The paper introduces a method to probabilistically select inducing points in sparse Gaussian processes.
problem The challenge is selecting the optimal number of inducing points in sparse Gaussian processes.
method A point process prior is applied to the inducing points, and the posterior is approximated using stochastic variational inference.
result The model learns which and how many inducing points to use, leading to fewer inducing points being preferred as they become less informative.
A new method selects inducing points to optimize high-throughput Bayesian optimisation.
problem Current inducing point selection methods sacrifice high-fidelity modeling of promising regions.
method Information-theoretic criterion to select inducing points maximizing global and maximum value uncertainties.
result Surrogate models support high-precision high-throughput Bayesian optimisation.
Local GP approach improves simulation efficiency for large datasets.
problem High computational cost of traditional Gaussian processes for large-scale simulations.
method Hybridizes global and local GP approximations with strategic placement of inducing points.
result Local inducing points enhance accuracy and computational efficiency.
Study investigates induced geometry on surfaces in 3D contact manifolds.
problem Understanding the metric structure on surfaces embedded in 3D contact sub-Riemannian manifolds.
method Defined a coefficient to characterize characteristic points and identified global conditions for finite induced distance.
result Proved induced distance finite for certain surfaces with isolated characteristic points.
Global inducing points improve Bayesian neural network performance.
problem Improving Bayesian neural network performance.
method Adapting correlated approximate posterior to all layers in a Bayesian neural network and deep Gaussian processes using learned global inducing points.
result State-of-the-art performance on CIFAR-10 (86.7%) without data augmentation or tempering.
HIP-GP improves GP inference for inter-domain observations with millions of inducing points.
problem Inference for Gaussian Processes across different domains.
method Hierarchical inducing point Gaussian process with grid structure and stationary kernel assumption.
result Improved approximation accuracy through increased number of inducing points.
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…
VNNGP uses nearest neighbors to approximate GPs, improving scalability and performance.
problem Scalability issues in Gaussian process approximations.
method Sparse precision structure via nearest neighbors, variational framework.
result VNNGP outperforms low-rank methods and is less prone to overfitting.
Sparse Gaussian Processes improve scalability by learning inducing points from data.
problem Scaling issues in Gaussian Processes due to cubic computational cost.
method Amortized learning of inducing points and variational posterior parameters using neural networks.
result Significant reduction in the number of inducing points, improving scalability.
New method optimizes Gaussian process allocation for BO.
problem Existing methods for inducing point allocation in BO hinder performance.
method Proposes a new allocation strategy using quality-diversity decomposition.
result Demonstrates improved BO performance through local high-fidelity modeling.
New method DDVI improves posterior inference for deep Gaussian processes.
problem Inference of inducing points in DGPs is challenging and biased.
method DDVI uses denoising diffusion SDE and score matching for posterior approximation.
result Empirically shows DDVI outperforms baseline methods in inducing point inference.
Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive performances but do not intrinsically provide uncertainty estimates. In contras…
Proposes FIPO-BC for efficient online calibration of complex models.
problem Efficiently calibrating computationally expensive models with large datasets.
method Fixed inducing points online Bayesian calibration (FIPO-BC) algorithm.
result FIPO-BC is at least ten times faster than standard methods and enables online updates.
Proposes IGN for scalable Gaussian process networks.
problem Scalability and expressivity challenges in Gaussian processes.
method Inducing Gaussian process networks with learned inducing points.
result Significant advances over state-of-the-art methods.
New method combines spectral and sparse methods for Gaussian processes.
problem Efficiently fitting Gaussian processes to large datasets.
method Orthogonally decoupled variational Fourier features.
result Competitive performance on synthetic and real-world data.
We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point a…
Adaptive selection of IPs improves online GP performance.
problem Efficiently training GPs in streaming data.
method Adaptive selection of inducing points (IPs) based on GP properties and data structure.
result Adaptive IPs enhance online GP performance.
New method improves stability of Gaussian process approximations.
problem Numerical instability in Gaussian process computations.
method Cover tree modification for inducing points, alternative sparse approximation.
result Improved stability and predictive performance in spatial tasks.
Proposes efficient Gaussian process approximations for large datasets.
problem Scalability issues in Gaussian processes for large data sets.
method Combines Vecchia approximations and inducing points methods.
result Efficient and accurate approximations for various data types.
VAR-GPs solve continual learning by updating posteriors sequentially.
problem Catastrophic forgetting in sequential learning tasks.
method Sparse inducing point approximations and auto-regressive variational distribution.
result VAR-GPs prevent catastrophic forgetting and outperform baselines.
Learning new representations of input observations in machine learning is often tackled using a factorization of the data. For many such problems, including sparse coding and matrix completion, learning these factorizations can be difficult, in terms of efficiency and to guarantee that the solution is a global minimum.…
New algorithms improve GP inference without approximations, achieving better results.
problem Inexact stochastic optimization methods in Gaussian Processes leading to biased results.
method Exact stochastic inference for GPs with finite dimensional RKHS, extending to infinite dimensions.
result Achieves better experimental results than existing methods in constrained resource settings.
Paper tightens variational GP approximations for large datasets.
problem Scaling Gaussian processes to large datasets.
method Relaxing the standard assumption about inducing points' posterior matching the prior, leading to a tighter variational approximation.
result The proposed approximation consistently matches or outperforms standard sparse variational GPs while maintaining computational cost.
We present Blitzkriging, a new approach to fast inference for Gaussian processes, applicable to regression, optimisation and classification. State-of-the-art (stochastic) inference for Gaussian processes on very large datasets scales cubically in the number of 'inducing inputs', variables introduced to factorise the mo…
ASkotch solves large-scale KRR faster and better than existing methods.
problem Challenges in scaling full Kernel Ridge Regression (KRR) to large datasets.
method ASkotch: A scalable, accelerated, iterative method for full KRR.
result ASkotch provides better solutions faster than state-of-the-art solvers for full and inducing points KRR.
PerfGD solves model-induced data shifts by finding optimal points.
problem Model-induced data shifts where model choice changes data distribution.
method Performative Gradient Descent (PerfGD) which explicitly captures model-data interactions.
result PerfGD provably converges to performatively optimal point.
We find a new relation among right-handed Dehn twists in the mapping class group of a k-holed torus for 4≤k≤9. This relation induces an elliptic Lefschetz pencil structure on the four-manifold \cp $#(9-k)$ \cpb with k base points and twelve singular fibers. By blowing up the base points we get an el…
The paper proposes a method to detect credit card fraud using sparse Gaussian approximations.
problem Detecting credit card fraud in financial institutions.
method Sparse Gaussian classification method with pseudo or inducing inputs and different kernels and inducing points.
result The RBF kernel with a higher number of inducing points achieved the best accuracy.
We establish a product formula for Gromov-Witten invariants for closed, connected, relatively semi-positive Hamiltonian fibrations over any symplectic base. Furthermore, we show that the fibration projection induces a locally trivial (orbi-)fibration map from the moduli space of pseudo-holomorphic maps with marked poin…
Real slices of parabolic opers on Riemann surfaces are studied.
problem Understanding the fixed-point locus of involutions on parabolic opers.
method Investigated the space of parabolic SL(r,C)-opers and their involutions.
result Fixed-point loci of involutions on different descriptions of parabolic opers coincide.
Sparse GPs improved with nearest neighbor inducing variables.
problem Sparse GPs struggle with large numbers of inducing variables.
method Introduced a hierarchical prior for inducing variables and used nearest neighbor information for sparsity.
result Significant computational gains compared to standard sparse GPs.
Efficient poisoning attack converges to any target classifier with provable convergence.
problem Inducing a corrupted model that misbehaves in favor of an adversary.
method Online convex optimization to find poisoning points incrementally.
result Provably converges to any attainable target classifier.
We introduce a representation theory for risk operations on locally compact groups in a partition of unity on a topological manifold for Markowitz-Tversky-Kahneman (MTK) reference points. We identify (1) risk torsion induced by the flip rate for risk averse and risk seeking behaviour, and (2) a structure constant or co…
DGKIP extends KIP for dataset distillation without bi-level optimization.
problem Efficiently distill datasets for various loss functions.
method Leverages duality theory to avoid bi-level optimization.
result DGKIP supports a wider range of loss functions.
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of inducing points. The inference is accurate only when data points have strong corre…
Gaussian processes (GPs) are flexible models that can capture complex structure in large-scale dataset due to their non-parametric nature. However, the usage of GPs in real-world application is limited due to their high computational cost at inference time. In this paper, we introduce a new framework, \textit{kernel di…
Bayesian approach improves performance in Gaussian process models.
problem Scalable posterior estimation in Gaussian process models.
method Revisiting variational inference techniques with Bayesian treatment of inducing variables and hyper-parameters.
result State-of-the-art performance demonstrated across various regression and classification problems.
This paper analyzes error in SKI for Gaussian Processes, providing conditions for linear time inference.
problem Lack of rigorous theoretical error analysis for SKI.
method Proved error bounds for SKI Gram matrix, examined error effects, provided practical guidelines.
result Identified two dimensionality regimes for SKI's scalability-accuracy trade-offs.
This paper constructs a family of coordinate systems about a point on a quaternionic contact manifold, called quaternionic contact pseudohermitian normal coordinates. Once defined, conformal variations of the quaternionic contact structure induce changes on the coordinates which are studied in an effort to simplify the…
The fine curve graph is hyperbolic and contains all countable graphs as induced subgraphs.
problem Characterizing the structure and properties of fine curve graphs.
method Analyzing the hyperbolicity and induced subgraph properties of fine curve graphs and their direct limits.
result The finitary curve graph has diameter 2, contains every countable graph as an induced subgraph, and has the homeomorphism group of the surface as its automorphism group.
CDP reduces point cloud dimensions by preserving detour-induced local non-convexity.
problem Preserving local non-convexity in point cloud dimensionality reduction.
method CDP builds a k-NN graph, identifies admissible pairs, aggregates normalized directions, and uses top-k eigenvectors for projection.
result CDP provides verifiable guarantees on post-projection distortion and direction energy.
Extends Khovanov homology to surfaces with singularities.
problem Computing invariants for surfaces with singularities.
method Functorial extension of Khovanov homology to surfaces with double points.
result Induces a map between Khovanov homology groups of boundary links.
Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional independence. We describe some conditional independencies through the conditions on t…
On the space of positive 3-forms on a seven-manifold, we study a natural functional whose critical points induce metrics with holonomy contained in G2. We prove short-time existence and uniqueness for its negative gradient flow. Furthermore, we show that the flow exists for all times and converges modulo diffeomorph…
Quantizes the standard hyperkähler space R^(4n) without a point.
problem Quantizing the standard hyperkähler space R^(4n) without a point.
method Constructs a quantization replacing the family of Berezin-Toeplitz quantizations.
result Provides semiclassical asymptotics for the constructed quantization.
Gaussian process classification is a popular method with a number of appealing properties. We show how to scale the model within a variational inducing point framework, outperforming the state of the art on benchmark datasets. Importantly, the variational formulation can be exploited to allow classification in problems…
We construct bosonic and fermionic locally covariant quantum field theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.
A connected regular surface in Lorentz-Minkowski 3-space is called a mixed type surface if the spacelike, timelike and lightlike point sets are all non-empty. Lightlike points on mixed type surfaces may be regarded as singular points of the induced metrics. In this paper, we introduce the L-Gauss map around non-degener…