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.
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.
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.
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.
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 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.
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. 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.
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.
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.
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.
New algorithm reduces dimensionality in federated learning.
problem Estimating central dimension reduction subspace and variable selection in federated learning.
method Federated sparse sliced inverse regression, convex optimization, linearized alternating direction method of multipliers.
result Upper bound of statistical error rate established under heterogeneous setting.
New algorithms for IV regression with streaming data, avoiding matrix inversions.
problem Instrumental variable regression with streaming data.
method Viewing IV regression as a stochastic optimization problem, developing algorithms that avoid matrix inversions and mini-batches.
result Rates of convergence of order O(logT/T) and O(1/T1−ι) for linear models. Sliced Inverse Regression reduces parameter space for estimating complex financial models.
problem High-dimensional parameter space in stochastic differential equations.
method Sliced Inverse Regression for dimension reduction.
result Reduced computational costs in estimating parameters.
R-Learning uses inverse-variance weights to estimate treatment effects more accurately.
problem Estimating heterogeneous treatment effects (CATEs) with stable and accurate methods.
method R-Learning with inverse-variance weights (IVWs) for pseudo-outcome regression.
result IVWs improve the stability and accuracy of CATE estimation.
Efficiently solves inverse classification problems for logistic and softmax models.
problem Finding instances that change classifier predictions.
method Closed-form solution for logistic regression, iterative optimization for softmax.
result Fast, exact solutions for high-dimensional instances and many classes.
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the covariates. The estimated linear combinations include all covariates, making res…
RADIS uses deep regression to create efficient importance sampling for model inversion and emulation.
problem Efficiently sampling from posterior distributions for model inversion and emulation.
method RADIS uses a deep architecture of nested importance sampling schemes to construct a non-parametric emulator that mimics the posterior distribution.
result RADIS asymptotically converges to an exact sampler under mild conditions and can be used as a surrogate model.
A new method recovers rewards from behavior policies using classification and regression.
problem Recovering meaningful rewards from observed behavior in reinforcement learning.
method GenPQR, a modular procedure that estimates behavior policy, evaluates soft Q-function, and recovers normalized reward using classification and regression.
result GenPQR matches or improves reward recovery compared to DeepPQR, while being simpler and more modular.
Efficiently solves inverse PDE problems with Gaussian processes.
problem Solving inverse problems in linear PDEs with noisy data.
method Gaussian process regression with algebraic priors.
result High accuracy and computational efficiency achieved.
New method optimizes hyperparameters for randomized algorithms like random feature regression.
problem Optimizing hyperparameters in randomized algorithms is challenging due to their stochastic nature.
method Introduced a random objective function and used ensemble Kalman inversion (EKI) for gradient-free optimization.
result Demonstrated successful optimization of hyperparameters in various randomized algorithms.
Unified framework for semi-supervised regression with misspecified models.
problem Estimating regression coefficients in conditional mean models with unlabeled data.
method Developed an augmented inverse probability weighted (AIPW) method using regularized calibrated estimators for PS and OR nuisance models.
result The proposed estimator is consistent, asymptotically normal, and provides valid confidence intervals even with misspecified OR models and high-dimensional data.
This paper studies model-inversion attacks, in which the access to a model is abused to infer information about the training data. Since its first introduction, such attacks have raised serious concerns given that training data usually contain privacy-sensitive information. Thus far, successful model-inversion attacks …
Splat Regression Models use mixtures of bump functions to approximate complex data.
problem Approximating complex data with high interpretability and accuracy.
method Model outputs are mixtures of heterogeneous and anisotropic bump functions (splats) weighted by output vectors. Fitting splat models reduces to optimization over mixing measures using Wasserstein-Fisher-Rao gradient flows.
result Unified theoretical framework for Gaussian Splatting and flexible approach for diverse problems.
Transformer learns context and regularization for ICL in inverse problems.
problem Learning context and effective regularization for transformer-based in-context learning (ICL) in inverse problems.
method Introduced a linear transformer to learn inverse mapping from contextual examples to weight vectors, addressing rank-deficient problems.
result Transformer implicitly learns a prior distribution and effective regularization strategy, outperforming traditional methods.
The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of a Hermitian matrix. Before that recursive algorithm was applied in [4], its impr…
Mixture models with Gamma and or inverse-Gamma distributed mixture components are useful for medical image tissue segmentation or as post-hoc models for regression coefficients obtained from linear regression within a Generalised Linear Modeling framework (GLM), used in this case to separate stochastic (Gaussian) noise…
In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response, such that the low-dimensional variable becomes the regressor, and which is tract…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is the LASSO problem, where the l1 norm regularizes a quadratic function. A multil…
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as symmetric generalized eigendecomposition problems. In this paper we outline how t…
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using ℓ1-penalization methods. We propose and study the following method. We combine a multiple regression approach with ideas of thresholding and refitting: first we infer a sparse u…
Meta-learning improves predictions with generalized ridge regression in high-dimensional settings.
problem Improving meta-learning performance in high-dimensional settings.
method Generalized ridge regression applied to high-dimensional multivariate random-effects linear models.
result Optimal predictive risk achieved when using the inverse of the covariance matrix of random coefficients.
We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale. We discuss the rates of convergence for the regularized solution under the prior assumptions and a certai…
Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated using regression techniques. We propose as regression method a tensor decompositi…
Solving inverse problems is central to geosciences and remote sensing. Radiative transfer models (RTMs) represent mathematically the physical laws which govern the phenomena in remote sensing applications (forward models). The numerical inversion of the RTM equations is a challenging and computationally demanding probl…
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributions, Negative binomial regression, Poisson-Gamma hierarchical models, …
We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors $\-x$ which can retain the statistical relationship between $\-x$ and the response variable y. We follow the idea of the sliced inverse regression (SIR) and the sliced average variance estimation (SA…
Study on estimating invertible functions with minimax analysis.
problem Minimizing risk of estimating invertible functions on a plane.
method Introduce two types of L2-risks, derive lower and upper rates for minimax values, develop an asymptotically almost everywhere invertible estimator. result Invertibility does not reduce the complexity of the estimation problem in terms of the rate.
This paper proposes the recursive and square-root BLS algorithms to improve the original BLS for new added inputs, which utilize the inverse and inverse Cholesky factor of the Hermitian matrix in the ridge inverse, respectively, to update the ridge solution. The recursive BLS updates the inverse by the matrix inversion…