arXiv research

Batch Active Learning uses derivative information for Gaussian Process regression.

This paper simplifies MTGP derivations for Gaussian processes.

Bayesian optimization sped up with scalable Gaussian processes.

Modeling counterparty risk is computationally challenging because it requires the simultaneous evaluation of all the trades with each counterparty under both market and credit risk. We present a multi-Gaussian process regression approach, which is well suited for OTC derivative portfolio valuation involved in CVA compu…

New method scales Gaussian processes with derivatives using variational inference.

Sharp Gaussian isoperimetry proven along Ricci flow.

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure and uniform error bounds have been derived, which allow safe control based on thes…

NGD improves multivariate Gaussian inference by optimizing Fisher information.

SLEIPNIR improves Gaussian process regression with derivatives, scaling up efficiently and accurately.

DSoftKI scales GP regression with full derivative observations.

This paper extends explainability methods to non-Gaussian Gaussian Processes.

Sharp Gaussian bounds derived for Schrödinger kernel on Ricci solitons.

Study utility maximization with delayed information in continuous time Gaussian markets.

Bayesian inference for wide neural networks using Edgeworth expansion.

Paper shows how sparse inversion speeds up log determinant derivatives.

Paper derives a simplified formula for Expected Improvement using log-transformed data.

We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the means and covariances of joint probabilities. This implies that novel filters and …

Optimal algorithms learn Gaussian trees and polytrees from data.

Paper studies Gaussian approximation in linear regression with rates derived.

Gaussian and bootstrap methods improve ATE estimator accuracy.

In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and corresponding Gaussian Process kernels are derived. Experimen- tal results demonstrat…

Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes using their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed…

TERA method speeds up derivative Gaussian processes in high dimensions.

The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In particular, we consider a Gaussian factor model where the short rate and the spreads are…

A new model for complex cells accounts for insensitivity to image shifts.

New non-separable covariance kernels for spatiotemporal data derived from harmonic oscillator physics.

Study on manifolds with kinks and Gaussian kernel behavior.

Researchers derive an analytic expression for Gaussian stochastic volatility models.

Improved Gaussian Process regression using TQFF over RFF and Gaussian QFF.

Derives RL framework for systems without velocity or acceleration measurements.

Study on surfaces with conical singularities and geodesic boundaries, deriving existence results.

Sharp risk bounds for early-stopping in Gaussian linear regression are derived.

This paper improves Gaussian process predictions by integrating prior knowledge.

We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the covariance kernel of a G…

We provide a correction to the expression for scoring Gaussian directed acyclic graphical models derived in Geiger and Heckerman [Ann. Statist. 30 (2002) 1414-1440] and discuss how to evaluate the score efficiently.

In this we paper we recast the Cox--Ingersoll--Ross model of interest rates into the chaotic representation recently introduced by Hughston and Rafailidis. Beginning with the ``squared Gaussian representation'' of the CIR model, we find a simple expression for the fundamental random variable X. By use of techniques fro…

Sparse Markovian Gaussian processes improve probabilistic model inference for large datasets.

Improved estimator for least squares using random projections achieves smaller error.

Extends Stein's lemma to exponential-family mixtures for gradient computation.

Directly proves Brioschi formula for Gaussian curvature.

Method estimates noise variance in Gaussian process regression.

Optimal classifiers derived from GMMs are approximated by deep neural networks.

Defines a new short rate model and convexity adjustment formulae.

We derive Gaussian approximations for random forest predictions using region-based stabilization.

We study active learning (AL) based on Gaussian Processes (GPs) for efficiently enumerating all of the local minimum solutions of a black-box function. This problem is challenging due to the fact that local solutions are characterized by their zero gradient and positive-definite Hessian properties, but those derivative…

Paper analyzes GP derivatives for error propagation in geoscience.

Fractional porous media equations yield q-Gaussian solutions for stock price returns.

Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$ dimensions requires linear solves and log determinants with an ${n(d+1) \times n(d…