Stochastic neural networks use Gaussian noise with monotonic activation functions.
problem Training RBM with non-linearities.
method Laplace approximation with Gaussian noise for monotonic activation functions.
result Exp-RBM learns useful representations using stochastic units.
Additive Gaussian process framework handles monotonicity constraints in high dimensions.
problem Handling monotonicity constraints in high-dimensional data.
method Additive Gaussian process framework with MaxMod algorithm for dimension reduction.
result Framework enables to satisfy monotonicity constraints everywhere in the input space.
The paper proves learning-curve monotonicity for maximum likelihood estimators in various parametric settings.
problem Establishing monotonicity guarantees for maximum likelihood estimators.
method Variants of GPT-5.2 Pro were used to derive the results.
result The paper proves monotonicity for maximum likelihood estimators in Gaussian and Gamma variables.
Modeling disease progression in brain images using monotonic Gaussian Processes.
problem Disentangling spatio-temporal disease trajectories from brain imaging data.
method Spatio-temporal matrix factorization with anatomically plausible priors, monotonic Gaussian Processes, and sparse codes.
result Monotonic Gaussian Processes model realistic disease trajectories in brain imaging data.
Monotonicity helps in safely optimizing unknown functions.
problem Sequentially maximizing an unknown function with safety constraints.
method Gaussian process with monotonicity assumption, inspired by GP-UCB and SafeOpt.
result The proposed M-SafeUCB algorithm achieves theoretical guarantees and safety.
Study learns a neuron with non-monotonic activation functions.
problem Learning a single neuron with non-monotonic activation functions.
method Gradient descent (GD) with conditions on activation function and input distribution.
result Learnability of non-monotonic activation functions is established without monotonicity assumption.
Novel framework for efficient Gaussian process models with monotonicity constraints.
problem Improving predictive accuracy and reducing uncertainty in high-dimensional problems with monotonicity constraints.
method Virtual point-based framework using regularized linear randomize-then-optimize (RLRTO) and No U-Turn Sampler (NUTS) for efficient sampling.
result Significant improvements in computational efficiency with the RLRTO method and NUTS enhancements.
Sharp Gaussian isoperimetry proven along Ricci flow.
problem Proving sharp Gaussian isoperimetric inequality for Ricci flow.
method Using monotonicity formula to prove inequality.
result Exact Gaussian enlargement theorem and concentration estimates.
Proposes a Bayesian nonparametric model for monotonic functions.
problem Imposing monotonicity constraints in Bayesian nonparametric models.
method Numerical solutions of stochastic differential equations for nonparametric model of monotonic functions.
result Demonstrates competitive results on benchmark functions and utility in temporal alignment of time-series data.
Novel GP-modulated Cox process framework with linear inequality constraints.
problem Modeling point patterns with positiveness and inequality constraints.
method Directly impose positiveness and inequality constraints on the Gaussian process without restrictions on covariance functions.
result Accurate inference of intensity functions with improved results for monotonic processes.
Monotonic improvement in uncertainty estimation with Gaussian processes as dimension increases.
problem Uncertainty quantification in machine learning models, especially with Gaussian processes, is challenging and poorly understood.
method Analyzing the behavior of marginal likelihood and cross-validation metrics as input dimension increases, and exploring the effects of cold posteriors.
result The marginal likelihood improves monotonically with input dimension, while cross-validation metrics exhibit double descent behavior.
Study on cut locus structure of a specific Randers surface.
problem Analyzing the cut locus of a Randers rotational 2-sphere.
method Examined Gaussian curvature monotonicity and its effect on cut locus.
result Cut locus properties depend on Gaussian curvature monotonicity.
A faster EM algorithm for unsupervised Gaussian mixture models.
problem Efficiently determining the number of components in Gaussian mixture models.
method Adaptive Anderson Acceleration (AA) for EM algorithm, with novel monotonicity control and covariance matrix preservation.
result Significantly faster convergence compared to non-accelerated EM, up to 60X in some cases.
New kernels model non-stationary data efficiently.
problem Efficiently modeling non-stationary data with Gaussian processes.
method Model spectral density as a mixture of frequency surfaces, solve generalised Fourier transform.
result Derives efficient inference methods for non-stationary kernels.
New work shows FP potential monotonicity equals low-degree polynomial estimators limits.
problem Establishing a precise mathematical relationship between statistical physics and polynomial estimators limits.
method Analyzing Gaussian additive models (GAMs) to show FP potential monotonicity equals low-degree polynomial estimators limits.
result For a broad family of Gaussian additive models, the power of low-degree polynomials is equivalent to the monotonicity of the annealed FP potential.
Develops a new flow with free boundary in barrier surfaces.
problem Free-boundary problems in barrier surfaces.
method Develops Brakke flow with free boundary, proves compactness, Gaussian monotonicity, and existence.
result Proves existence of free-boundary Brakke flows.
Solves a long-standing convex geometry problem about mixed volumes.
problem Characterizing the support of mixed area measures.
method Geometric approach to convex bodies in R^n and R^3.
result Resolved one direction of Schneider's conjecture for arbitrary convex bodies.
Bayesian optimization improves Monte-Carlo tree search for better state value estimation.
problem Slow convergence in Monte-Carlo tree search due to averaging in backpropagation.
method Softmax MCTS and Monotone MCTS, using Bayesian optimization with Gaussian process prior.
result Our framework outperforms previous methods in computer Go.
A new GP method enforces physical constraints in probabilistic terms.
problem Unbounded model in GP regression leading to infeasible values.
method Introduces a new GP method using QHMC to enforce soft inequality and monotonicity constraints.
result Improves accuracy and reduces variance in GP model.
A method for inferring ground-truth signals from degraded sensor data.
problem Inferring ground-truth signals from multiple degraded sensor signals.
method Iterative correction of degraded signals using a Bayesian multi-sensor data fusion method.
result The method effectively infers ground-truth signals from noisy and degraded sensor data.
Near-optimal private tests for simple and MLR hypotheses developed under Gaussian differential privacy.
problem Developing private tests for simple and MLR hypotheses under Gaussian differential privacy.
method A private mean estimator with data-driven clamping bounds, constructing private test statistics.
result Private tests achieve the same asymptotic relative efficiency as non-private most powerful tests.
Algorithm identifies and corrects noisy labels using Gaussian process regression.
problem Detecting and correcting real-valued noisy labels from mixed data.
method Gaussian process regression with heteroscedastic noise model and leave-one-out cross-validation.
result The method can pinpoint corrupted sample points and improve regression models.
Unified model improves multi-task learning by accounting for temporal misalignment.
problem Poor predictive performance and uncertainty quantification due to temporal misalignment in multi-task learning.
method Uses Gaussian processes to model correlations and includes a monotonic warp of the input data to account for temporal misalignment.
result Improves predictive performance and uncertainty quantification in multi-task learning.
Improves active learning efficiency by warping input space based on observed outputs.
problem Insensitivity of Gaussian process uncertainty to actual observations.
method Input warping with learned monotone reparameterization to adjust acquisition function behavior.
result Significantly improved sample efficiency across various benchmarks, especially in non-stationary conditions.
Diffusion models optimize objectives similar to ELBO with Gaussian noise augmentation.
problem Optimizing diffusion models for high perceptual quality.
method Showed diffusion objectives are weighted ELBOs over noise levels, with Gaussian noise augmentation.
result Diffusion objectives equate to ELBO with Gaussian noise augmentation under monotonic weighting.
A new copula model for multi-attribute data using optimal transport.
problem Relaxing the Gaussian assumption for multi-attribute graphical models.
method Introducing a new copula (Cyclically Monotone Copula) and using optimal transport theory.
result The model allows arbitrary continuous distributions and is more flexible than classical methods.
Proposes a method to incorporate hunches in experimental design for faster convergence.
problem Expensive experiments and expert hunches in experimental design.
method Two-stage Gaussian process modeling with monotonicity information.
result Faster convergence in experimental design problems.
Survey of Gaussian process constraints for modeling expensive data.
problem Modeling expensive data with physical constraints.
method Overview of various Gaussian process constraints and their implementation.
result Discussion of computational challenges introduced by constraints.
New method for optimizing risk in financial models using Fourier transforms.
problem Optimizing risk in financial models with multi-period mean-CVaR.
method Strictly monotone 2D integration scheme via Fourier-trained transition kernels.
result Established robust and accurate optimization method for financial models.
Smoothed SGD improves quantile estimation without crossing curves.
problem Estimating quantiles without crossing estimated curves.
method Smoothed SGD algorithm with Bahadur representation and Gaussian approximation.
result Smoothed SGD provides non-asymptotic tail probability bounds and a Gaussian approximation for quantile estimates.
We prove a generalization of the Li-Yau estimate for a board class of second order linear parabolic equations. As a consequence, we obtain a new Cheeger-Yau inequality and a new Harnack inequality for these equations. We also prove a Hamilton-Li-Yau estimate, which is a matrix version of the Li-Yau estimate, for these …
The paper solves curvature prescription on a disk with negative Gaussian curvature.
problem Prescribing Gaussian curvature and geodesic curvature on a disk with negative Gaussian curvature.
method Variational approach, critical points of a functional, perturbation argument, monotonicity trick, blow-up analysis, Morse index estimates.
result General existence results for the curvature prescription problem.
Extends Gaussian process approach to handle linear inequality constraints.
problem Real-world problems with inequality constraints.
method Finite-dimensional Gaussian approach with linear inequality constraints, MCMC techniques.
result Efficient results on data fitting and uncertainty quantification.
Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with…
Eigenfunction value distribution shows unimodal density with maximum at zero.
problem Understanding the value distribution of Laplace eigenfunctions.
method Analyzing the measure μ whose density is ∣ablaf∣2 and proving a monotonicity formula. result Eigenfunction value distribution under μ is unimodal with maximum at zero. In this note, we study Liouville type theorem for conformal Gaussian curvature equation (also called the mean field equation) −Δu=K(x)eu,inR2 where K(x) is a smooth function on R2. When K(x)=K(x1) is a sign-changing smooth function in the real line R, we have a non-existence result for the finite to…
Stein variational gradient descent improves inference in Gaussian process models.
problem Inference in Gaussian process models with non-Gaussian likelihoods and large data volumes is computationally intensive and inaccurate with traditional methods.
method Stein variational gradient descent (SVGD) for non-parametric inference.
result SVGD monotonically decreases the Kullback-Leibler divergence from the sampling distribution to the true posterior.
Algorithm reduces regret in safe Bayesian optimization with monotonicity constraints.
problem Sequentially maximize unknown function with safety constraints.
method Sequential algorithms using Gaussian processes with safety constraints modeled as monotonicity.
result Sublinear regret achieved for expanding safe region and finding optimal s. A new approach to kernel adaptive filters reduces sparsity for monotonic signals.
problem Kernel adaptive filters struggle with trivial monotonic signals, leading to inaccurate predictions and high computational complexity.
method Proposes a unit-norm Gaussian kernel and sparsification criterion to compare new observations against dictionary samples.
result The method achieves more accurate predictions and smaller dictionary size compared to standard KAF.
Evidence found for critical behavior in financial data.
problem Understanding the statistical properties of financial markets.
method Analysis of normalized return distributions for top companies, modeling with q-Gaussians.
result Monotonic relationship between q and β, indicating critical behavior.
A novel approach finds optimal compromise solutions in many-objective Bayesian optimization.
problem Extending multiobjective Bayesian optimization to many objectives.
method Kalai-Smorodinski solution in copula space, tailored Bayesian optimization algorithm.
result The Kalai-Smorodinski solution is found to be interpretable and insensitive to objective transformations.
Gradient EM converges globally for over-parameterized Gaussian mixtures.
problem Global convergence of gradient EM for Gaussian mixtures with more than 2 components.
method Likelihood-based convergence analysis framework.
result Gradient EM converges globally with a sublinear rate of O(1/√t).
Study reveals how neural network smoothness affects their vulnerability to adversarial attacks.
problem Understanding adversarial vulnerability in deep learning networks.
method Analysis of manifold smoothness and generalization capability of deep neural networks trained with local errors.
result High generalization accuracy requires a fast power-law decay of eigen-spectrum of hidden representations.
A scalable method for estimating spatial data using VREML.
problem Costly computation of REML for large, sparse precision matrices in spatial data.
method Proposes VREML framework approximating marginal likelihood with Gaussian variational distribution and deriving a coordinate-ascent algorithm.
result Empirically shows VREML outperforms MLE and INLA.
This work provides guaranteed bounds on the total variation distance for univariate mixtures.
problem Lack of closed-form expressions for total variation distance between mixtures.
method Two methods: information monotonicity for lower bounds and geometric envelopes for upper bounds.
result Demonstrated tightness of bounds on Gaussian, Gamma, and Rayleigh mixtures.
The paper addresses monotonicity in machine learning models for fairness and accountability.
problem Ensuring fairness and accountability in transparent machine learning models.
method Study of three types of monotonicity (individual, weak pairwise, strong pairwise) and propose monotonic groves of neural additive models.
result Monotonic groves of neural additive models maintain transparency, accountability, and fairness.
Variational Gaussian approximates Poisson data for Bayesian inference.
problem Analytically intractable posterior distribution for Poisson data.
method Variational Gaussian approximation minimizing Kullback-Leibler divergence.
result Explicit lower bound for optimization, efficient algorithm for solving.
There is no known efficient method for selecting k Gaussian features from n which achieve the lowest Bayesian classification error. We show an example of how greedy algorithms faced with this task are led to give results that are not optimal. This motivates us to propose a more robust approach. We present a Branch and …