Study of Gaussian distributions using entropic Gromov-Wasserstein and inner product Gromov-Wasserstein.
problem Optimal transportation between Gaussian distributions with different dimensions.
method Entropic Gromov-Wasserstein and inner product Gromov-Wasserstein, with closed-form expressions and von Neumann's trace inequality.
result Closed-form expressions for the entropic IGW and its unbalanced variant between Gaussian distributions.
Study on Gaussian ensemble of matrix products with mixed moments computed.
problem Understanding the statistical properties of matrix products of Gaussian matrices.
method Analysis of a multi-Wishart ensemble and enumeration of non-crossing pairings.
result Mixed moments of the product matrix are computed and found to be weighted by Fuss-Catalan numbers at large N. The study finds complete translating solitons for certain powers of Gaussian curvature in Riemannian products.
problem Exploring translating solitons in Riemannian products with powers of Gaussian curvature.
method Investigating Kα-flows in Riemannian products MimesR for M=Rn,Sn,HFm. result Existence of complete rotational translating solitons for certain values of α in MimesR. New method calibrates Gaussian product experts for better predictions.
problem Erratic predictions and uncalibrated uncertainty in Gaussian product experts.
method Calibration via tempered softmax and Wasserstein barycenter for predictions.
result Improved predictions with better mean and uncertainty quantification.
Proposes using entity embedding vectors to improve Gaussian Process models for knowledge transfer across cell lines.
problem Lack of reuse of experimental data for predicting novel processes.
method Hybrid Gaussian Process models with entity embedding vectors to represent product identity.
result Improved performance in predicting novel processes compared to traditional methods.
This work extends entropic optimal transport to non-product reference couplings, focusing on Gaussian cases.
problem Finding a diffuse coupling between two measures with non-product reference couplings.
method Reduction of the entropic optimal transport problem to a matrix optimization problem.
result Complete description of the solution for non-product reference couplings, including primal and dual variables.
Scalable Gaussian processes with latent Kronecker structure for large datasets.
problem Limited scalability of Gaussian processes for large datasets.
method Leveraging latent Kronecker structure, projecting kernel matrix onto latent Kronecker product, using iterative linear system solvers and pathwise conditioning.
result Outperforms state-of-the-art sparse and variational GPs on real-world datasets with up to five million examples.
The study classifies parallel mean curvature spheres in a sphere-hyperbolic product space.
problem Understanding surfaces with parallel mean curvature in a specific Riemannian product space.
method Analyzing the holomorphic quadratic differential and topological constraints.
result Classification of all parallel mean curvature spheres with vanishing differential.
Generalizes randomized SVD for better matrix approximations using Gaussian vectors.
problem Computing accurate rank-k approximations of matrices with limited data.
method Extends randomized SVD to multivariate Gaussian vectors, incorporating prior knowledge and using Gaussian processes.
result Demonstrates improved accuracy in approximating matrices and Hilbert-Schmidt operators.
Embeddings in machine learning are low-dimensional representations of complex input patterns, with the property that simple geometric operations like Euclidean distances and dot products can be used for classification and comparison tasks. The proposed meta-embeddings are special embeddings that live in more general in…
Study on non-gradient Ricci almost solitons in warped products.
problem Understanding non-gradient Ricci almost solitons.
method Construction method and explicit example in warped products.
result Rigidity result for Gaussian soliton.
PoGDiff improves diffusion models on imbalanced datasets.
problem Diffusion models struggle with imbalanced text-image pairs.
method PoGDiff replaces ground-truth with a Product of Gaussians.
result PoGDiff enhances generation accuracy and quality on imbalanced datasets.
The study optimizes wind farm yaw control using Gaussian process regression and high-fidelity simulations.
problem Improving yaw control inputs for maximum power production in wind farms.
method Gaussian process regression and modifier adaptation scheme based on high-fidelity simulation data.
result Both modifier adaptation and Bayesian optimization improve power production with smaller yaw misalignments.
Sum-product networks have recently emerged as an attractive representation due to their dual view as a special type of deep neural network with clear semantics and a special type of probabilistic graphical model for which inference is always tractable. Those properties follow from some conditions (i.e., completeness an…
Paper improves SDR estimation speed and conditions.
problem Improving sufficient dimension reduction for multi-index models.
method Estimating expected smoothed gradient outer product.
result Achieves fast parametric convergence rate of Cd⋅n−1/2. Paper learns Cartesian product graphs with Laplacian constraints.
problem Learning Cartesian product graphs from Laplacian constraints.
method Penalized maximum likelihood estimation (MLE) and efficient algorithm.
result Statistical consistency for Cartesian product Laplacian estimation.
Paper proposes efficient AL algorithms for optimizing product performance under environmental variability.
problem Optimizing product performance under varying environmental conditions.
method Formulated as Bayesian Quadrature Optimization problems for probabilistic threshold robustness measure using Gaussian Process model.
result Proposed algorithms provide credible intervals for probabilistic threshold robustness measure and demonstrate efficiency in real-world applications.
We define cuspidal curvature κc (resp. normalized cuspidal curvature μc) along cuspidal edges (resp. at swallowtail singularity) in Riemannian 3-manifolds, and show that it gives a coefficient of the divergent term of the mean curvature function. Moreover, we show that the product κΠ called the product curva…
The paper studies Lagrangian surfaces in a specific Riemannian product space.
problem Characterizing and classifying Lagrangian surfaces in a particular geometric space.
method Analyzes various types of Lagrangian surfaces and their properties.
result Classification of different types of Lagrangian surfaces.
There are examples of complete spacelike surfaces in the Lorentzian product H2×R1 with constant Gaussian curvature K≤−1. In this paper, we show that there exists no complete spacelike surface in H2×R1 with constant Gaussian curvature K>−1.
We study pseudo-Riemannian Einstein manifolds which are conformally equivalent with a metric product of two pseudo-Riemannian manifolds. Particularly interesting is the case where one of these manifolds is 1-dimensional and the case where the conformal factor depends on both manifolds simultaneously. If both factors ar…
Recent work shows that inference for Gaussian processes can be performed efficiently using iterative methods that rely only on matrix-vector multiplications (MVMs). Structured Kernel Interpolation (SKI) exploits these techniques by deriving approximate kernels with very fast MVMs. Unfortunately, such strategies suffer …
The study classifies warped products with harmonic curvature on surfaces, showing two possibilities for the metric.
problem Classifying warped products with harmonic curvature on surfaces.
method Analyzing the properties of nonconstant warping functions and Gaussian curvature.
result Both possibilities of metrics are realized on closed orientable surfaces of genus greater than 1.
A method for quickly determining deployment schedules that meet a given fuel cycle demand is presented here. This algorithm is fast enough to perform in situ within low-fidelity fuel cycle simulators. It uses Gaussian process regression models to predict the production curve as a function of time and the number of depl…
It is of fundamental importance to find algorithms obtaining optimal performance for learning of statistical models in distributed and communication limited systems. Aiming at characterizing the optimal strategies, we consider learning of Gaussian Processes (GPs) in distributed systems as a pivotal example. We first ad…
Paper proposes a new method to optimize feature coordinates for better image classification.
problem Improving feature extraction for better machine learning classification.
method Mutual-energy inner product optimization method.
result The method enhances low-frequency features and suppresses high-frequency noise, leading to better classification results.
Model predicts epileptic seizures with high accuracy using EEG signals.
problem Predicting epileptic seizures with high accuracy for diagnosis and treatment.
method Pearson's product-moment correlation coefficient with a linear classifier on generalized Gaussian modeling.
result 100% effectiveness for sensitivity and specificity greater than 83%.
Cylinders in warped product spaces have zero curvature.
problem Characterizing cylinders in warped product spaces.
method Proving cylinders have zero extrinsic and intrinsic curvatures.
result Cylinders in M2imesRn have zero curvature. We study products of random matrices in the regime where the number of terms and the size of the matrices simultaneously tend to infinity. Our main theorem is that the logarithm of the ℓ2 norm of such a product applied to any fixed vector is asymptotically Gaussian. The fluctuations we find can be thought of as a…
Flat surfaces in Lie groups with constant curvature are flat.
problem Characterizing surfaces in Lie groups with constant Gaussian curvature.
method Analyzing surfaces as products of curves and using bi-invariant metrics.
result All surfaces of constant curvature in 3D Lie groups are flat.
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data. Sparsity in the kernel weights is obtained by adopting a hierarchical Bayesian approa…
Sum-Product Networks (SPNs) can be regarded as a form of deep graphical models that compactly represent deeply factored and mixed distributions. An SPN is a rooted directed acyclic graph (DAG) consisting of a set of leaves (corresponding to base distributions), a set of sum nodes (which represent mixtures of their chil…
The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We provide closed-form expressions for the mean function and the covariance function of t…
Electricity production via solar energy is tackled via short-term forecasts and risk management. Our main tool is a new setting on time series. It allows the definition of "confidence bands" where the Gaussian assumption, which is not satisfied by our concrete data, may be abandoned. Those bands are quite convenient an…
The study proves a theorem for surfaces using Codazzi operators and investigates parallel mean curvature surfaces.
problem Understanding surfaces with parallel mean curvature in product spaces.
method Intrinsic Klotz-Osserman theorem and Simons' formula.
result The existence of surfaces with parallel mean curvature in product spaces with non-positive Gaussian curvature.
Unified sampling approach for Bayesian imaging problems.
problem Sampling from complex prior and posterior distributions in Bayesian imaging.
method Gaussian latent machine model for efficient prior and posterior sampling.
result Unified and generalized sampling algorithms for various imaging problems.
Factorable surfaces, i.e. graphs associated with the product of two functions of one variable, constitute a wide class of surfaces. Such surfaces in the pseudo-Galilean space with zero Gaussian and mean curvature were obtained in [1]. In this study, we provide new classification results relating to the factorable surfa…
The paper improves sparse Gaussian processes by optimizing predictive loss.
problem Optimizing predictive loss in sparse Gaussian processes.
method Direct loss minimization (DLM) for log-loss and square loss, with product sampling (uPS) and biased Monte Carlo (bMC) for non-conjugate cases.
result DLM shows significant performance improvement in both log-loss and square loss cases.
SA-REMBO adapts to nonstationary high-dimensional optimization.
problem Bayesian Optimization in high-dimensional spaces is limited by the curse of dimensionality and rigidity of global assumptions.
method SA-REMBO uses multiple random Gaussian embeddings and an index variable to adaptively select the best embedding for the optimization problem.
result SA-REMBO outperforms traditional REMBO and other low-rank BO methods across synthetic and real-world benchmarks.
Efficiently models learning curves using Gaussian processes with latent Kronecker structure.
problem Joint modeling of machine learning model performance across hyper-parameters and training progress.
method Imposes latent Kronecker structure to leverage efficient product kernels and handle missing values.
result Matches the performance of a Transformer on a learning curve prediction task.
Deep neural networks approximate analytic functions in high dimensions with exponential rates.
problem Approximating analytic functions in high-dimensional spaces using neural networks.
method Analyzing convergence rates of ReLU and ReLU^k activations in L2(Rd,γd) for d∈N∪{∞}. result Exponential convergence rates for analytic functions in L2(Rd,γd) for d∈N, and dimension-independent bounds for d=∞. Proposes efficient Gaussian approximations for non-Gaussian likelihoods.
problem Computational challenges in learning and inference with non-Gaussian likelihoods.
method Variational inference and moment matching in transformed bases.
result Good approximation quality for binary and multiclass classification.
A scalable method for efficient inference in Gaussian process regression networks.
problem Intractable inference in Gaussian process regression networks (GPRN).
method Tensorization of output space, tensor/matrix-normal variational posteriors, joint optimization, and exploiting Kronecker product structure.
result Captures posterior dependencies and improves inference quality for large number of outputs.
Improves efficiency of random feature approximations for dot product kernels.
problem Efficiency of random feature approximations for dot product kernels.
method Generalization of existing random feature approximations using complex-valued random features, theoretical analysis of variances, data-driven optimization approach.
result Complex-valued random features can significantly reduce the variances of approximations.
The abstract conjectures and proves conditions for scalar-flat Kähler surfaces with specific tensor properties.
problem Conditions for scalar-flat Kähler surfaces with special tensor properties.
method Conjecture and prove in three special cases.
result The conjecture is proven in three special cases.
For any closed Riemannian manifold X we prove that large isoperimetric regions in X×Rn are of the form X×(Euclidean ball). We prove that if X has non-negative Ricci curvature then the only soap bubbles enclosing a large volume are the products X×(Euclidean sphere). We give an example…
We introduce a kernel approximation strategy that enables computation of the Gaussian process log marginal likelihood and all hyperparameter derivatives in O(p) time. Our GRIEF kernel consists of p eigenfunctions found using a Nystrom approximation from a dense Cartesian product grid of inducing points. B…
In this work, we propose a generalized product of experts (gPoE) framework for combining the predictions of multiple probabilistic models. We identify four desirable properties that are important for scalability, expressiveness and robustness, when learning and inferring with a combination of multiple models. Through a…