Article provides Bernstein gradient estimates for heat equations with potential terms.
problem Gradient estimates for heat equations with potential terms on weighted Riemannian manifolds.
method Derived Bernstein type gradient estimates for two systems of heat equations with linear, exponential, and combined potentials.
result Resolves part of the problem raised by Bhattacharyya et al. in \cite{SB-1}.
Unified approach for estimating quantiles of potential outcomes using inverse estimating equations.
problem Estimating quantiles of potential outcomes for causal inference.
method Inverse estimating equations and moment function.
result Unified approach to estimate mean and quantiles of potential outcomes.
Estimates classical potential from stock price data using quantum mechanics.
problem Estimating classical potential from empirical stock price data.
method Quantum mechanical model of stock price distribution, estimating potential from wave function.
result Suggests methods to evaluate classical potential for Schrodinger equation.
Gradient estimates for subelliptic harmonic maps with potential.
problem Estimating gradients of subelliptic harmonic maps.
method Investigation of subelliptic harmonic maps with potential from specific manifolds.
result Gradient estimates and Liouville type result established.
The paper applies potential theory to conformal geometry, proving theorems and dimension estimates.
problem Understanding the behavior of solutions near singularities in conformal geometry.
method Linear and nonlinear potential theory applied to conformal geometry problems.
result Established Huber's type theorems and Hausdorff dimension estimates for conformal geometry.
CCN estimates full potential outcome distributions without restrictive assumptions.
problem Estimating CATE is insufficient; full potential outcome distributions provide greater insights.
method Collaborating Causal Networks (CCN) learns full potential outcome distributions without restrictive assumptions.
result CCN learns distributions that asymptotically capture true potential outcome distributions.
Uniform estimates for Calabi-Yau degenerations proved.
problem Calabi-Yau degenerations of polarised algebraic manifolds.
method Uniform Skoda and L∞-estimates for Kähler potentials. result Uniform Skoda type estimate and L∞-estimate for Calabi-Yau Kähler potentials proved. Improves decision making by estimating bounds on potential outcomes.
problem Estimating individual treatment effects is complex and hard to estimate.
method Developed an algorithm to learn upper and lower bounds on potential outcomes that optimize an objective function defined by the decision maker.
result Our algorithm outperforms baselines, providing tighter, more reliable bounds.
Study uses Open Banking data to estimate customer value, showing potential 21% increase.
problem Limited CLV estimation using single-entity data.
method Introduces PCLV framework using Open Banking data for comprehensive customer value estimation.
result Open Banking data can estimate PCLV per competitor, showing a 21.06% increase over Actual CLV.
Estimates Schrödinger potentials with minimal sample size.
problem Estimating Schrödinger potentials for generative modeling.
method Empirical Kullback-Leibler risk minimizer over log-potentials.
result Excess KL-risk decreases as fast as O(log2n/n). Study clarifies variance of stratification estimators for causal effects.
problem Estimating average causal effects with discrete covariates.
method Combines insights from potential outcomes, causal diagrams, and structural models.
result Derives expressions for the variance of stratification estimators.
Study examines wave equation decay and Strichartz estimates on conic manifolds.
problem Analyzing wave equation behavior on conic spaces with critical electromagnetic potentials.
method Established decay and Strichartz estimates through localized spectral measure construction.
result Extended and improved previous results on wave equation behavior with critical potentials.
Discovering a correlation from one variable to another variable is of fundamental scientific and practical interest. While existing correlation measures are suitable for discovering average correlation, they fail to discover hidden or potential correlations. To bridge this gap, (i) we postulate a set of natural axioms …
We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator in the case when the potential is strongly convex. In particular, if the Hessian of the potential is bounded from below by a positive constant, the gap has a lower bound independent of the dimension. We also estimate the gap wh…
The paper introduces metrics to rank potential outcomes for better decision-making.
problem Optimal action selection in uncertain situations using causal reasoning.
method Introducing two new metrics: probabilities of potential outcome ranking (PoR) and probability of achieving the best potential outcome (PoB). Establishing identification theorems and deriving bounds for these metrics, and presenting estimation methods.
result The estimators' finite-sample properties and their application to a real-world dataset are demonstrated.
Proposes a method to improve CATE estimation by imputing missing potential outcomes.
problem Statistical discrepancy between distinct treatment groups in CATE estimation.
method Contrastive learning approach to reliably impute missing potential outcomes for a subset of individuals.
result Improves the accuracy and robustness of CATE estimation models.
Study Kähler-Einstein potentials on stable varieties near singularities
problem Asymptotic behavior of Kähler-Einstein potentials on stable varieties near singularities
method Using iterated logarithmic functions and refined lower bounds
result Improved estimates for Kähler-Einstein potentials
Study on special Lagrangian curvature potential equation, proving existence and uniqueness of smooth solutions.
problem Second boundary value problem for special Lagrangian curvature potential equation.
method Method of continuity with a-priori estimate.
result Existence and uniqueness of smooth uniformly convex solutions.
Study on compact Quasi-Einstein manifolds yields diameter estimates and Hitchin-Thorpe inequality conditions.
problem Estimating diameters and verifying Hitchin-Thorpe inequality for compact Quasi-Einstein manifolds.
method Derive geometric estimates relating potential function oscillation to manifold diameter; derive lower bounds for diameter.
result Diameter conditions ensure compact Quasi-Einstein manifolds satisfy Hitchin-Thorpe inequality in dimension four.
We investigate a potential obtained as the convolution of a radially symmetric function and the characteristic function of a body (the closure of a bonded open set) with exterior cones. In order to restrict the location of a maximizer of the potential into a smaller closed region contained in the interior of the body, …
New work shows FP potential monotonicity equals low-degree polynomial estimators limits.
problem Establishing a precise mathematical relationship between statistical physics and polynomial estimators limits.
method Analyzing Gaussian additive models (GAMs) to show FP potential monotonicity equals low-degree polynomial estimators limits.
result For a broad family of Gaussian additive models, the power of low-degree polynomials is equivalent to the monotonicity of the annealed FP potential.
The quality of an induced model by a learning algorithm is dependent on the quality of the training data and the hyper-parameters supplied to the learning algorithm. Prior work has shown that improving the quality of the training data (i.e., by removing low quality instances) or tuning the learning algorithm hyper-para…
In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution of the time-dependent heat equation.
The paper finds geodesics in Kähler potentials with no degeneration.
problem Finding geodesics in Kähler potentials without degeneration.
method Establishing a lower bound estimate for eigenvalues of complex Hessian.
result Geodesics can connect close points in Kähler potentials without degeneration.
We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator with a nonconvex potential in terms of a distance associated with the potential. The results here can be applied to the double well potential.
Paper introduces GDR-learners for estimating potential outcomes from observational data.
problem Lack of theoretical property of general Neyman-orthogonality in deep generative models.
method Develops flexible GDR-learners based on various deep generative models.
result GDR-learners possess quasi-oracle efficiency and rate double robustness, asymptotically optimal.
We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator −4d2/ds2+κ2(s) with potential given by the curvature of a closed curve.
Extends potential theory to Carnot groups, estimating Hausdorff dimension.
problem Estimating Hausdorff dimension of polar sets in Carnot groups.
method Geometric completeness and Riesz potential inequalities in Carnot groups.
result Developed applications in CR geometry and quaternionic CR geometry.
New method estimates Schrödinger bridge potentials via empirical risk minimization.
problem Estimating Schrödinger bridge potentials from samples.
method Rewriting Schrödinger system as a fixed-point equation and estimating the potential via empirical risk minimization.
result Uniform concentration of empirical risk around population counterpart under sub-Gaussian assumptions.
Researchers find a way to estimate potential functions for quaternionic metrics.
problem Existence of quaternionic Gauduchon metrics with prescribed volume form.
method Reframed as a fully nonlinear elliptic equation and established a uniform estimate.
result Uniform estimate for the potential function.
We propose a procedure for supervised classification that is based on potential functions. The potential of a class is defined as a kernel density estimate multiplied by the class's prior probability. The method transforms the data to a potential-potential (pot-pot) plot, where each data point is mapped to a vector of …
Method estimates CATE using RCT data to handle hidden confounders.
problem Estimating CATE in the presence of hidden confounders.
method Pseudo-confounder generator and CATE model alignment.
result Method reduces bias in CATE estimation.
The paper derives estimates for linear potentials and applies them to improve Hausdorff dimensions of singular sets in conformal geometry.
problem Estimating linear potentials and understanding their impact on singular sets in conformal geometry.
method Derives estimates for linear potentials and applies them to improve Hausdorff dimensions of singular sets.
result Improves the Hausdorff dimensions of singular sets in conformal geometry, achieving stronger results in dimension 4.
The article derives some novel independence measures and contrast functions for Blind Source Separation (BSS) application. For the kth order differentiable multivariate functions with equal hyper-volumes (region bounded by hyper-surfaces) and with a constraint of bounded support for k>1, it proves that equality …
We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated…
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…
This paper explores how entropic regularization improves Wasserstein estimators' performance.
problem Improving the approximation and estimation properties of Wasserstein estimators.
method Entropic regularization of optimal transport costs to smooth Wasserstein estimators.
result Entropic regularization can achieve comparable statistical performance to un-regularized estimators at lower computational cost.
The paper analyzes stability and convergence rates of entropic and Sinkhorn potentials.
problem Stability and convergence rates of entropic and Sinkhorn potentials.
method Semiconcavity properties of entropic potentials and Schrödinger bridges.
result Exponential convergence rates for gradient and Hessian of Sinkhorn iterates.
Optimistic estimate predicts best fitting performance of nonlinear models.
problem Evaluating the potential of nonlinear models in fitting.
method Proposes an optimistic estimate to quantify the smallest sample size for fitting nonlinear models.
result Predicts specific subsets of targets that can be fitted at overparameterization.
In this paper a growth estimate on the soliton potential is shown for a large class of cohomogeneity one manifolds. This is used to construct continuous families of complete steady and expanding Ricci solitons in the set-ups of Lü-Page-Pope and Dancer-Wang. It also provides a different approach to the two summands syst…
Efficiently predicts optimal transport plans using sliced potentials.
problem Predicting optimal transport plans across multiple measure pairs efficiently.
method Regression-based and objective-based amortization strategies using sliced optimal transport potentials.
result Efficient and accurate prediction of optimal transport plans for various tasks.
This study examines how well GANs estimate the Wasserstein metric.
problem Estimating the Wasserstein metric from samples in GANs.
method Analyzes c-transform formulation to improve Wasserstein metric estimation. result The c-transform does not perform best in the generative setting. Let (M,g) be an dimensional complete Riemannian manifold. In this paper we prove local Li-Yau type gradient estimates for all positive solutions to the following nonlinear parabolic equation \begin{equation*} (\partial_t - Δ_g + \mathcal{R}) u(x, t) = - a u(x, t) \log u(x, t) \end{equation*} along the generalised ge…
We use a geometric construction to exhibit examples of autonomous Lagrangian systems admitting exactly two homoclinics emanating from a nondegenerate maximum of the potential energy and reaching a regular level of the potential having the same value of the maximum point. Similarly, we show examples of Hamiltonian syste…
We derive global estimates in critical scale invariant norms for solutions of elliptic systems with antisymmetric potentials and almost holomorphic Hopf differential in two dimensions. Moreover we obtain new energy identities in such norms for sequences of solutions of these systems. The results apply to harmonic maps …
The study extends GBM to include stable nonzero prices and finds a pronounced potential well.
problem The standard GBM model cannot describe stable nonzero prices in financial dynamics.
method Generalized GBM with polynomial drift of order q, model selection, and Markov chain Monte Carlo ensembles of potential functions.
result The optimal model for financial data is q=2, indicating the existence of a stable price.
In the absence of unobserved confounders, matching and weighting methods are widely used to estimate causal quantities including the Average Treatment Effect on the Treated (ATT). Unfortunately, these methods do not necessarily achieve their goal of making the multivariate distribution of covariates for the control gro…
This tutorial introduces causal modeling methods for researchers.
problem Understanding causal relationships in research studies.
method Integrates potential outcomes and graphical methods for causal modeling.
result Clear notation and practical examples for applied researchers.