Improved agnostic learning time via Gaussian surface area analysis.
problem Learning polynomial threshold functions under Gaussian marginals.
method Improvement of polynomial degree required for approximation.
result Near optimal bounds on agnostic learning complexity.
New algorithm speeds up online mapping of unknown terrains.
problem Increasing computational demands of GP mapping as area expands.
method Recursive GP mapping using local basis functions in an information filter.
result Reduces overall computational complexity and speeds up mapping.
Non-negative L1-approximating polynomials for Gaussian distributions are proven for certain classes of sets.
problem Existence of non-negative L1-approximating polynomials for Gaussian distributions. method Proving the existence of degree-k non-negative polynomials that approximate indicator functions of sets with Gaussian surface area in L1-norm. result Proves the existence of non-negative L1-approximating polynomials for certain classes of sets with Gaussian surface area. Algorithm estimates Gaussian parameters under unknown truncation sets.
problem Estimating Gaussian parameters when samples are truncated to unknown sets.
method Efficient algorithm for arbitrary unknown truncation sets, using Gaussian surface area as complexity measure.
result Algorithm works for large families of sets including intersections of halfspaces and general convex sets.
Minimal Gaussian surface area is achieved by cones over a regular simplex for m>3 sets partitioning Rn.
problem Finding the minimal Gaussian surface area of m sets partitioning Rn. method Volume-preserving variations of the sets, avoiding matrix-valued partial differential inequalities.
result Strengthened Milman-Neeman Gaussian multi bubble theorem and first known dimension-independent bounds for the Plurality is Stablest Conjecture.
Gaussian processes adapted for Riemannian manifolds using gauge-independent kernels.
problem Deploying Gaussian processes on non-Euclidean domains like Riemannian manifolds.
method Developed techniques to generalize Gaussian processes to vector fields on Riemannian manifolds using gauge-independent kernels.
result Enabled training of vector-valued Gaussian processes on Riemannian manifolds using standard Gaussian process methods.
Improves Gaussian process factor models for multi-population recordings.
problem Cubic runtime scaling with trial length and group number limits application to large-scale recordings.
method Two approximate approaches: inducing variables and frequency domain.
result Achieved orders of magnitude speed-up with minimal statistical performance impact.
PriorVAE uses VAEs to efficiently encode spatial priors for small-area estimation.
problem Efficiently encoding spatial priors for small-area estimation using Gaussian processes.
method Approximating Gaussian process priors with a variational autoencoder (VAE).
result Efficient spatial inference through a low-dimensional latent Gaussian space representation.
The paper proves that symmetric sets with minimal Gaussian surface area are nearly convex cylinders.
problem Finding the shape of symmetric sets with minimal Gaussian surface area.
method Analyzing the boundary of symmetric sets and applying isoperimetric inequalities.
result Symmetric sets with minimal Gaussian surface area are nearly convex cylinders.
Paper bounds prediction error for misspecified Gaussian process models.
problem Guaranteeing model confidence for nonparametric Gaussian process regression.
method Derives an upper bound for mean square prediction error using pseudo-concave optimization.
result Upper bound for mean square prediction error of misspecified models.
Minimal Gaussian surfaces partitioning space with minimum area.
problem Partitioning space with minimal Gaussian surface area.
method Second variation argument using infinitesimal translations, combined with Colding-Minicozzi theory and Euclidean Double Bubble Conjecture arguments.
result Triple and Quadruple Bubble Conjectures for Gaussian measure.
New GP model for multi-view learning combining views with regularization.
problem Lack of multi-view learning applications in Gaussian processes.
method Regularizes marginal likelihood with consistency among latent functions from different views, and improves model with point selection scheme.
result Improves performance in multi-view learning across multiple real-world datasets.
Minimal Gaussian surface area sets must be round cylinders if they are convex.
problem Finding sets with minimal Gaussian surface area under symmetry constraints.
method Colding-Minicozzi theory for Gaussian minimal surfaces and randomly chosen degree 2 polynomial.
result Convex sets with minimal Gaussian surface area are round cylinders.
Proves entropy conjecture for closed surfaces, improving on previous results.
problem Entropy of closed surfaces and its relation to self-shrinking surfaces.
method Min-max theory applied to Gaussian area functional in R^3.
result Entropy of all closed embedded 2-spheres is at least that of the self-shrinking two-sphere.
Survey on Gaussian processes and their deep variants.
problem Limitations of Gaussian processes and their derivatives.
method Comprehensive review of existing methods and research themes.
result Advancements in Deep Gaussian Processes over the past decade.
We study stable smooth solutions to the isoperimetric type problem for a Gaussian weight on Euclidean Space. That is, we study hypersurfaces Σn⊂Rn+1 that are second order stable critical points of compact variations that minimize Gaussian weighted area and preserve Gaussian weighted volume. We sho…
Paper proposes a transfer learning framework for tensor Gaussian graphical models.
problem Pooling heterogeneous tensor data for improved estimation and variable selection.
method Transfer learning framework that uses data-adaptive weights from auxiliary domains.
result Significant improvement in estimation errors and variable selection consistency.
Consider a random smooth Gaussian field G(x):F→R, where F is a compact in Rd. We derive a formula for average area of a surface generated by the equation G(x)=0 and give some applications. As an auxiliary result we obtain an integral expression for area of a surface induced by zeros of a \e…
A novel GPDA method for high-dimensional functional data.
problem Classification and feature selection challenges in high-dimensional, non-stationary functional data.
method Unified two-layer non-stationary Gaussian process with Ising prior for variable selection and classification.
result Demonstrated superior performance on simulated and proteomics datasets.
Optimal neuron activation functions improve neural network performance.
problem Limited expressive power of standard neuron activation functions in neural networks.
method Additive Gaussian process regression to construct individual neuron activation functions.
result Optimal neuron activation functions lead to better performance and reduced overfitting.
Improved self-supervised denoising for Poisson-Gaussian noise.
problem Handling Poisson-Gaussian noise in self-supervised denoising.
method Extended blindspot model, improved training scheme without hyperparameters.
result Improved denoising performance on microscope image benchmarks.
MO-GP models fill gaps in biophysical data with across-domain info transfer.
problem Gap filling of biophysical parameters LAI and fAPAR over rice areas.
method Multi-output Gaussian Processes (MO-GP) based on Linear Model of Coregionalization (LMC).
result MO-GP models successfully predict biophysical variables even in high missing data regimes.
The paper extends curvature concepts to surfaces in normed spaces.
problem Extending curvature concepts to surfaces in normed spaces.
method Using Birkhoff orthogonality and surface areas, the paper characterizes Minkowski Gaussian curvature.
result Characterizations and generalizations of classical theorems for curvature in Minkowski spaces.
Study spherical convex bodies using Lp-floating areas and curvature entropy.
problem Analogous isoperimetric inequalities for spherical convex bodies.
method Introduced Lp-floating areas and curvature entropy for spherical convex bodies. result Established isoperimetric inequalities and dual isoperimetric inequalities.
Paper improves AI adaptability in uncertain aerial dogfighting scenarios.
problem Adapting AI to new, volatile objective functions in aerial dogfighting.
method Hybrid Repeat/Multi-point Sampling combined with Bayesian optimization.
result Improved model of objective function leads to better AI adaptability.
New method improves regression models by optimizing correntropy with variable center.
problem Improving regression models by optimizing correntropy with variable center.
method Proposed a new optimization criterion called Maximum Correntropy Criterion with Variable Center (MCC-VC) and an efficient approach to optimize kernel width and center location.
result Simulation results show desirable performance of the new method.
We develop a scoring and classification procedure based on the PAC-Bayesian approach and the AUC (Area Under Curve) criterion. We focus initially on the class of linear score functions. We derive PAC-Bayesian non-asymptotic bounds for two types of prior for the score parameters: a Gaussian prior, and a spike-and-slab p…
Study on spin random fields using chaos decomposition for cosmic microwave background modeling.
problem Modeling polarization of Cosmic Microwave Background using spin random fields.
method Explicit Wiener-Itô chaos decomposition of area measures of level sets.
result Reveals a clear difference between high frequency regime and zero spin case.
Paper analyzes convergence rate of noisy Bayesian Optimization with Expected Improvement.
problem Theoretical convergence behaviors and rates of Expected Improvement (EI) in Bayesian optimization.
method Analyzes Expected Improvement (EI) under Gaussian process (GP) prior assumption, considering noisy observations.
result Established asymptotic error bound and rate for GP-EI with noisy observations.
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gauss…
Introduces new weighted floating functions and affine surface areas.
problem Developing new mathematical concepts for convex bodies.
method Introducing weighted floating functions and weighted functional affine surface areas.
result New relations to traditional and classical affine surface areas.
Characterizes area-minimizing maps for surfaces of genus ≥ 2.
problem Equivariant area-minimizing maps on surface covers.
method Classifies minimal surfaces in Hilbert spheres with constant negative Gaussian curvature.
result Characterizes all equivariantly area-minimizing maps from the universal cover of a surface to a Hilbert sphere.
This paper addresses error bounds and posterior variance for Gaussian process regression.
problem Deriving performance guarantees for Gaussian process regression without prior knowledge.
method Lipschitz continuity and analysis of posterior variance function.
result Uniform error bounds for Gaussian process regression are derived.
Horseshoe priors improve small area estimation by borrowing strength globally but locally.
problem Improving precision of small area estimators through global-local borrowing of strength.
method Developed a tail-robust horseshoe model for Fay-Herriot small area estimation, using heteroscedastic Tweedie identity and regular variation theory.
result The horseshoe model outperforms structured Gaussian smoothing on strongly spatial data, identifying exceptional areas that smoothing suppresses.
Paper optimizes AI for fighter pilots using Bayesian optimization.
problem Optimizing AI behavior for aerial dog fighting with uncertain objectives.
method Bayesian optimization with Gaussian Process surrogate and Hybrid Repeat/Multi-point Sampling.
result Improved model of objective function for better prediction of performance.
Researchers use Gaussian processes with non-stationary kernels to model precipitation patterns in the Upper Indus Basin.
problem Uncertainty in precipitation patterns in the Upper Indus Basin, Himalayas.
method Proposes Gaussian processes with structured non-stationary kernels to model precipitation patterns, accounting for spatial variation with a latent Gaussian process.
result The proposed model adapts to varying precipitation patterns across distinct topography and outperforms stationary models in ablation experiments.
Unified framework for Gaussian process approximations using Power EP.
problem Computational and analytical intractabilities in Gaussian process applications.
method Power Expectation Propagation for pseudo-point approximations of Gaussian processes.
result Unified framework outperforms existing methods on regression and classification tasks.
Develops Gaussian processes on non-Euclidean spaces with symmetries.
problem Invariance to symmetries in non-Euclidean spaces.
method Constructive techniques for stationary Gaussian processes on compact and non-compact spaces.
result Makes non-Euclidean Gaussian processes compatible with standard software.
Develops Gaussian processes on non-compact Lie groups.
problem Invariance to symmetries in non-Euclidean spaces.
method Constructive techniques for stationary Gaussian processes.
result Makes non-Euclidean Gaussian processes compatible with standard software.
Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inf…
The paper shows how heat flow approximates area functional on specific geometric spaces.
problem Approximating the area functional on $\RCD(K,\infty)$ spaces.
method Using heat flow and properties of $\RCD(K,\infty)$ spaces.
result The area functional coincides with its relaxation in $\RCD(K,\infty)$ spaces.
Probabilistic matrix factorization (PMF) is a powerful method for modeling data associated with pairwise relationships, finding use in collaborative filtering, computational biology, and document analysis, among other areas. In many domains, there is additional information that can assist in prediction. For example, wh…
Study on discrete Gaussian curvature for polyhedral surfaces.
problem Discretization of Gaussian curvature for polyhedral surfaces.
method Generalization of discrete conformal equivalence to define discrete Gaussian curvature and classify polyhedral surfaces.
result Existence of polyhedral surfaces with constant discrete Gaussian curvature in every discrete conformal class.
Proves strong Morse inequalities for area functional in low dimensions.
problem Proving Morse inequalities for area functional in specific dimensions.
method Analyzes area functional in codimension one, proving inequalities under given dimension constraints.
result Strong Morse inequalities for area functional in specified dimensions.
The paper develops inequalities for log-concave functions and related surface areas.
problem Understanding log-concave functions and their inequalities.
method Establishing new inequalities through f-divergences and functional affine surface areas.
result New inequalities on functional affine surface area and bounds for Kullback-Leibler divergence.
New algorithm improves Gaussian process hyperparameter tuning for large datasets.
problem Scalable hyperparameter tuning for Gaussian processes on large datasets.
method Estimates smoothness and length-scale parameters in Matern kernel using novel loss functions.
result Improved uncertainty quantification over traditional methods.
AI learns to optimize dog-fighting performance using Bayesian optimization.
problem Optimizing AI decision-making in dynamic, volatile combat environments.
method Developed Gaussian process Bayesian optimization (GPBO) techniques with RS and HRMS to improve surrogate model accuracy.
result HRMS improves surrogate model accuracy, allowing AI to more accurately predict and optimize performance.
Generative model for Lévy area improves SDE simulation accuracy.
problem Simulating Lévy areas for high-order SDEs is challenging due to non-Gaussian nature and lack of fast sampling algorithms.
method LévyGAN, a deep-learning model with a GNN-inspired architecture, generates approximate samples of Lévy area.
result LévyGAN matches all joint and conditional odd moments exactly and achieves state-of-the-art performance in 4D Brownian motion.