regions.
problem Heavy computational load in diffusion maps for modern data analysis.
method Compressed diffusion process between data regions using an adapted MGC kernel.
result Efficient pointwise diffusion map embedding from data regions.
A recurring problem when building probabilistic latent variable models is regularization and model selection, for instance, the choice of the dimensionality of the latent space. In the context of belief networks with latent variables, this problem has been adressed with Automatic Relevance Determination (ARD) employing…
We study the Automatic Relevance Determination procedure applied to deep neural networks. We show that ARD applied to Bayesian DNNs with Gaussian approximate posterior distributions leads to a variational bound similar to that of variational dropout, and in the case of a fixed dropout rate, objectives are exactly the s…
Bayesian Neural Networks improve credit card default prediction and provide feature importance.
problem Lack of interpretability and uncertainty measures in neural network models for credit risk.
method Developed and compared BNNs trained by Gaussian approximation and Hybrid Monte Carlo.
result BNNs with Automatic Relevance Determination outperform normal BNNs in credit card default prediction.
Kernel-smoothed scores improve diffusion models by reducing memorization.
problem Diffusion models can memorize training data, leading to biased samples.
method Interpret empirical score as noisy version of true score, kernel-smoothed.
result Kernel-smoothing reduces variance and improves generalization.
Unified kernel framework extends to stochastic systems, improving numerical stability.
problem Extending kernel methods to stochastic dynamical systems with diffusion.
method Unified kernel framework, Feynman-Kac path-integral representations, collocation-based computational framework.
result Kernel equivalence under uniform ellipticity assumptions and improved numerical stability with moderate diffusion.
New method circumvents curse of dimensionality in Laplacian estimation.
problem High-dimensional data challenges spectral clustering and diffusion maps.
method Kernelized Laplacian estimation via reproducing kernel Hilbert space.
result Non-asymptotic statistical rates show improved performance in high dimensions.
SJDs unify masked, continuous, and hybrid diffusion models.
problem Unified modeling of diffusion processes.
method Continuous-time Markov processes with token embeddings and hazard rates.
result Unified model recovers masked, continuous, and hybrid diffusion as limits.
Method learns SDEs from data snapshots.
problem Learning drift and diffusion of SDEs from data.
method Two-step process: learn drift by expected value, learn diffusion by SDP.
result Validated on examples and simulations.
Diffusion Maps framework is a kernel based method for manifold learning and data analysis that defines diffusion similarities by imposing a Markovian process on the given dataset. Analysis by this process uncovers the intrinsic geometric structures in the data. Recently, it was suggested to replace the standard kernel …
New method reduces computational cost for learning stationary diffusions.
problem Learning parameters of stationary diffusions efficiently.
method Stein-type discrepancy (SKDS) for estimating generator expectations.
result SKDS guarantees alignment with target stationary distribution.
HyBO optimizes hybrid structures using diffusion kernels.
problem Optimizing complex interactions between discrete and continuous variables.
method HyBO uses diffusion kernels over hybrid spaces with additive kernel formulation.
result HyBO significantly outperforms state-of-the-art methods on real-world benchmarks.
DKPCA improves WSD accuracy with scarce labeled data.
problem Word sense disambiguation in natural language processing.
method DKPCA combines Kernel PCA and Semantic Diffusion Kernel.
result DKPCA outperforms SVM and KPCA on SensEval data.
BKTF uses tensor factorization for Bayesian optimization of complex functions.
problem Complex functions with nonstationary, nonseparable, and multimodal features.
method Bayesian Kernelized Tensor Factorization (BKTF) approximates complex functions using a low-rank tensor CP decomposition with GP priors.
result BKTF provides flexible and effective surrogate modeling with uncertainty quantification.
GP model for time series forecasting with priors.
problem Automatic selection of optimal kernels and reliable estimation of hyperparameters.
method Fixed composition of kernels, automatic relevance determination (ARD), empirical Bayes priors.
result GP model is more accurate than state-of-the-art models.
Kernel analysis reveals rumor truth from diffusion patterns alone.
problem Detecting unverified rumors on Twitter using text and user identities.
method Graph kernels to extract diffusion patterns from Twitter cascade structures.
result Diffusion patterns are highly informative of rumor truth or falsehood.
A new method estimates SDEs using occupation kernels.
problem Learning multivariate stochastic differential equations (SDEs).
method Two-step procedure: estimate drift, then diffusion. Occupation kernels used in RKHS.
result Validated on simulated and real-world data.
The paper introduces new methods for Asian option pricing using Laguerre quadrature.
problem Developing accurate pricing models for Asian options.
method Utilizes Laguerre quadrature and diffusion kernel approach.
result Demonstrates new techniques to solve complex Asian option pricing equations.
The paper connects Riemannian Gaussian distributions to random matrix theory and diffusion kernels.
problem Analyzing Riemannian Gaussian distributions on symmetric spaces.
method Analytical computation of marginals using orthogonal and skew orthogonal polynomials, and diffusion kernels.
result Riemannian Gaussian distributions are random matrix types, and their probability density functions can be computed analytically.
Jointly learns feature and sample relevancies for robust sparse recovery.
problem Sparse recovery sensitivity to data contaminants like outliers or misspecified noise.
method Jointly learns feature and sample relevancies via marginal likelihood optimization.
result Consistent sparse and robust prediction models across diverse tasks.
New graph kernels capture spatio-temporal interactions.
problem Lack of justified spatio-temporal graph kernels for graph problems.
method Derive graph kernels via SPDEs for spatio-temporal modelling.
result Non-separable spatio-temporal graph kernels outperform existing ones.
EntroPath learns manifold geometry from diffusion paths.
problem Learning geodesic geometry from data graphs with spurious shortcuts.
method Maximum Entropy Path Ensemble Embedding (MERW) with k-step diffusion paths.
result EntroPath converges to squared geodesic distance in the short-time limit.
Improved image generation quality using closed-form discriminator guidance in diffusion models.
problem Enhancing the quality of images generated by diffusion models.
method Theoretical framework to analyze GAN discriminator's effect on Langevin sampling, proposing IPM-GAN optimization as smoothed score-matching.
result Closed-form kernel-based discriminator guidance improves metrics like CLIP-FID and KID.
This paper introduces methods to handle discrete data by dequantization.
problem Handling discrete data in deep learning models.
method Dequantization framework, including importance-weighted and Rényi dequantization objectives, and autoregressive dequantization.
result Improved performance on uniform dequantization distributions and state-of-the-art negative log-likelihood on CIFAR10.
This paper analyzes error bounds for biased SMC samplers in conditional sampling.
problem Analyzing error bounds for biased SMC samplers in conditional sampling.
method Develops a non-asymptotic error analysis for SMC samplers with biased mutation kernels.
result Derives the first non-asymptotic error bound for conditional sampling with score-based diffusion models.
Generative model on manifolds reduces divergence computation and improves scalability.
problem Difficulties in modeling data on non-Euclidean spaces due to expensive divergence computation and approximations of heat kernel.
method Riemannian Diffusion Mixture, a principled framework using a mixture of bridge processes.
result Achieves superior performance on diverse manifolds with reduced simulation steps.
We solve a Schrödinger bridge with a quadratic state cost, finding a closed-form solution.
problem Optimizing diffusion processes between given distributions.
method Regularized Schrödinger bridge with a quadratic state cost.
result Closed-form solution for the Markov kernel of the regularized Schrödinger bridge.
Algorithm learns interaction kernels for particle systems from data.
problem Understanding and modeling interactions in systems of interacting particles.
method Nonparametric algorithm using least squares with regularization, probabilistic error functional, and reproducing kernel Hilbert space convergence.
result The algorithm converges optimally and accurately learns interaction kernels.
Uniform heat kernel and diffusion bridge asymptotics for sub-Riemannian geometry.
problem Analyzing sub-Riemannian heat kernels and their derivatives on incomplete manifolds.
method Localized asymptotic analysis, focusing on minimizing geodesics and the non-abnormal cut locus.
result Uniform bounds and expansions for heat kernels and their derivatives on compacts, including the diffusion bridge measure.
Efficient diffusion model for symmetric manifolds reduces training and computation costs.
problem Heat kernel computations for manifold diffusion models are computationally expensive and infeasible.
method Spatially-varying covariance diffusion model, efficient objective derived via Ito's Lemma.
result Our model reduces training time and arithmetic operations by orders of magnitude.
Spectral algorithms on manifolds using diffusion kernels improve convergence rates.
problem The limitations of existing spectral algorithms in RKHSs for data on manifolds.
method Integrating manifold structure into spectral algorithms using heat kernel diffusion spaces.
result Spectral algorithms converge to the target function and its derivatives in a strong sense, with rates dependent on manifold intrinsic dimension.
RNE provides a flexible framework for diffusion models, enabling inference-time control and energy-based training.
problem Insufficient knowledge of marginal densities in diffusion models.
method Introduces Radon-Nikodym Estimator (RNE) to reveal the connection between marginal densities and transition kernels.
result RNE delivers strong results in inference-time control and energy-based diffusion training.