Solves optimal stopping for Gauss-Markov bridges using time-space transformation.
problem Optimal stopping problem of a Gauss-Markov bridge.
method Time-space transformation approach, Picard iteration algorithm.
result Lipschitz continuity of the optimal stopping boundary and its characterization.
Extended Gauss-Markov theorem for linear estimation with bounded bias.
problem Linear estimation with bounded bias operator.
method Derive optimal estimator formulas for Nuclear and Spectral norms, analyze generalization error.
result Cross-validated Nuclear and Spectral regressors outperform Ridge regression in simulations.
Fenrir uses probabilistic numerics to simplify solving initial value problems.
problem Solving initial value problems in ordinary differential equations.
method Probabilistic numerics and Gauss--Markov regression.
result The method simplifies parameter estimation in ODEs, making it easier and more robust.
New method improves Kalman filtering and smoothing for large state spaces.
problem High computational cost and uncertainty in large-scale Kalman filtering.
method Probabilistic numerical method leveraging GPU acceleration and tunable trade-off.
result Mitigates scaling issues and provides more accurate uncertainty estimates.
Fast algorithm solves BVPs in linear time with probabilistic uncertainty.
problem Solving boundary value problems efficiently and accurately.
method Gauss--Markov prior tailored to BVPs, linear-time computation.
result Probabilistic solution with linear time complexity and comparable quality.
The paper shows how to answer future and past questions from high-dimensional time series data.
problem Challenges in answering probabilistic inference questions from high-dimensional time series data.
method Temporal contrastive learning to learn Gaussian representations that enable compact closed-form solutions.
result Representations learned via contrastive learning follow a Gauss-Markov chain, enabling efficient inference and planning.
Optimal sensor placement minimizes information loss from simulations.
problem Designing efficient sensor networks for spatiotemporal processes.
method Model-based sensor placement criterion with sparse variational inference and Gauss-Markov priors.
result Our method identifies sensor networks that minimize information loss from simulated data.
Enhances machine learning interpretability using category theory.
problem Improving machine learning interpretability and social implementation.
method Develops a categorical framework for structured understanding of supervised learning.
result Introduces the Gauss-Markov Adjunction for clarifying residuals and parameters.
Bayesian approach improves ODE solution accuracy.
problem Improving numerical solutions of ordinary differential equations.
method Bayesian inference with Gaussian filtering and smoothing.
result Maximum a posteriori estimate converges to true solution at polynomial rate.
Runge-Kutta methods are the classic family of solvers for ordinary differential equations (ODEs), and the basis for the state of the art. Like most numerical methods, they return point estimates. We construct a family of probabilistic numerical methods that instead return a Gauss-Markov process defining a probability d…
Fermat-Torricelli points help assess investment risks by smoothing series data.
problem Analyzing investment risks in series with large variance, nonlinear trends, or non-normal distributions.
method Construct Fermat-Torricelli points to reduce random component influence.
result Smoothing series by Fermat-Torricelli points reduces risk assessment errors.
New Hida-Matérn kernels enable flexible process priors and efficient GP inference.
problem Flexible modeling of stationary processes with oscillatory components.
method Introducing a new class of covariance functions (Hida-Matérn kernels) and their state space representations.
result Efficient Gaussian Process inference and improved numerical stability.
A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution x and its first q derivatives \emph{a priori} as a Gauss--Markov process X, which is…
Improves deep learning performance on noisy datasets using inverse-variance weighting.
problem Heteroscedastic regression with varying noise levels.
method Batch Inverse-Variance (BIV) loss function for neural networks.
result Significantly improves network performance on noisy datasets compared to other methods.
The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in the inverse covariance matrix, commonly referred to as the precision matrix, cor…
We consider the question of learning in general topological vector spaces. By exploiting known (or parametrized) covariance structures, our Main Theorem demonstrates that any continuous linear map corresponds to a certain isomorphism of embedded Hilbert spaces. By inverting this isomorphism and extending continuously, …
Paper proposes a bias-constrained deep learning approach to non-linear estimation.
problem Designing unbiased estimators for non-linear models.
method Bias Constrained Estimator (BCE) using deep learning with bias constraints.
result Asymptotic MVUEs with Cramer Rao bound performance.
Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds
problem Convergent approximation of Gaussian Whittle-Matern fields on Riemannian manifolds
method Finite Element approximation of SPDEs
result Universal approximation of precision and covariance matrices
Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In this paper, we study the family of GGMs with small feedback vertex sets (FVSs), whe…