arXiv research

Method estimates sparse inverse covariance and partial correlation matrices efficiently.

The paper estimates gradients for a weighted parabolic equation under geometric flow.

New characterizations of partial positivity using Hörmander's $L^2$-estimate.

Gradient estimate proved for Donaldson's equation on Kähler manifolds.

Estimates mode from partial feedback, improving AI learning pipelines.

The paper develops methods to estimate POMDPs from partial information.

Paper proposes methods to learn DAGs from partial orderings.

Study efficient inference for network quantile causal effects with partial interference.

Ranked data appear in many different applications, including voting and consumer surveys. There often exhibits a situation in which data are partially ranked. Partially ranked data is thought of as missing data. This paper addresses parameter estimation for partially ranked data under a (possibly) non-ignorable missing…

Paper introduces a new test for conditional independence using weighted partial copulas.

Study uses deep neural networks for inference in partially linear models with dependent data.

Proposes a partially linear structure to capture nonlinear relationships in mixture of experts models.

Estimates smooth functions and their derivatives from noisy data.

We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as…

For a convex domain $D$ bounded by the hypersurface $\partial D$ in a space of constant curvature we give sharp bounds on the width $R-r$ of a spherical shell with radii $R$ and $r$ that can enclose $\partial D$, provided that normal curvatures of $\partial D$ are pinched by two positive constants. Furthermore, in the …

Paper introduces efficient methods for estimating cross-partial derivatives and sensitivity indices.

Establishes uniform Hörmander estimates for flat line bundles on Kähler manifolds.

Paper identifies and estimates CAPCEs in continuous treatment settings.

The paper examines partial regularity of Lipschitz solutions to minimal surface system.

Let $(M, g(t))$, $t\in[0,T)$ be a closed Riemannian $n$-manifold whose Riemannian metric $g(t)$ evolves by the geometric flow $\frac{\partial }{\partial t} g_{ij}=-2S_{ij}$, where $S_{ij}(t)$ is a symmetric two-tensor on $(M,g(t))$. We discuss differential Harnack estimates for positive solution to the porous medium …

Unified method for inference on partially identified causal effects using covariates.

This paper studies the partial estimation of Gaussian graphical models from high-dimensional empirical observations. We derive a convex formulation for this problem using $\ell_1$-regularized maximum-likelihood estimation, which can be solved via a block coordinate descent algorithm. Statistical estimation performance …

Derives gradient estimation for a specific heat equation on evolving manifolds.

Let $Ω$ be a pseudoconvex domain with $C^2$-smooth boundary in $\mathbb CP^n$. We prove that the $\bar\partial-Neumann operator$N$exists for$(p,q)$-forms on$Ω$. Furthermore, there exists a$t_0>0$such that the operators$N$,$\bar\partial^*N$,$\bar\partial N$ and the Bergman projection are regular in the Sobolev …

Estimates Bergman kernels on Kähler manifolds with Ricci bounds.

Robustly aligns datasets with partial GW distance to handle contamination.

For a Riemannian manifold $M^{n+1}$ and a compact domain $Ω\subset M^{n+1}$ bounded by a hypersurface $\partial Ω$ with normal curvature bounded below, estimates are obtained in terms of the distance from $O$ to $\partial Ω$ for the angle between the geodesic line joining a fixed interior point $O$ in $Ω$ to a point on…

In the modern age, rankings data is ubiquitous and it is useful for a variety of applications such as recommender systems, multi-object tracking and preference learning. However, most rankings data encountered in the real world is incomplete, which prevents the direct application of existing modelling tools for complet…

Paper proves Hamilton-Tian conjecture using partial C0-estimate.

We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal pseudo-profile likelihood estimator (MaPPLE) for which we prove $\sqrt{n}$-sparsisten…

New algorithm for risk-sensitive reinforcement learning with natural policy gradients.

We prove that the partial $C^0$-estimate holds for metrics along Aubin's continuity method for finding Kähler-Einstein metrics, confirming a special case of a conjecture due to Tian. We use the method developed in recent work of Chen-Donaldson-Sun on the analogous problem for conical Kähler-Einstein metrics.

Let $M^n$ be an $n$-dimensional Riemannian manifold with boundary $\partial M$. Assume that Ricci curvature is bounded from below by $(n-1)k$, for $k\in \RR$, we give a sharp estimate of the upper bound of $ρ(x)=\dis(x, \partial M)$, in terms of the mean curvature bound of the boundary. When $\partial M$ is compact, th…

Study shows offline RL under $Q^\star$-approximation and partial coverage is harder than previously thought.

AdaptOn achieves logarithmic regret in adaptive control of unknown partially observable linear systems.

We establish a new partial $C^{0}$-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted $(1,1)$-form on Fano manifolds. As an application, this estimate enables us to show the reductivity of the automorphism group of the limit space, which leads t…

Let $Ω$ be a bounded domain with $C^\infty$ boundary in an $n$-dimensional $C^\infty$ Riemannian manifold, and let $\varrho$ be a non-negative bounded function defined on $\partial Ω$. It is well-known that for the biharmonic equation $Δ^2 u=0$ in $Ω$ with the 0-Dirichlet boundary condition, there exists an infinite se…

Meta-learners estimate CATE from multiple environments with partial identification.

Sharp estimates for Bergman metrics derived from Kähler quantization.

A new approach uses partial likelihood to improve tree-based density estimation and inference.

Estimates error for robust M-estimators with convex penalties.

Study on estimating sparse transition matrix of partially-observed VAR with noisy and sparse data.

This paper provides estimation and inference methods for an identified set's boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary using a semiparametric moment equation. Combining Neyman-orthogonality and sample s…

New method uses sparse deep neural networks for high-dimensional regression with improved parameter estimation.

Estimates smooth graph signals from partial measurements.

PRL improves off-policy evaluation in partially observed MDPs.

Paper develops a method for estimating PFLM with minimized rates in high dimensions.

Uniform estimates for complex equations on compact manifolds found.