Python package automates causal parameter estimation using Riesz regression.
problem Efficient estimation of causal and structural parameters.
method Automatic DML and generalized Riesz regression framework.
result Automatic construction of balancing link functions for generalized Riesz regression.
The paper approximates forward curve models in commodity markets using finite dimensional models.
problem Approximating forward curve models in commodity markets with finite dimensional arbitrage-free models.
method Construction of a convenient Riesz basis on the state space of the term structure dynamics.
result Recovery of a closed form representation of the forward price dynamics in the approximation models and uniform convergence to the true dynamics.
The paper argues for using Neyman orthogonal score for balancing in debiased machine learning.
problem Debiased machine learning requires a proper approach to balance covariates.
method The paper advocates for using Riesz regression with basis functions of X for balancing.
result Covariate balancing is only valid when the score-relevant regression error is a function of covariates alone.
Paper studies Riesz transform stability under metric perturbations.
problem Stability of Riesz transform boundedness under metric perturbations.
method Derives conditions for stability of Lp-boundedness of Riesz transform. result Provides counter-examples for instability of Riesz transform boundedness.
Uniform boundedness of Riesz transforms on Riemannian manifolds is established with a dichotomy.
problem Establishing uniform boundedness of Riesz transforms on Riemannian manifolds.
method Constructing a complete Riemannian manifold M to demonstrate the dichotomy. result A dichotomy concerning uniform boundedness of Riesz transforms on Riemannian manifolds.
Riesz regression connects to density ratio estimation for causal inference.
problem Estimating average treatment effects in causal inference.
method Riesz regression as a signed density ratio and least-squares importance fitting.
result Riesz regression and DRE are equivalent, allowing transfer of DRE results.
We investigate the boundness of the Riesz transform on Lp for connected sum of manifolds where the Riesz transform is bounded on Lp.
Unified framework for debiased machine learning using Riesz representer and Bregman divergence.
problem Estimating causal and structural parameters in machine learning.
method Generalized Riesz regression for fitting Riesz representer via Bregman divergence minimization.
result Automatic covariate balancing and Neyman orthogonality properties for debiased estimation.
Study proves NN matching is equivalent to Riesz regression for debiased machine learning.
problem Addressing bias in machine learning models.
method Interprets NN matching as Riesz regression and derives it from LSIF.
result NN matching is shown to be equivalent to Riesz regression.
New manifolds show Riesz transform unbounded for p > 2.
problem Understanding Riesz transform behavior on manifolds.
method Constructing Riemannian manifolds with specific properties.
result Riesz transform unbounded on Lp(M) for all p>2. Develops a direct debiased machine learning framework using Bregman divergence.
problem Reduces bias in machine learning estimates of causal effects or structural models.
method Neyman targeted estimation and generalized Riesz regression using Bregman divergence.
result Improves estimation of parameters of interest in causal models.
Gradient boosting estimates Riesz representer for causal inference.
problem Estimating causal quantities using traditional methods is challenging and prone to variance issues.
method Gradient boosting algorithm to directly estimate Riesz representer.
result Gradient boosting performs similarly or better than traditional methods in estimating causal quantities.
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 show a perturbation result for the boundedness of the Riesz transform : if M and M0 are complete Riemannian manifolds satisfying a Sobolev inequality of dimension n, which are isometric outside a compact set, and if the Riesz transform on M0 is bounded on Lq, then for all $\frac{n}{n-2}, the Riesz trans…
Balls, circles, and spheres identified by energy of distances.
problem Identifying shapes using energy of distances.
method Using generalized Riesz energy to identify shapes.
result Balls, circles, and spheres identified by energy of distances.
In this paper we prove mixed norm estimates for Riesz transforms related to Laplace--Beltrami operators on compact Riemannian symmetric spaces of rank one. These operators are closely related to the Riesz transforms for Jacobi polynomials expansions. The key point is to obtain sharp estimates for the kernel of the Jaco…
We investigate the Lp-boundness of the Riesz transform on Riemannian manifolds whose Ricci curvature has quadratic decay. Two criteria for the Lp-unboundness of the Riesz transform are given. We recover known results about manifolds that are Euclidean or conical at infinity.
Study Lp boundedness of Riesz transform on differential forms for certain manifolds.
problem Investigate Lp-boundedness of the covariant Riesz transform on differential forms. method Analyze Lp-boundedness on weighted Riemannian manifolds under curvature-dimension and lower bound conditions. result Derive Calderón-Zygmund inequality for 1<p≤2 under curvature-dimension condition. Two approaches to directly estimating Riesz representer are shown to be numerically equivalent under certain conditions.
problem Estimating Riesz representer in semiparametric statistics.
method Two distinct optimization problems solved by automatic debiased machine learning and sieve methods for conditional moment models.
result Numerical equivalence of estimators under specific regularization schemes, but not for others.
New Riesz distributions for differential forms on Euclidean space.
problem No new problem introduced.
method Developed a family of operator-valued distributions acting on differential forms.
result Natural generalization of Riesz distributions to differential forms.
New function found with spherical harmonic divergent sums almost everywhere.
problem Divergence of spherical harmonic expansions almost everywhere.
method Study of Cesàro, Riesz, and Bochner-Riesz means.
result Found an integrable function whose means diverge almost everywhere.
The study bounds Riesz transforms on manifolds with controlled curvature.
problem Bounding Riesz transforms on manifolds with controlled curvature.
method Established Lp-boundedness of local covariant Riesz transforms for differential forms. result Calderón-Zygmund estimates for manifolds with bounded Riemannian curvature.
Two regularization methods show similar results for Riesz energies of submanifolds.
problem Analyzing Riesz energies of submanifolds in Euclidean space.
method Comparing Hadamard's finite part and analytic continuation for regularization.
result Regularization techniques give similar results for Riesz energies.
Embeds LCK manifolds with potential into Hopf manifolds using Riesz-Schauder theorem.
problem Embedding LCK manifolds with potential into Hopf manifolds.
method Functional-analytic proof based on Riesz-Schauder theorem and Montel theorem; alternative argument for complex surfaces.
result Embeds LCK manifolds with potential into Hopf manifolds for dimensions at least 3.
Estimates heat kernel gradients on fractal-like cable systems.
problem Bounding gradients of heat kernels on complex fractal structures.
method Pointwise upper estimates for heat kernel gradients.
result Derives Lp-boundedness of quasi-Riesz transforms. 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.
Graph continuous operators become Riesz continuous after multiplication by unitary operators.
problem Characterizing Riesz continuity of graph continuous operators.
method Multiplication by unitary operators to transform graph continuity to Riesz continuity.
result The index of graph continuous families of Fredholm operators coincides with N. Ivanov's index.
Proposes adversarial method to estimate Riesz representer.
problem Estimating causal parameters as linear functionals of an underlying regression.
method Adversarial framework using general function spaces.
result Nonasymptotic mean square rate proved for neural networks, random forests, and RKHS.
Study on minimal energy problems for Riesz kernels on manifolds.
problem Minimal energy problems for strongly singular Riesz kernels on manifolds.
method Formulation of natural regularization using Hadamard's partie finie integral operator and analysis of measures with finite energy in Sobolev space.
result The minimal energy problem admits a unique solution and is related to discrete minimal energy problems.
We study the validity of the Lp inequality for the Riesz transform when p>2 and of its reverse inequality when p<2 on complete Riemannian manifolds under the doubling property and some Poincaré inequalities.
In this paper we study the Riesz transform on complete and connected Riemannian manifolds M with a certain spectral gap in the L2 spectrum of the Laplacian. We show that on such manifolds the Riesz transform is Lp bounded for all p∈(1,∞). This generalizes a result by Mandouvalos and Marias and extend…
This paper approximates scattered data using samplet coordinates with sparsity constraints.
problem Scattered data approximation with sparsity constraints.
method Samplet basis pursuit with ℓ1-regularization, multiresolution techniques, and semi-smooth Newton method. result The proposed method provides faster convergence and better signal sparsity compared to existing methods.
ScoreMatchingRiesz improves debiased machine learning and policy effects estimation.
problem Improving debiased machine learning and policy effects estimation.
method Score matching and Riesz representer estimation.
result Estimates policy path for continuous treatments, improving interpretability.
Researchers study Riesz transforms on complex groups, proving boundedness results.
problem Analyzing Riesz transforms on solvable extensions of stratified groups.
method Proving boundedness of Riesz transforms using large-time bounds for heat kernel derivatives.
result Weak type (1,1) and Lp-boundedness for p∈(1,2], and H1oL1 boundedness of Riesz transforms. The paper proves boundedness of a Riesz transform on weighted manifolds.
problem Establishing \(L^p\)-boundedness of the covariant Riesz transform on differential forms.
method Heat-kernel criterion, volume doubling, heat kernel estimates, curvature control, gradient bounds.
result The covariant Riesz transform is \(L^p\)-bounded for \(p>2\) on weighted Riemannian manifolds.
We prove an optimal reverse Poincaré inequality for the heat semigroup generated by the sub-Laplacian on a Carnot group of any step. As an application we give new proofs of the isoperimetric inequality and of the boundedness of the Riesz transform in Carnot groups.
Improved AutoDML estimator for causal inference using outcome-adapted shared covariate representation.
problem Efficiency in estimating treatment or policy effects in causal inference.
method Outcome-adapted AutoDML estimator that uses a shared covariate representation that is predictive of the outcome but not the Riesz representer.
result Outcome-adapted AutoDML estimator is asymptotically more efficient than baseline AutoDML.
Let M be a smooth Riemannian manifold which is the union of a compact part and a finite number of Euclidean ends, $\RR^n \setminus B(0,R)$ for some R>0, each of which carries the standard metric. Our main result is that the Riesz transform on M is bounded from Lp(M)→Lp(M;T∗M) for 1<p<n and unbou…
This is the fourth article of our series. Here, we study weighted norm inequalities for the Riesz transform of the Laplace-Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Gaussian upper bounds.
DPI quantifies phase differences in 1D and multidimensional signals using Riesz transform.
problem Quantifying phase differences in signals of varying dimensions.
method Riesz transform framework for harmonic analysis.
result DPI detects hypersynchronization and subtle changes in images and artworks.
Local Hardy spaces defined for Riemannian manifolds with bounded geometry.
problem Defining Hardy spaces for Riemannian manifolds with specific curvature conditions.
method Using local Riesz transforms and atomic Goldberg-type spaces.
result Atomic Hardy spaces and local Hardy spaces are equivalent on Riemannian manifolds with bounded geometry.
Paper improves MMD flow efficiency with Riesz kernels for image generation.
problem High computational costs in MMD flows for large scale computations.
method Introduces Riesz kernels and sliced MMD for efficient computation.
result Efficient computation of MMD gradients in one-dimensional setting.
Let (M∘,g) be an asymptotically conic manifold, in the sense that M∘ compactifies to a manifold with boundary M in such a way that g becomes a scattering metric on M. A special case of particular interest is that of asymptotically Euclidean manifolds, where ∂M=Sn−1 and the induced me…
Prediction-powered causal inference achieves smaller asymptotic variance than traditional methods.
problem Estimating causal and structural parameters in a semi-supervised setting.
method Combining efficient influence function with debiased machine learning and semi-supervised Riesz regression.
result Asymptotic variances of estimators match the derived efficiency bound.
The paper generalizes spectral section concepts to non-compact spaces.
problem Generalizing spectral sections to non-compact base spaces.
method Generalization to arbitrary base spaces, applications to cobordism theorems, investigation of Riesz continuity.
result If a family of operators has a spectral section, it is Riesz continuous.
In this paper we study the problem of deriving further Sobolev inequalities from a given Sobolev inequality. We use several different methods, including Bessel potentials and Riesz transforms. We apply the results to the Ricci flow to extend the author's results on the W1,2 Sobolev inequality along the Ricci flow …
One considers the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is Lp bounded on such a manifold, for p ranging in an open interval above 2, if and only if the gradient of the heat kernel satisfies a certai…
In this paper, we show the equivalence between the boundedness of the Riesz transform dΔ−1/2 on Lp, p∈(2,p0), and the equality Hp=Lp, p∈(2,p0), in the class of manifold whose measure is doubling and for which the scaled Poincaré inequalities hold. Here, Hp is a Hardy space of exact 1−forms, …