The Brownian bridge serves as a physics-informed prior for solving the Poisson equation.
problem Reconstructing physical fields from limited and noisy data with known governing equations.
method Formalizing inverse problems via Bayesian inference in function spaces using a Brownian bridge Gaussian process.
result The Brownian bridge Gaussian process can be viewed as a physics-constrained prior for the Poisson equation, allowing for a fully Bayesian framework.
Method reduces complexity of spatial interaction networks.
problem Complex spatial interaction networks.
method Empirical Bayes approach with tree partitioning and generalized double Pareto prior.
result Compact vectorial representations and interpretable visualizations.
Develops a data augmentation method for models with gamma functions.
problem Models with gamma functions lack natural conjugate priors, complicating inference and prediction.
method Derives Pólya Inverse Gamma distributions and applies them to scalable EM and MCMC algorithms.
result Provides scalable algorithms for inference and prediction in models with gamma functions.
BART is extended to handle various response variables.
problem Modeling nonlinear regression functions for diverse response types.
method Generalized Bayesian Additive Regression Trees (GBART) for exponential family distributions.
result The posterior concentrates at a minimax rate for certain response distributions.
Researchers calculated EVaR for various distributions using Lambert function.
problem Difficulty in finding analytical representation of EVaR measure.
method Used Lambert function to calculate EVaR for multiple distributions.
result Successfully calculated EVaR for 7 specific distributions.
Developed shrinkage methods for Poisson regression models with experts to handle multicollinearity.
problem Multicollinearity in Poisson regression models with experts.
method Ridge and Liu-type shrinkage methods.
result Shrinkage methods offer more reliable estimates for coefficients in multicollinearity.
We extend the correspondence between Poisson maps and actions of symplectic groupoids, which generalizes the one between momentum maps and hamiltonian actions, to the realm of Dirac geometry. As an example, we show how hamiltonian quasi-Poisson manifolds fit into this framework by constructing an ``inversion'' procedur…
Novel Bayesian framework for Poisson inverse problems using Bregman geometry.
problem Solving Poisson inverse problems with non-Euclidean geometry and positivity constraints.
method Develops a Monte Carlo sampling algorithm that accounts for Bregman geometry, data augmentations, and conditional conjugacy properties.
result Efficient sampling via Gibbs steps and Hessian Riemannian Langevin Monte Carlo (HRLMC) for positivity constraints.
Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.
problem Handling sparse multiway count data corrupted by false zeros.
method Zero-truncated Poisson regression with tensor completion.
result Accurate estimation of multiway count data from approximately IR2log22(I) non-zero counts. We investigate the Banach Lie groupoids and inverse semigroups naturally associated to W*-algebras. We also present statements describing relationship between these groupoids and the Banach Poisson geometry which follows in the canonical way from the W*-algebra structure.
V1 cortex reconstructs images as Poisson equation solutions with varying weights.
problem Reconstructing images from V1 cortical cell receptive profiles.
method Solves a heterogeneous Poisson equation with varying weights representing neural connectivity.
result Reconstructions converge to homogeneous solutions using homogenization techniques.
Gaussian surrogates improve Poisson imaging performance at low doses.
problem Improving Poisson imaging performance at low doses.
method Analysis of Poisson and Gaussian surrogate reconstruction objectives under Poisson noise.
result Gaussian surrogates can achieve MSE comparable to Poisson MAP at low doses.
The paper reformulates regression in infinite dimensions as an inverse problem, showing it's equivalent to compact inverse problems.
problem Learning a linear operator between Hilbert spaces from empirical observations.
method Reformulates regression as an inverse problem, proving equivalence to compact inverse problems under specific conditions.
result The inverse problem is equivalent to compact inverse problems in terms of spectral properties and regularisation theory.
The nonlinear equations for the general nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived and the integrability of these equations by the method of inverse scattering problem is proved. For these equations, the Lax pairs with a spectral parameter are presented. Moreover, we demo…
Develops data subsampling techniques for Poisson regression models.
problem Efficiently approximating Poisson regression loss functions with coresets.
method Introduces coresets for Poisson regression with novel complexity parameters and domain shifting.
result Sublinear coresets exist for Poisson regression with 1±ε approximation guarantee. Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Extends diffusion models to handle exponential family distributions for inverse problems.
problem Intractability of likelihood score for non-Gaussian observations.
method Evidence trick to approximate likelihood score for exponential family distributions.
result Effective Bayesian inference on complex Poisson processes and malaria prevalence prediction.
New methods tackle complex inverse problems with scalable optimization-based MCMC.
problem Estimating high-dimensional model parameters and hyperparameters in nonlinear hierarchical statistical inverse problems.
method Optimization-based Markov chain Monte Carlo (MCMC) methods using RTO and pseudo-marginal MCMC.
result Efficient sampling tools for hierarchical Bayesian inversion with robust performance to model parameter dimensions.
Method estimates sparse inverse covariance and partial correlation matrices efficiently.
problem Sparse high-dimensional inverse covariance and partial correlation matrix estimation.
method Two-stage estimation method using partial regression with positive semi-definiteness.
result Efficient estimation of inverse covariance and partial correlation matrices with derived non-asymptotic rates.
This paper reviews SDR methods for multivariate response regression.
problem Handling sufficient dimension reduction for multivariate response regression.
method Characterizes SDR estimators as inverse or forward regression methods.
result Pooled marginal, projective resampling, distance-based, ordinary least squares, partial least squares, and semiparametric SDR estimators are discussed.
Proposes an online method for high-dimensional streaming data.
problem Increasing variable dimensions with sample size in online kernel sliced inverse regression.
method Introduces approximate linear dependence condition and dictionary variable sets to address the problem. Transforms into online generalized eigen-decomposition problem and uses stochastic optimization for updates.
result Achieves close performance to batch processing kernel sliced inverse regression.
A group, defined as set with associative multiplication and inverse, is a natural structure describing the symmetry of a space. The concept of group generalizes to group objects internal to other categories than sets. But there are yet more general objects that can still be thought of as groups in many ways, such as qu…
Study shows sample complexity for logistic regression with normal covariates.
problem Estimating parameters of logistic regression with normal design.
method Analyzes sample complexity in terms of dimension and inverse temperature.
result Shows two change-points in sample complexity curve based on inverse temperature.
It is well known that functions in involution with respect to Poisson brackets have a privileged role in the theory of completely integrable systems. Finding functionally independent functions in involution with a given function h on a Poisson manifold is a fundamental problem of this theory and is very useful for th…
In this paper we discuss Bayesian nonconvex penalization for sparse learning problems. We explore a nonparametric formulation for latent shrinkage parameters using subordinators which are one-dimensional Lévy processes. We particularly study a family of continuous compound Poisson subordinators and a family of discrete…
Survey of SDR methods for high-dimensional regression and embedding.
problem Reducing dimensionality in high-dimensional data.
method Involves both statistical and machine learning approaches, covering inverse and forward regression methods.
result Supervised Kernel Dimension Reduction is equivalent to supervised PCA.
Sliced inverse regression (SIR) is a pioneer tool for supervised dimension reduction. It identifies the effective dimension reduction space, the subspace of significant factors with intrinsic lower dimensionality. In this paper, we propose to refine the SIR algorithm through an overlapping slicing scheme. The new algor…
Machine learning models solve inverse eigenvalue problems for symmetric potentials and refractive indices.
problem Solving inverse eigenvalue problems for symmetric potentials and refractive indices.
method Supervised regression models (k-Nearest Neighbours, Random Forests, Multi-Layer Perceptron) trained on eigenvalue datasets.
result Machine learning methods can numerically solve inverse eigenvalue problems under appropriate parameter tuning.
The logistic regression model is known to converge to a Poisson point process model if the binary response tends to infinitely imbalanced. In this paper, it is shown that this phenomenon is universal in a wide class of link functions on binomial regression. The proof relies on the extreme value theory. For the logit, p…
Investigates consistency of FX rate dynamics under inversion.
problem Consistency of jump-diffusion dynamics for FX rates under inversion.
method Calibrated Heston and SABR models, analyzed jumps in domestic and foreign measures.
result Determines conditions for consistency in FX rate dynamics under inversion.
Paper proposes a new method for estimating conditional densities using logistic regressions.
problem Estimating conditional densities for complex distributions.
method Parametric conditional density estimation via weighted logistic regressions.
result Maximum likelihood estimates can be obtained efficiently via a block-wise alternating maximization scheme and local case-control sampling.
The paper proposes differentially private sliced inverse regression algorithms for high-dimensional data.
problem Privacy concerns in high-dimensional data analysis.
method Differentially private sliced inverse regression algorithms designed for privacy preservation.
result Achieves minimax lower bounds up to logarithmic factors.
A Kaehler-Nijenhuis manifold is a Kaehler manifold M, with metric g, complex structure J and Kaehler form F, endowed with a Nijenhuis tensor field A that is compatible with the Poisson stucture defined by F in the sense of the theory of Poisson-Nijenhuis structures. If this happens, and if either AJ=JA or AJ=-JA, M is …
Gaussian process regression helps approximate Bayesian inverse problems efficiently.
problem Computational intractability of Bayesian posterior distributions in inverse problems.
method Gaussian process regression to build a surrogate model for the likelihood.
result Error between true and approximate posterior can be bounded by weighted L2-norm error between true and approximate likelihood. Paper tackles Bayesian image restoration in low-photon Poisson imaging problems.
problem Bayesian inference in challenging low-photon Poisson imaging problems.
method Plug-and-play (PnP) Langevin sampling strategies with accelerated methods and mirror sampling.
result Effective PnP Langevin sampling methods for low-photon Poisson imaging problems.
Diffusion models tackle noisy inverse problems with posterior sampling.
problem Efficiently solving general noisy inverse problems.
method Approximation of posterior sampling for diffusion models.
result Diffusion models can handle various noise statistics and nonlinear problems.
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also enables us to expand the possible space where the dimension reduction functions bel…
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.
New method for GLMs under DP provides private uncertainty quantification.
problem Private inference for GLMs with uncertainty quantification.
method Noise-aware DP Bayesian inference method for GLMs.
result Posterior uncertainty allows determination of statistically significant coefficients.
FSIR extends SIR for federated learning with privacy and efficiency.
problem Privacy-preserving dimension reduction in federated learning.
method FSIR employs sliced inverse regression with differential privacy and collaborative variable screening.
result FSIR achieves effective dimension reduction and privacy protection in federated learning.
Proposes stabilized weights for causal inference using isotonic calibration.
problem Stability and bias issues in inverse propensity weighting.
method Post-hoc isotonic calibration of inverse propensity weights.
result Improves performance of doubly robust estimators of average treatment effect.
In this paper we show how to augment classical methods for inverse problems with artificial neural networks. The neural network acts as a prior for the coefficient to be estimated from noisy data. Neural networks are global, smooth function approximators and as such they do not require explicit regularization of the er…
Paper uses SGD for solving linear inverse problems, improving empirical performance.
problem Solving statistical inverse problems in science and engineering.
method Stochastic Gradient Descent (SGD) for linear inverse problems, with smoothing techniques.
result Consistency and finite sample bounds for excess risk demonstrated.
Advocates for MLE in regression and forecasting for better inductive biases and post-hoc optimization.
problem Designing effective loss functions for regression and forecasting.
method Maximum Likelihood Estimation (MLE) approach for regression and forecasting.
result MLE approach outperforms direct empirical risk minimization under certain conditions and for various datasets.
DRIFT uses neural flows to replace distributional regression models.
problem Lack of neural network representations for distributional regression models.
method Inverse flow transformations (DRIFT) for distributional regression.
result Neural representations in DRIFT match classical statistical methods in performance.
A VAE model predicts material properties and microstructures.
problem Building forward and inverse structure-property linkages in materials science.
method Combines VAE with regression, using a two-level prior and multi-modal Gaussian mixture.
result The model achieves accurate forward and inverse predictions of material properties and microstructures.
New method stabilizes machine learning for physics-informed inverse problems.
problem Reconstructing physical quantities from PDE-compliant measurements.
method Physics-informed learning with smooth inductive bias.
result PDE operators stabilize variance and prevent overfitting in fixed dimensions.
ISR creates analytical relationships from data via invertible maps.
problem Creating analytical relationships from datasets.
method Combines INNs and EQL, using invertible maps and sparsity promoting regularization.
result ISR can serve as a normalizing flow for density estimation and solve inverse problems.