Study of coloured invariants of torus knots using W algebras.
problem Understanding coloured invariants of torus knots T(p,p′). method Representation theory of principal affine W algebras and asymptotic weight multiplicities. result Limits of renormalized invariants are equal to characters of W algebra modules. Estimates multiple means in high dimensions using convex combinations.
problem Estimating multiple multi-dimensional means from samples.
method Convex combinations of empirical means with data-dependent weights.
result Our methods asymptotically approach oracle (minimax) improvement.
Given a weighted line arrangement in the projective plane, with weights satisfying natural constraint conditions, we show the existence of a Ricci-flat Kähler metric with cone singularities along the lines asymptotic to a polyhedral Kähler cone at each multiple point. Moreover, we discuss a Chern-Weil formula that expr…
PEARL combines multiple representation learning methods to enhance model performance.
problem Different representation learning methods extract distinct data aspects, potentially missing important insights.
method Combines multiple representation learning approaches using surrogate loss functions for efficient weight estimation.
result Asymptotically achieves optimal performance in downstream tasks, assigning nonzero weights to correctly specified models.
Estimates RL data for dynamic treatment effects using GMM.
problem Estimating dynamic treatment effects from RL data with nonstationary behavior policies.
method Weighted GMM approach to stabilize variance in adaptive RL settings.
result Valid hypothesis testing and confidence regions for dynamic treatment effects.
New method selects best HTE estimator without ground-truth treatment effects.
problem Selecting best HTE estimator from multiple candidates.
method Cross-fitted, exponentially weighted test statistic with two-way sample splitting.
result Empirically, reliable error control and reduced false selections.
Let G be a torus and M a G-Hamiltonian manifold with Kostant line bundle L and proper moment map. Let P be the weight lattice of G. We consider a parameter k and the multiplicity m(λ,k) of the quantized representation associated to M and the k-th power of L . We prove that the weighted sum ∑m(λ,k)f(λ/k) of the…
LASLA improves multiple testing accuracy with network-structured data.
problem Efficiently incorporating complex side information into multiple testing.
method Locally adaptive structure learning algorithm (LASLA) integrating auxiliary information.
result LASLA asymptotically controls FDR and enhances power with side information.
Researchers extend asymptotic analysis to Bergman projections with Gevrey weights.
problem Analyzing Bergman projections with Gevrey weights.
method Extending direct approach to semiclassical asymptotics to Gevrey weights using Fourier integral operators.
result Gevrey symbol amplitude of asymptotic Bergman projection with Gevrey weights and Gevrey-type growth rate.
A new metric, Weighted Regret, unifies FDR and power evaluation in online multiple testing.
problem The asymmetric costs of false positives and false negatives in automated pipelines.
method Introducing Weighted Regret and Decoupled-OMT (DOMT) to unify FDR and power evaluation.
result DOMT achieves an order-optimal sublinear mitigation of threshold depletion in bursty environments.
New method constructs synthetic treatment groups without mean exchangeability assumption.
problem Violations of mean exchangeability assumption in randomized controlled trials.
method Weighted mixture of treatment groups from source populations, minimizing conditional maximum mean discrepancy.
result Asymptotic normality of synthetic treatment group estimator established.
Paper extends positive energy theorem to anti-de Sitter spacetimes.
problem Proving positive energy theorem for weighted anti-de Sitter spacetimes.
method Generalized positive energy theorem for 3D anti-de Sitter initial data sets.
result Positive energy theorem proved for weighted anti-de Sitter spacetimes.
Develops theory of weightings for Lie groupoids and algebroids.
problem Understanding differential geometry of weightings for Lie groupoids and algebroids.
method Extending work on weighted manifolds, defining weighted submanifolds, and developing theories of linear weightings and multiplicative weightings.
result Characterizes infinitesimally multiplicative weightings for Lie algebroids and classifies multiplicative weightings of Lie groupoids.
In recent studies, several asymptotic upper bounds on generalization errors on deep neural networks (DNNs) are theoretically derived. These bounds are functions of several norms of weights of the DNNs, such as the Frobenius and spectral norms, and they are computed for weights grouped according to either input and outp…
Paper explores weighted averaging schemes for SGD, achieving asymptotic normality and optimality.
problem Improving convergence of SGD in various settings.
method Develops a general weighted averaging scheme for SGD and establishes asymptotic normality.
result Establishes asymptotic normality and optimality of weighted averaged SGD solutions.
New method improves covariance estimation for weighted samples.
problem Improving covariance estimation for weighted sample data.
method Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
result Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
Best-of-∞ improves LLM performance by efficiently allocating inference-time computation.
problem Achieving optimal performance in test-time LLM ensembling with infinite budget.
method Adaptive generation scheme and weighted ensembles of LLMs, formulated as mixed-integer linear program.
result Optimal ensemble weighting improves performance over individual models.
In his seminal paper, A. N. Varchenko precisely investigates the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase. He expresses the order of this term by means of the geometry of the Newton polyhedron of the phase. The purpose of this paper is to generalize and improve his re…
The paper quantizes concatenated noisy vectors to a common cluster center, improving performance over naive methods.
problem Clustering concatenated noisy vectors from multiple sources.
method Asymptotic analysis of weighted sum of distances to a common cluster center.
result The clustering approach outperforms naive methods in terms of average distortion.
New insights into choosing between two data integration methods based on SVD.
problem Choosing between two data integration methods (Stack-SVD and SVD-Stack) for shared latent structure across multiple datasets.
method Derive exact expressions for the asymptotic performance and phase transitions of Stack-SVD and SVD-Stack, and develop optimal weighting schemes.
result Optimally weighted Stack-SVD outperforms optimally weighted SVD-Stack in the asymptotic regime.
New insights on how weight structure affects generalization in deep Gaussian feature models.
problem Understanding how weight structure impacts generalization in deep learning models.
method Using the replica trick from statistical physics to derive learning curves for models with structured Gaussian features.
result Allowing correlations between the rows of the first layer of features can aid generalization, while structure in later layers is generally detrimental.
Estimates causal contributions of multiple causes on outcome changes.
problem Quantifying the effect of multiple causes on an outcome change.
method Develops a multiply robust estimation strategy combining regression and re-weighting methods.
result The method recovers the target parameter under partial misspecification and is consistent and asymptotically normal.
New strategy optimally identifies best arm in unknown variance Gaussian bandits.
problem Identifying the best arm in two-armed Gaussian bandits with unknown variances.
method Proposes a Neyman Allocation (NA)-Augmented Inverse Probability weighting (AIPW) strategy to estimate variances and draw arms adaptively.
result Demonstrates asymptotic optimality of the proposed strategy in the small-gap regime.
Study shows robust method for estimating density ratios even with heavy contamination.
problem Estimating density ratios in the presence of heavy contamination.
method Weighted density ratio estimation (DRE) with doubly strong robustness.
result Weighted DRE achieves sparse consistency under heavy contamination.
Proves Laplacian and Lichnerowicz Laplacian are sectorial in weighted Hölder spaces.
problem Analyzing sectoriality of Laplacian and Lichnerowicz Laplacian on asymptotically hyperbolic spaces.
method Proves sectoriality in weighted Hölder spaces using asymptotically hyperbolic metrics.
result Analytic semigroups apply, yielding well-posedness results for parabolic evolution equations.
Explains weightings along submanifolds, focusing on Lie groupoids.
problem None explicitly stated; focuses on theory review.
method Reviews basic notions and emphasizes multiplicative weightings.
result Provides a comprehensive overview of weightings along submanifolds.
Paper proves multiplicative weight updates can train neural networks without learning rate tuning.
problem Vanishing and exploding gradients in gradient descent for compositional functions.
method Proves descent lemma for compositional functions using multiplicative weight updates and derives Madam optimizer.
result Madam optimizer trains state-of-the-art neural networks without learning rate tuning.
We give a construction of Kirby weight systems associated to sl(2) and valued into the finite field Z/pZ. We show that it is possible to apply this sequence of weight systems on the universal invariant of framed link. We also show that the corresponding sequence admits a Fermat limit, which defines an asymptotic ration…
Optimal model averaging for conditional generative models improves performance across various data types.
problem Multiple plausible generators for conditional distributions can vary in performance.
method Sample-based maximum mean discrepancy, static model averaging, and mixture-of-experts model averaging.
result MoEMA improves over competing baselines across various data types.
Under the assumption of asymptotic relative Chow-stability for polarized algebraic manifolds (M,L), a series of weighted balanced metrics ωm, m≫1, called polybalanced metrics, are obtained from complete linear systems ∣Lm∣ on M. Then the asymptotic behavior of the weights as m→∞ will be stud…
Gradient descent on normalized networks reveals sparsity preferences.
problem Understanding the inductive bias of gradient descent on normalized neural nets.
method Analysis of gradient descent on weight-normalized smooth homogeneous neural nets, focusing on SWN and EWN.
result EWN causes weights to be updated in a way that prefers asymptotic relative sparsity.
Annealed Entropic Allocation improves ranking and selection by mitigating hard switching and improving finite-budget discrimination.
problem Sequential budget allocation in ranking and selection
method Annealed weighted soft-min framework
result Surrogate converges uniformly to the hard minimum, soft-min weights concentrate on active challengers, and target allocation map is continuous.
Proofs high-dimensional spectrum convergence of weighted sample covariance.
problem High-dimensional spectrum convergence of weighted sample covariance.
method Proposes a new, concise proof with stronger assumptions.
result Spectrum convergence proven for different weight distributions.
Toeplitz operators linked to submultiplicative filtrations and weighted Bergman kernels.
problem Analyzing the asymptotics of weighted Bergman kernels for submultiplicative filtrations.
method Demonstrated that weight operator is a Toeplitz operator; analyzed asymptotics of weighted Bergman kernels.
result Local refinement of convergence of jumping measures towards geodesic ray pushforward measure.
Combines control variates and adaptive importance sampling for Monte Carlo integration.
problem Improving Monte Carlo integration accuracy with control variates and adaptive sampling.
method A quadrature rule combining control variates and adaptive importance sampling.
result Non-asymptotic bound on the probabilistic error of the procedure.
The rapid development of high-throughput technologies has enabled the generation of data from biological or disease processes that span multiple layers, like genomic, proteomic or metabolomic data, and further pertain to multiple sources, like disease subtypes or experimental conditions. In this work, we propose a gene…
The strength of association between a pair of data vectors is represented by a nonnegative real number, called matching weight. For dimensionality reduction, we consider a linear transformation of data vectors, and define a matching error as the weighted sum of squared distances between transformed vectors with respect…
Optimal weighted random forests improve prediction accuracy.
problem Unequal prediction performance among random forest trees.
method Proposes 1-step and 2-step optimal weighting algorithms.
result Asymptotically optimal in terms of squared loss and risk.
Develops methods to identify and estimate causal effects with instrumental variables.
problem Causal inference with confounded treatment assignment and unobserved variables.
method General nonparametric causal framework, debiased machine learning, semiparametric theory.
result Consistent and asymptotically normal estimators for average treatment effect.
Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metric tensor is only assumed to be bounded and measurable. This is known as a rough Riemannian manifold. For a large class of boundary condition…
In this paper, we construct an asymptotically hyperbolic metric with scalar curvature -6 on unit ball D3, which contains multiple horizons.
New quantum invariant is asymptotically multiplicative under cyclic covers.
problem Quantum invariants are not multiplicative under finite covers.
method Introduced a perturbative power series invariant of cusped hyperbolic 3-manifolds.
result The power series is asymptotically multiplicative under cyclic covers.
New asymptotic e-values improve inference by eliminating data-dependent scaling inefficiency.
problem Data-dependent scaling inefficiency in existing asymptotic e-values.
method Drawing on Bentkus's near-optimal concentration inequalities, introduce Bentkus-type asymptotic e-values.
result Bentkus-type asymptotic e-values consistently deliver sharper inference than existing alternatives.
We prove by Hilbert-Mumford criterion that a slope stable polarized weighted pointed nodal curve is Chow asymptotic stable. This generalizes the result of Caporaso on stability of polarized nodal curves, and of Hasset on weighted pointed stable curves polarized by the weighted dualizing sheaves. It also solved a questi…
Proves unknottedness of certain 3D shapes with multiple ends.
problem Determining the structure of complex 3D shapes.
method Used mean curvature flow to analyze shapes with multiple ends.
result Proves unknottedness of shapes with multiple asymptotically conical ends.
Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in hyperbolic space and to establish the existence of floating areas in Hilbert geometries. Results on weighted best and random approximation and the new approach to floati…
The paper analyzes methods for estimating linear functionals from observational data, proving upper bounds and showing optimal procedures.
problem Estimating linear functionals from observational data in causal inference and bandit literature.
method Two-stage procedures that first estimate treatment effect function, then use it to estimate the linear functional.
result Proves non-asymptotic upper bounds on mean-squared error for two-stage procedures and shows instance-dependent optimality.
The paper calculates asymptotic Betti numbers and homology multiplicities for graph configuration spaces.
problem Understanding the homology of ordered configuration spaces of graphs.
method Explicit formulas for asymptotic Betti numbers and homology multiplicities in characteristic zero.
result Explicit formulas for asymptotic multiplicities in homology of irreducible representations of the symmetric group.