Paper tackles unbounded density ratio estimation for covariate shift adaptation.
problem Understudied challenge in statistical learning: unbounded density ratios.
method Three-step estimation method: relative density ratio, truncation, and transformation.
result Established rigorous convergence guarantees for density ratio and regression estimators.
Proposes a robust method for predicting missing outcomes in covariate shift adaptation.
problem Predicting missing outcomes in test data with covariate shift.
method Doubly robust estimator for covariate shift adaptation via importance weighting, incorporating an additional estimator for the regression function.
result Shows robustness against density-ratio estimation errors, maintaining consistency if either estimator is consistent.
This study optimizes covariate density and propensity score for efficient ATE estimation.
problem Efficiently estimating average treatment effects (ATEs) with minimal variance.
method Adaptive experiment optimizing both covariate density and propensity score.
result Proposed method minimizes the semiparametric efficiency bound for ATE estimation.
Paper develops estimators for unbounded density ratios with applications in error control.
problem Estimating density ratios with unbounded domains and ranges.
method Least squares and logistic regression loss functions for density ratio estimation.
result Established upper bounds on estimation errors with optimal rates for unbounded density ratios.
This paper tackles continuous covariate shift by adaptively training predictors.
problem Continuous covariate shift where input distributions change over time.
method Online density ratio estimation method to adaptively train predictors.
result Excess risk guarantee for the predictor through dynamic regret bound.
Optimizes spectral density estimation for stationary and nonstationary processes.
problem Estimating spectral density of time series with complex structure.
method Optimally adaptive Bayesian spectral density estimation using smoothing spline covariance structure.
result Optimal eigendecomposition provides superior performance compared to alternative covariance functions.
Interactive privacy mechanisms improve spectral density estimation under local differential privacy.
problem Estimating spectral density of Gaussian time series with local differential privacy constraints.
method Two-stage process: Laplace mechanism followed by privatized sample analysis.
result Interactive mechanisms achieve faster rates for spectral density estimation.
CoDrug uses KDE to create valid prediction sets for drug molecules under covariate shift.
problem Creating reliable uncertainty estimates for drug properties from computational models.
method CoDrug employs an energy-based model and KDE to assess and rectify distribution shift.
result CoDrug reduces the coverage gap by over 35% compared to non-adjusted conformal prediction sets.
Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of the unknown data generating density. This paper contributes to the mathematical understanding of this phenomenon and helps define better justified sampling algorithms for deep learning based on auto-encoder v…
Unified theory for causal inference using various methods.
problem Estimating causal effects in ATE estimation.
method Riesz regression, covariate balancing, DRE, TMLE, matching estimator.
result Unified theory integrating multiple methods for ATE estimation.
We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for uncorrelated samples. The method allows for exact determination of the experimental spectru…
Survey on smooth function and form density in Riemannian Sobolev spaces.
problem Density of smooth functions and forms in Sobolev spaces on Riemannian manifolds.
method Careful examination of weak covariant derivatives and partial derivatives.
result Equivalence of weak covariant derivatives to weak partial derivatives.
Spectral algorithms improve under covariate shift with novel weighted techniques.
problem Improving spectral algorithms' performance under covariate shift.
method Analysis of spectral algorithms in non-parametric regression over RKHS, proposing a weighted spectral algorithm with clipped weights.
result Normalized weighted spectral algorithm achieves optimal capacity-independent convergence rates, and clipped weights can approach optimal capacity-dependent rates.
Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge is the analytically intractable inference. In this paper, we present approximat…
Random forests is a common non-parametric regression technique which performs well for mixed-type data and irrelevant covariates, while being robust to monotonic variable transformations. Existing random forest implementations target regression or classification. We introduce the RFCDE package for fitting random forest…
Paper proposes a novel approach to density ratio estimation using projection pursuit.
problem Density ratio estimation challenges in high dimensions and model misspecification.
method The approach uses projection pursuit to approximate density ratios, addressing high dimensionality and model flexibility issues.
result The proposed estimator is consistent and converges at a certain rate, outperforming existing methods in experiments.
We provide a method to prepare covariance matrices for quantum datasets.
problem No concrete protocol for preparing covariance matrices for quantum datasets.
method Amplitude encoding of data, exploiting global phase symmetry to center the dataset.
result Covariance matrix can be prepared for arbitrary quantum datasets or centered classical datasets.
Researchers create a family of conformally covariant operators.
problem Developing a comprehensive set of conformally covariant operators.
method Constructing a family of conformally covariant tridifferential operators as tangential operators in the Fefferman--Graham ambient space.
result Symmetrization of ambient operators is formally self-adjoint.
We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed in the frame bundle lead …
Unified framework for estimating density ratios in causal inference.
problem Estimating density ratios for causal inference is challenging due to instability and curse of dimensionality.
method Bregman-Riesz regression unifies three methods: Bregman divergences, probabilistic classification, and Riesz loss.
result Unified framework improves density ratio estimation in causal inference.
Paper tackles imbalanced time series classification with a novel oversampling method.
problem Imbalanced time series classification challenges due to high dimensionality and correlation.
method Density-ratio based clustering followed by shrinkage technique for covariance estimation, then generating synthetic samples.
result OHIT outperforms state-of-the-art methods in F1, G-mean, and AUC metrics.
Adapts RKHS methods to estimate density ratios with optimal error.
problem Estimating density ratios from limited data.
method Minimizes regularized Bregman divergence in RKHS, with Lepskii type parameter choice.
result Adaptive minimax optimal error rate for quadratic loss.
SPQR package uses neural networks for flexible quantile regression.
problem Flexible modeling of non-linear relationships in quantile regression.
method Monotonic splines and neural networks for density estimation; model-agnostic covariate effects.
result Allows for non-linear and quantile-specific effects.
A new metric tensor improves Riemann manifold Monte Carlo for Bayesian models.
problem Improving sampling efficiency in Bayesian hierarchical models.
method Metric tensor derived from log-density gradient covariance matrices.
result Metric tensors enhance sampling for complex Bayesian models.
The paper analyzes geometric densities and compression radii for knot types.
problem Optimizing geometric quantities associated with knot types.
method Develops a factorization framework for scale-covariant size functionals.
result Different minimizing sequences for density, compression, packing, and ropelength problems.
CDRE estimates density ratios in streaming data without historical samples.
problem Online learning with shifting data distributions.
method Iterative estimation of density ratios between initial and current distributions.
result CDRE outperforms standard DRE in estimating divergences between distributions.
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For d covariates, there are 2d basis coefficients to estimate, which renders conventional approaches computationally prohibitive …
We consider complete Riemannian manifolds with a controlled growth of the covariant derivatives of Ricci curvatures up to order k−2 and a controlled decay of the injectivity radii. On such manifolds we construct distance-like functions with a control on covariant derivatives up to order k. Alternatively, the assump…
This work tackles sequential data learning challenges by improving neural network robustness to non-iid distribution shifts.
problem Sequential data learning challenges, particularly non-iid distribution shifts across batches.
method Cramér-Rao-based regularization using Fisher Information Matrix to adapt to sequential covariate shifts.
result Achieves 19% accuracy improvement over state-of-the-art methods.
A regression algorithm uses Green's function and covariance matrix for predictive distributions.
problem Regression and uncertainty quantification for machine learning.
method Green's function theory, Bayesian approach, covariance matrix of normalized Green's function.
result The covariance matrix provides predictive distributions with mean and confidence intervals.
Generative model for tabular data density regression.
problem Estimating conditional distribution of outcomes given covariates.
method Tree-based flow model for efficient sampling and likelihood evaluation.
result Our method achieves comparable or superior performance with reduced training and sampling costs.
In the covariate shift learning scenario, the training and test covariate distributions differ, so that a predictor's average loss over the training and test distributions also differ. In this work, we explore the potential of extreme dimension reduction, i.e. to very low dimensions, in improving the performance of imp…
We conduct a study of the aliased spectral densities of Matérn covariance functions on a regular grid of points, providing clarity on the properties of a popular approximation based on stochastic partial differential equations; while others have shown that it can approximate the covariance function well, we find that i…
Scattering representations simplify SBI for images without extra compression.
problem Efficiently performing simulation-based inference on images with limited data.
method Use scattering representations for compression and learning, combined with spatial averaging and expressive density estimators.
result Scattering representations provide more information than traditional methods, without requiring additional simulations.
Estimates high-dimensional posterior densities by marginal distributions and neural networks.
problem High-dimensional probability density estimation for inference is difficult.
method Direct estimation of lower-dimensional marginal distributions, using Moment Networks for fast computation of moments.
result Demonstrates estimation of gravitational wave time series and applications in cosmology.
QNA uses quantum-inspired density operators to diagnose market dependence and structural risk.
problem Lack of unified operator representation for market dependence and structural risk diagnostics.
method Quantum Network of Assets (QNA) framework using density operators.
result QNA entropy remains strongly related to covariance spectral entropy but becomes distinct with multi-feature rolling trajectories.
P.Lecomte has proposed to take into account the covariant derivatives used to build ordering prescriptions for the naturality of transformation properties and has conjectured that there exists an natural ordering prescription for differential operators of any orders between density bundles which in addition is invarian…
In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either non-parametrically or using finite mixture models. Thus, clusters are closely related to certain regions around the density modes, and every cluster corr…
Paper analyzes spectral algorithms under covariate shift, providing convergence rates.
problem Addressing distributional mismatch in regression models.
method Incorporates importance weights into spectral algorithms in RKHS.
result Establishes minimax-optimal convergence rates for misspecified cases.
We apply random matrix theory to derive spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2) processes. In particular, we consider a limit where the number of random variables N and the number of consecutive time measurements T are large but the ratio N/T is fix…
The salient properties of large empirical covariance and correlation matrices are studied for three datasets of size 54, 55 and 330. The covariance is defined as a simple cross product of the returns, with weights that decay logarithmically slowly. The key general properties of the covariance matrices are the following…
New GMM models fit high-dimensional data with fewer parameters.
problem Overparameterization and lack of flexibility in GMMs for high-dimensional data.
method Piecewise-constant covariance eigenvalue profiles, EM and penalized EM algorithms.
result Superior likelihood-parsimony tradeoffs in density fitting, clustering, and denoising.
We develop a family of infinite-dimensional (non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class Cbk with respect to appropriate reference measures. The case k=∞, in which the manifolds are modelled on Fréchet spaces, is included.…
This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact subset of Rd. On this approximate eigenbasis the eigenvalues of the c…
Building on the Utiyama principle we formulate an approach to Lagrangian field theory in which exterior covariant differentials of vector-valued forms replace partial derivatives, in the sense that they take up the role played by the latter in the usual jet bundle formulation. Actually a natural Lagrangian can be writt…
TraDE uses self-attention for better density estimation of tabular and image data.
problem Improving density estimation for tabular and image data.
method Self-attention-based architecture trained with a penalized maximum likelihood objective.
result TraDE produces significantly better density estimates than existing methods.
Method tackles missing covariates in large-scale datasets.
problem Cross-population missing data problem in large-scale datasets.
method Augmented transfer regression learning method combining importance-weighted estimating equations and imputation terms.
result Estimator is n1/2-consistent and asymptotically normal, attaining semiparametric efficiency bound under correct specification. Estimates Gaussian location model with ridge regularization, comparing variational and spectral methods.
problem Estimating parameters in Gaussian location model with regularization.
method Ridge-regularized log-density-ratio estimation, variational and spectral approaches.
result Regularized variational estimator has lower risk with many observations, spectral estimator with fewer observations.