New boundary treatment improves accuracy for complex PDEs.
problem Order reduction in high-order IMEX schemes for multidimensional PDEs.
method Novel boundary treatment algorithms for Cartesian meshes, treating implicit-explicit stages similarly to interior points.
result Recovery of designed order of convergence by numerical verification.
Paper improves feature selection for predicting outcomes from observational data.
problem Feature selection for post-intervention outcome prediction from pre-intervention variables in healthcare settings.
method Extends Markov boundary concept to treatment-outcome pairs, uses observational and experimental data.
result Combining observational and experimental data improves feature selection and effect estimation.
Paper extends transfer learning for decision rules, improving treatment rule estimation.
problem Estimating optimal individualized treatment rules under changing conditions.
method Bayes decision rules and low-dimensional empirical risk minimization.
result Consistent estimators and risk bounds established under mild conditions.
In this expository note, we illustrate phenomena and conjectures about boundaries of hyperbolic groups by considering the special cases of certain amalgams of hyperbolic groups. While doing so, we describe fundamental results on hyperbolic groups and their boundaries by Bowditch and Haissinsky, along with special treat…
Proposes a framework to reconcile policy learning and profit maximization in CATE estimation.
problem Aligning CATE estimation with profit maximization for optimal customer treatment decisions.
method Optimizes a novel objective function that concentrates learning capacity near the decision boundary, ensuring consistency with the original profit function.
result Consistent CATE estimates can be recovered from existing profit-maximization pipelines, allowing firms to navigate the trade-off between accuracy and profit.
Extends expected value framework for cost-sensitive causal decision-making.
problem Optimizing operational decision-making with cost-sensitive causal classification.
method Introduces a cost-sensitive decision boundary based on estimated individual treatment effects, positive outcome probability, and cost parameters.
result Effective in maximizing expected causal profit, outperforming cost-insensitive ranking approach.
Study curves evolving on hypersurfaces with free boundaries, preserving length.
problem Evolution of curves on hypersurfaces with free boundaries.
method Nonlocal evolution equation with nonlinear boundary conditions, short-time existence, uniqueness, and parabolic energy estimates.
result Global existence and convergence to critical points proved.
Q-learning adapted to find near-equivalent treatment strategies.
problem Finding optimal treatment sequences in dynamic treatment regimes.
method Introducing a worst-value tolerance criterion to find sets of near-equivalent policies.
result Constructs families of near-equivalent treatment strategies.
Improved fourth-order compact scheme for option valuation with Robin boundary condition.
problem Lower convergence rates in numerical methods for American options.
method High-order compact scheme, Robin boundary condition, coupled nonlinear PDEs.
result Fourth-order convergence rate achieved without mesh refinement.
In this paper, we define an energy-momentum vector at the spatial infinity of either asymptotically flat or asymptotically hyperbolic initial data sets carrying a non-compact boundary. Under suitable dominant energy conditions (DECs) imposed both on the interior and along the boundary, we prove the corresponding positi…
For an embedded conformal hypersurface with boundary, we construct critical order local invariants and their canonically associated differential operators. These are obtained holographically in a construction that uses a singular Yamabe problem and a corresponding minimal hypersurface with boundary. They include an ext…
Adapts Stein's method for geometric inequalities, addressing boundary terms.
problem Geometric inequalities and their stability under constraints.
method Uses elliptic PDE with oblique boundary condition to handle boundary terms.
result Stability results for various geometric inequalities with respect to a new distance.
Develops deep learning methods for non-linear PDEs in credit risk.
problem Solving option XVA pricing problems with non-linear PDE models.
method Boundary-safe PINNs approach, using automatic differentiation.
result Eliminates heuristic boundary condition weights, improves accuracy.
Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov's higher signatures on closed manifolds; - the problem of cut-and-paste invariance of Novikov's higher signatures on closed manifolds; - the problem of defining higher signa…
New model predicts grain boundary migration in metals.
problem Anisotropic grain boundary migration in polycrystals.
method Level set-finite element formulation based on thermodynamics and mechanics.
result First analytical solution for anisotropic grain boundary configurations.
Manifolds with fibered hyperbolic cusp metrics include hyperbolic manifolds with cusps and locally symmetric spaces of Q-rank one. We extend Vaillant's treatment of Dirac-type operators associated to these metrics by weaking the hypotheses on the boundary families through the use of Fredholm perturbations as in the fam…
Study shows contractibility of certain metrics on 3-manifolds.
problem Topology of metrics on 3-manifolds with boundary constraints.
method Proves contractibility of spaces of metrics under specific constraints.
result Spaces of constrained metrics are contractible when non-empty.
Ordinal data are often seen in real applications. Regular multicategory classification methods are not designed for this data type and a more proper treatment is needed. We consider a framework of ordinal classification which pools the results from binary classifiers together. An inherent difficulty of this framework i…
Proposes a new Bayesian learning method for optimal treatment regimes.
problem Sub-optimal policies in offline data due to lack of exploration.
method Integrates pessimism principle with Thompson sampling and Bayesian machine learning.
result Derives a credible set that uniformly lower bounds the optimal Q-function.
Develops a method for conformal parameterization of point clouds without fixed boundaries.
problem Desirable distortion in fixed-boundary parameterizations of point clouds.
method Free-boundary conformal parameterization method involving approximation of point cloud Laplacian and boundary treatment.
result High-quality point cloud meshing achieved through the proposed method.
We study parabolic G-Higgs bundles over a compact Riemann surface with fixed punctures, when G is a real reductive Lie group, and establish a correspondence between these objects and representations of the fundamental group of the punctured surface in G with arbitrary holonomy around the punctures. Three interesting fe…
GraphITE estimates individual effects of graph-structured treatments.
problem Estimating individual effects of complex treatment structures.
method Graph neural networks and Hilbert-Schmidt Independence Criterion regularization.
result GraphITE outperforms baselines in estimating treatment effects for large numbers of treatments.
M3E2 neural network estimates multiple treatment effects.
problem Estimating effects of multiple treatments simultaneously.
method Multi-task learning neural network model for multiple treatments, continuous and binary.
result M3E2 outperforms baselines in synthetic datasets.
Proposes a new method to estimate continuous treatment policies and match treatments effectively.
problem Current methods struggle with continuous treatment policies and complex matching.
method Formulates treatment effectiveness as a parametrizable model, using deep learning for optimization.
result Significant improvement in treatment effectiveness and matching efficiency.
We present a variational formulation of electrodynamics using de Rham even and odd differential forms. Our formulation relies on a variational principle more complete than the Hamilton principle and thus leads to field equations with external sources and permits the derivation of the constitutive relations. We interpre…
Framework generates personalized insulin treatment strategies using deep models.
problem Developing optimal personalized treatment strategies for diabetes patients.
method Combines deep generative time series models with decision theory.
result Demonstrated improved personalized insulin treatment strategies for diabetes patients.
The Reynolds Transport Theorem, colloquially known as 'differentiation under the integral sign', is a central tool of applied mathematics, finding application in a variety of disciplines such as fluid dynamics, quantum mechanics, and statistical physics. In this work we state and prove generalizations thereof to subman…
Develops deep jump learning for continuous treatment OPE.
problem Estimating mean outcomes under new treatment rules using historical data from different rules.
method Adaptive deep discretization of continuous treatment space using deep learning and multi-scale change point detection.
result Validated method through theoretical results, simulations, and real application to Warfarin Dosing.
A new method for generating counterfactual explanations in high-dimensional datasets.
problem Creating realistic counterfactual explanations in complex, high-dimensional data.
method A discretized approach using binary search and boundary approximation.
result Our method reduces the distance between counterfactuals by 5% to 50% in terms of the L2 norm.
Method controls treatment risk in learning beneficial allocations.
problem Learning beneficial treatment allocations with risk control in precision medicine.
method Proposes a certifiable learning method that controls treatment risk with finite samples in the partially identified setting.
result Illustrates method using both simulated and real data.
Optimal adaptive experiment for choosing best treatment with binary outcomes.
problem Choosing the best treatment from binary options in an adaptive experiment.
method Adaptive experiment with two phases: treatment allocation and choice. Neyman allocation method used.
result Neyman allocation is minimax and Bayes optimal, matching lower bounds for regret.
Proposes a fusion method for many treatment groups in ITRs.
problem Challenges in handling many treatment groups with data sparsity and covariate imbalance.
method Calibration-weighted treatment fusion procedure that balances covariates and fuses similar treatments.
result Ensures robust treatment group recovery and policy value compared to existing methods.
Dynamic treatment effects estimated over time using covariate balancing.
problem Estimating treatment effects in panel data with dynamic treatments.
method Dynamic covariate balancing with potential local projections.
result Established inferential guarantees for the proposed method.
CRN model estimates treatment effects over time using adversarial balancing.
problem Estimating treatment effects over time in medical settings.
method Adversarial domain balancing to remove time-varying confounders.
result CRN achieves lower error in estimating counterfactuals and treatment timing.
Heteroskedasticity biases uplift model rankings, leading to inefficient treatment allocation.
problem Bias in uplift model rankings due to heteroskedasticity.
method Theoretical analysis and simulation on real-world data.
result Heteroskedasticity can cause individuals with high treatment effects to be ranked at the bottom, leading to inefficient treatment allocation.
Estimates heterogeneous treatment effects in panel data with a new method.
problem Estimating heterogeneous treatment effects in panel data with general treatment patterns.
method Partition observations into clusters with similar treatment effects using a regression tree, then estimate average treatment effects for each cluster.
result Our method achieves superior accuracy compared to alternative approaches.
In treatment allocation problems the individuals to be treated often arrive sequentially. We study a problem in which the policy maker is not only interested in the expected cumulative welfare but is also concerned about the uncertainty/risk of the treatment outcomes. At the outset, the total number of treatment assign…
NICE model estimates causal effects for image treatments.
problem Challenges in causal effect estimation for multi-dimensional treatments.
method Proposes NICE model for image treatments, incorporating rich multidimensional information.
result NICE significantly outperforms existing models in estimating causal effects for image treatments.
Constructs many black hole spacetimes in de Sitter space.
problem Creating well-controlled many black hole spacetimes in de Sitter space.
method Gluing Schwarzschild-de Sitter or Kerr-de Sitter black hole metrics into neighborhoods of points on the future conformal boundary of de Sitter space, under certain balance conditions.
result Solves the Einstein equation directly for the metric, given scattering data at the future conformal boundary.
XTNet estimates complex cross-treatment effects in multi-category, multi-valued settings.
problem Challenges in estimating causal effects for multi-category, multi-valued treatments.
method Dynamic Neural Masking for capturing treatment interactions without restrictive assumptions.
result XTNet consistently outperforms state-of-the-art baselines in multi-category, multi-valued treatment effect estimation.
Personalized medicine aims at identifying best treatments for a patient with given characteristics. It has been shown in the literature that these methods can lead to great improvements in medicine compared to traditional methods prescribing the same treatment to all patients. Subgroup identification is a branch of per…
The paper proposes a method to precisely decompose confounders and estimate treatment effects.
problem Estimating treatment effects from observational data with confounder identification and balancing.
method Learning decomposed representations to identify and balance confounders and non-confounders.
result The method achieves more precise treatment effect estimation than existing methods.
RATE metrics evaluate treatment prioritization rules, subsuming existing methods.
problem Comparing and testing the quality of treatment prioritization rules.
method Rank-weighted average treatment effect (RATE) metrics.
result RATE metrics enable asymptotically exact inference in various study settings.
Selective imputation improves treatment effect estimation from missing data.
problem Missing data complicates treatment effect estimation, especially with treatment variables.
method Introduced mixed confounded missingness (MCM) and selective imputation.
result Selective imputation provides unbiased treatment effect estimates.
TV-SurvCaus improves causal inference for dynamic treatments in survival analysis.
problem Estimating causal effects of time-varying treatments on survival outcomes.
method Representation balancing techniques extended to time-varying treatment regimes with survival outcomes.
result TV-SurvCaus outperforms existing methods in estimating individualized treatment effects with time-varying covariates and treatments.
Develops methods for near-optimal personalized treatment recommendations.
problem Assigning optimal treatments to patients based on individual characteristics.
method Outcome weighted learning framework to estimate near-optimal alternative individualized treatment recommendations (A-ITR).
result Consistency of proposed methods and upper bound for risk between optimal and estimated recommendations.
Given two possible treatments, there may exist subgroups who benefit greater from one treatment than the other. This problem is relevant to the field of marketing, where treatments may correspond to different ways of selling a product. It is similarly relevant to the field of public policy, where treatments may corresp…
Optimizes treatment allocation in networks considering indirect effects.
problem Finding optimal treatment allocation in network settings with interference.
method OTAPI: Optimizing Treatment Allocation in the Presence of Interference, integrating causal estimators into IM algorithms.
result OTAPI outperforms classic IM and UM approaches on synthetic and semi-synthetic datasets.