We outline a cohomological treatment for multivalued (classical) action functionals. We point out that an application of Takens' theorem, after Zuckerman, Deligne and Freed, allows to conclude that multivalued functionals yield globally defined variational equations.
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48 results for “Multivalued Treatments”
New methods for estimating causal effects with limited overlap, using Stable Probability Weighting.
problem Estimating causal effects with limited overlap in multivalued treatments.
method Stable Probability Weighting (SPW) and Finite-Sample Stable Probability Weighting (FPW) methods.
result SPW and FPW provide practical solutions for estimating and inferring causal effects with limited overlap.
Defines finite type Multivalued Shape using hyperspaces.
problem No specific problem stated; focuses on definition.
method Construction over metric compacta using hyperspaces.
result Defines finite type Multivalued Shape.
Paper constructs multivalued harmonic functions on R^3 using twistor methods.
problem Constructing multivalued harmonic functions on R^3.
method Twistor methods to construct multivalued harmonic functions.
result Found a family of multivalued harmonic functions with branching sets as ellipses and quadratic growth at infinity.
Bayesian method models multivalued power data from wind farms.
problem Accurate modeling of power curves with multivalued relationships.
method Overlapping mixture of probabilistic regression models.
result Model accurately represents practical power data.
We extend the work of Simon and Wickramasekera, who constructed a large class of multivalued solutions to the minimal surface equation, to produce multivalued solutions to more general classes of elliptic equations and systems, including the minimal surface system with small boundary data and the La…
We consider harmonic sections of a bundle over the complement of a codimension 2 submanifold in a Riemannian manifold, which can be thought of as multivalued harmonic functions. We prove a result to the effect that these are stable under small deformations of the data. The proof is an application of a version of the Na…
Restricted Boltzmann Machine with Multivalued Hidden Variables: a model suppressing over-fittingstat.ML
Generalization is one of the most important issues in machine learning problems. In this study, we consider generalization in restricted Boltzmann machines (RBMs). We propose an RBM with multivalued hidden variables, which is a simple extension of conventional RBMs. We demonstrate that the proposed model is better than…
This article is a survey of the Novikov problem of the structure of leaves of the foliations induced by a collection of closed 1-forms in a compact manifold . Equivalently, this is to the study of the level sets of multivalued functions on . To date, this problem was thoroughly investigated only for …
This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our…
Extragradient-Type Methods with Last-Iterate Convergence Rates for Co-Hypomonotone Inclusionsmath.OC
Two accelerated extragradient methods converge at rate for co-hypomonotone inclusions.
problem Solving co-hypomonotone inclusions with sum of Lipschitz and multivalued operators.
method Developed two Nesterov's accelerated extragradient methods for co-hypomonotone inclusions.
result Achieve last-iterate convergence rates on the residual norm.
Framework for universal graph function approximators outperforms existing methods.
problem Graph classification and separation of graph classes.
method Inspired by persistent homology, dependency parsing, and multivalued functions, the framework constructs universal approximators on graph isomorphism classes.
result Achieves state-of-the-art performance on four graph datasets.
In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp.
The Gauss Image Measure uniquely identifies dual convex bodies up to dilation.
problem Identifying dual convex bodies based on their Gauss Image Measure.
method Analyzing the Gauss Image Measure and its properties to establish the uniqueness of dual bodies.
result Dual convex bodies are equal up to a dilation on each path-connected component of the support of the measure.
The paper explores eigenfunctions of spherical conical metrics using harmonic maps to spheres.
problem Existence and properties of eigenfunctions for spherical conical metrics.
method Application of multivalued harmonic maps to spheres and algebraic constructions.
result New criteria and examples of metrics with many 2-eigenfunctions.
In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts. In contrast to the Normal- Hedge bound, which mainly depends on the effective number of experts but also weakly depends on the nominal…
Let M be a closed n-dimensional manifold, n > 2, whose first real cohomology group H 1 (M ; R) is non-zero. We present a general method for constructing a Morse 1-form on M , closed but non-exact, and a pseudo-gradient X such that the differential X of the Novikov complex of the pair (, X) has at leas…
Extends holomorphic functions on complex manifolds to larger spaces.
problem Extending holomorphic functions on complex manifolds.
method Proving the existence of a larger space for continuous maps that allows holomorphic continuation.
result Bounded holomorphic functions on can be extended to holomorphic functions on .
We develop a multivalued theory for the stability operator of (a constant multiple of) a minimally immersed submanifold of a Riemannian manifold . We define the multiple valued counterpart of the classical Jacobi fields as the minimizers of the second variation functional defined on a Sobolev space of …
Machine learning finds Z/2 eigenfunctions on a sphere.
problem Finding Z/2 eigenfunctions on the sphere.
method Created a multivalued neural network and used JAX to implement it. Fixed branch points at tetrahedron and cube vertices, and allowed AI to move them in the third case.
result Found Z/2 eigenfunctions for three cases.
Dynamics in fractal spacesphysics.class-ph
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm. We use the mathematical concept of fiber bundle to characterize the multivalued …
A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found using mean-shift algorithms. We describe the theory and practice behind clustering…
The purpose of the paper is to introduce some conjectures regarding the analytic continuation and the arithmetic properties of quantum invariants of knotted objects. More precisely, we package the perturbative and nonperturbative invariants of knots and 3-manifolds into two power series of type P and NP, convergent in …
EDML is a recently proposed algorithm for learning MAP parameters in Bayesian networks. In this paper, we present a number of new advances and insights on the EDML algorithm. First, we provide the multivalued extension of EDML, originally proposed for Bayesian networks over binary variables. Next, we identify a simplif…
We first describe the local and global moduli spaces of germs of foliations defined by analytic functions in two variables with p transverse smooth branches, and with integral multiplicities (in the univalued holomorphic case) or complex multiplicities (in the multivalued ''Darboux'' case). We specify normal forms in e…
Cieliebak, Mundet i Riera and Salamon recently formulated a definition of branched submanifold of Euclidean space in connection with their discussion of multivalued sections and the Euler class. This note proposes an intrinsic definition of a weighted branched manifold Z that is obtained from the usual definition of or…
Proves resurgent nature of a series solution to deformed Painlevé I equation.
problem Analyzing the resurgent nature of a series solution to the deformed Painlevé I equation.
method Proves resurgent nature through formal -power series solution and Borel summability.
result Borel transform defines a global multivalued holomorphic function on a Fermat quintic surface.
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.
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.
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.
Study on eigenfunctions on sphere configurations, proving non-existence and construction of critical eigensections.
problem Existence and rigidity of critical Z2 eigenvalues on sphere configurations.
method Algebraic identities and finite group representation theory.
result Construction of infinitely many configurations admitting critical eigensections and proof of deformation rigidity of Taubes-Wu tetrahedral eigensections.
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 covariate balancing: estimating treatment effects over time with potential local projectionsecon.EM
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.
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.
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.