The paper examines conditions for linearity in a conditional mean estimator under vector Poisson noise.
problem Conditions for linearity of the conditional mean estimator in vector Poisson noise.
method Analyzes prior distributions and their impact on the conditional mean estimator's linearity.
result The only prior distribution that induces linearity is a product gamma distribution, and non-zero dark current parameter prevents linearity.
New estimators reduce computation for Kendall's tau and conditional Kendall's tau matrices under structural assumptions.
problem Efficient estimation of Kendall's tau and conditional Kendall's tau matrices for large dimensions.
method Averaging pairwise estimates over blocks or conditional estimates, exploiting structural assumptions.
result Improved estimators with reduced computational cost and similar error level.
Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of cond…
Estimates conditional mutual information using a minmax formulation.
problem Estimating conditional mutual information in high dimensions.
method Uses a minmax optimization problem to train a neural network.
result Improves estimation accuracy compared to existing methods.
New estimator for survival function with missing not at random censoring indicators.
problem Estimating survival function with missing not at random censoring indicators.
method Proposes a new estimator based on a conditional copula model for the missingness mechanism.
result Provides a new method for estimating conditional survival function with MNAR censoring indicators.
We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate the conditional mode by finding the maximum of the estimated conditional density…
Estimates conditional Brenier maps using entropic optimal transport.
problem Non-parametric estimation of conditional Brenier maps.
method Entropic optimal transport for scalable non-parametric estimation.
result Entropic optimal transport maps asymptotically converge to conditional Brenier maps.
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.
MCD reformulates conditional density estimation into binary classification.
problem Conditional density estimation in statistical and machine learning.
method Marginal Contrastive Discrimination, reformulating into marginal and ratio density functions for binary classification.
result Significantly outperforms existing methods on most density models and regression datasets.
Proposes CCME framework for estimating heterogeneous treatment effects.
problem Estimating heterogeneous treatment effects in complex distributions.
method Embeds conditional distributions into RKHS, develops meta-estimators for CCME.
result Establishes finite-sample convergence rates and double robustness for CCME estimators.
We introduce a unified framework for random forest prediction error estimation based on a novel estimator of the conditional prediction error distribution function. Our framework enables simple plug-in estimation of key prediction uncertainty metrics, including conditional mean squared prediction errors, conditional bi…
Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional distributions which cannot be meaningfully summarized using expectation only (due to e…
Improved nonparametric regression with debiasing for root-n consistency.
problem Challenges in achieving root-n consistency and normal distribution for nonparametric estimators.
method Debiasing technique by adding a correction term to nonparametric estimators.
result Achieves root-n consistency and asymptotic normality.
New estimator robust to adversarial noise and data heterogeneity.
problem Sensitive to adversarial noise and poor performance with heterogeneous data.
method Distributionally robust estimator minimizing worst-case conditional expected loss over adversarial distributions.
result Efficiently finds non-parametric local estimates via convex optimization.
The paper improves eigenvalue estimates for manifolds with Ricci curvature conditions.
problem Eigenvalue estimates for manifolds with Ricci curvature conditions.
method Proves eigenvalue estimates using a Kato condition on the negative part of Ricci curvature.
result Optimal eigenvalue estimates for Zhong-Yang type and Cheng-type bounds.
A two-step nonparametric method estimates financial systemic risk.
problem Estimating CoVaR due to unobservability of multivariate-quantiles.
method Two-step nonparametric approach using Monte-Carlo simulation and kernel method.
result Consistency and asymptotic normality of the two-step estimator established.
The paper estimates gradients on graphs under specific conditions and applies these estimates to heat equations.
problem Estimating gradients on graphs with the CDψ(n,−K) condition. method Investigates gradient estimates for positive solutions of heat equations and a heat-type equation.
result Derives heat kernel bounds and Harnack inequalities using gradient estimates.
Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference problems such as graphical models, causal learning, feature selection and time-se…
New method avoids IV limitations for flexible estimation.
problem Nonparametric estimation of IV regressions with multiple solutions.
method Minimax penalized estimator avoiding identification and closedness conditions.
result Strong L2 convergence rate without closedness condition. A method learns representations for conditional moment models with controlled ill-posedness.
problem Efficient estimation of nonparametric conditional moment models with flexible models is challenging.
method Proposes a procedure that learns spectral representations with controlled measures of ill-posedness.
result The proposed method can efficiently estimate representations from data and is L2 consistent.
We study the positivity properties of Hermitian (or even Finsler) holomorphic vector bundles in terms of Lp-estimates of ∂ˉ and Lp-extensions of holomorphic objects. To this end, we introduce four conditions, called the optimal Lp-estimate condition, the multiple coarse Lp-estimate condition, th…
Directly estimates CQC, improving interpretability and accuracy.
problem Inability to model and interpret CQC due to inversion issue.
method Direct doubly robust estimation of CQC without inversion.
result Improved estimation accuracy and interpretability.
A new diffusion model uses efficient conditional estimators for discrete data.
problem Efficient estimation of conditional probabilities for discrete data.
method Discrete denoising diffusion framework with sample-efficient NeurISE conditional estimation.
result The method outperforms existing approaches in various metrics on binary and scientific data.
SLS optimizes minimum-volume regions for conditional quantiles, bypassing density estimation.
problem Constructing minimum-volume prediction regions that satisfy conditional coverage.
method Super-level-set regression (SLS) directly optimizes geometric boundaries of conditional level sets.
result SLS optimizes regions directly, capturing complex conditional structures end-to-end.
Non-convex regularizers usually improve the performance of sparse estimation in practice. To prove this fact, we study the conditions of sparse estimations for the sharp concave regularizers which are a general family of non-convex regularizers including many existing regularizers. For the global solutions of the regul…
Integrates estimation and optimization for uncertain parameters.
problem Optimizing with uncertain parameters whose distributions can be estimated.
method Integrated Conditional Estimation-Optimization (ICEO) framework.
result Asymptotically consistent and provides finite performance guarantees.
This work shows that Gaussian is the only prior for optimal linear estimation in L1 loss.
problem Optimal linear estimation of a random variable from noisy observations under L1 fidelity criterion. method Analyzes the conditions under which the conditional median is a linear estimator and identifies the Gaussian distribution as the only prior that induces linearity.
result Gaussian is the only prior distribution that induces linearity in the conditional median for L1 loss. We present a novel approach for estimating conditional probability tables, based on a joint, rather than independent, estimate of the conditional distributions belonging to the same table. We derive exact analytical expressions for the estimators and we analyse their properties both analytically and via simulation. We …
We tackle causal inference under conditional moment restrictions using importance weighting.
problem Challenges in causal inference under conditional moment restrictions, especially in high-dimensional settings.
method Transform conditional moment restrictions to unconditional moment restrictions through importance weighting.
result Successfully estimate nonparametric functions defined under conditional moment restrictions.
This article reviews and compares various methods for estimating conditional distributions.
problem Inference of conditional distributions in statistics.
method Classical nonparametric methods and modern generative models.
result A systematic numerical comparison of methods using performance metrics.
Paper improves confidence intervals and variance estimation for deep learning models.
problem Improving confidence intervals and variance estimation in deep learning models.
method Residual-based framework for conditional variance estimation; robust bootstrap procedure for confidence intervals.
result First non-asymptotic bounds for variance estimation using ReLU networks.
Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable x and a dependent variable y by modeling their conditional probability p(y∣x). The paper develops best practices for conditional den…
A novel k-NN method estimates conditional mean and variance efficiently.
problem Joint estimation of conditional mean and variance.
method Integrates k-NN with automated variance selection.
result Achieves fast convergence rates and improved precision.
The paper establishes gradient estimates for harmonic and heat equation solutions on manifolds with boundary.
problem Gradient estimates for harmonic and heat equation solutions on manifolds with boundary.
method Yau and Souplet-Zhang type gradient estimates for harmonic and heat equation solutions under Dirichlet boundary condition.
result Established gradient estimates for harmonic and heat equation solutions on manifolds with boundary.
Transforms conditional density estimation into a nonparametric regression problem.
problem Conditional density estimation in high dimensions.
method Introduces auxiliary samples to transform into nonparametric regression.
result Estimator converges to true conditional density in data limit.
Estimates for harmonic functions in curved spaces.
problem Quantifying harmonic functions in curved spaces.
method Quantitative Sobolev estimates for p-harmonic functions in manifolds with curvature conditions. result Established a quantitative second order Sobolev estimate for p-harmonic functions. Heat kernel estimates on manifolds with mixed boundary conditions.
problem Estimating heat kernels on manifolds with ends and mixed boundary conditions.
method Global harmonic function construction and h-transform technique. result Two-sided heat kernel estimates for Riemannian manifolds with mixed boundary conditions.
Partition Tree estimates conditional densities for mixed continuous and categorical variables.
problem Estimating conditional densities for mixed data types.
method Tree-based framework modeling conditional distributions as piecewise-constant densities on adaptive partitions, minimizing conditional negative log-likelihood.
result Improved probabilistic prediction compared to CART-style trees and state-of-the-art methods.
New estimator adapts to various error distributions.
problem Adapting to different error distributions in nonparametric regression.
method Introduces outrigger local polynomial estimator with modified weighted least squares.
result Minimax optimal over Hölder classes with multiplicative factor.
Deep learning improves causal effect estimation from complex observational data.
problem Estimating causal effects from complex observational data with low bias.
method Unified deep learning framework using multitask recurrent neural networks.
result Deep learning estimator shows lower bias in causal effect estimates.
Proposes a method to create shorter, more accurate prediction intervals.
problem Challenges in achieving both conditional validity and interval efficiency in complex settings.
method Uses a conformal-style calibration method for neural network responses, adjusting to empirical PIT distribution.
result Demonstrates better conditional calibration and shorter intervals than existing methods.
Unified framework for estimating high-dimensional conditional factor models.
problem Estimating high-dimensional conditional latent factor models with practical limitations.
method Constrained nuclear norm regularization and cross-validation for parameter selection.
result Imposing homogeneity improves model predictability, with new method outperforming alternatives.
Paper identifies and estimates CAPCEs in continuous treatment settings.
problem Estimating heterogeneous causal effects of continuous treatments.
method Instrumental variable approach to identify CAPCEs under weaker conditions.
result Developed three families of CAPCE estimators with statistical properties analyzed.
The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model inference, causal strength estimation and time-series problems. In several appl…
Proposes a new method for selecting regularization parameters in sparse precision matrix estimation.
problem Selecting an appropriate regularization parameter for sparse precision matrix estimation.
method Developed a closed-form matrix-valued regularization parameter based on the sampling distribution of optimality conditions.
result The proposed method achieves comparable estimation accuracy and superior support recovery to cross-validation, with significant runtime improvements.
New recursive algorithm estimates conditional kernel mean embeddings in Hilbert space.
problem Estimating conditional distributions in RKHS for supervised learning.
method Recursive algorithm in L2 space for conditional kernel mean map. result Strong L2 consistency of recursive estimator proved. Unified framework for pattern recovery in penalized and thresholded estimation.
problem Pattern recovery in penalized and thresholded estimation methods.
method Defining a novel pattern notion based on subdifferentials, introducing accessibility and noiseless recovery conditions.
result Unified and extended conditions for pattern recovery in a broad class of penalized estimators.
Gradient estimate for harmonic functions with boundary condition proved.
problem Proving gradient estimates for harmonic functions with boundary conditions.
method Using weighted f-harmonic functions and infinite dimensional Bakry-Emery Ricci tensor. result Gradient estimates for positive f-harmonic functions with Dirichlet boundary condition.