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 show that many hyperbolic monopoles can be distinguished from each other via their asymptotic values in contrast to the case of Euclidean monopoles.
The paper analyzes network models with binary values and sub-Gamma noise, deriving asymptotic properties.
problem Analyzing network models with binary values and sub-Gamma noise.
method Derives asymptotic properties of network models with binary values and sub-Gamma noise.
result Established asymptotic consistency and normality of parameter estimators in network models.
Study on spectral asymptotics in elasticity on smooth manifolds.
problem Analyzing spectral asymptotics in linear elasticity on smooth manifolds.
method Established two-term spectral asymptotics for boundary value problems in linear elasticity.
result Corrected erroneous results in previous studies.
Study tail behavior of sum of heavy-tailed risks with copulas.
problem Analyzing the tail behavior of sums of heavy-tailed risks with dependence modeled by copulas.
method Modeling dependence with copulas and analyzing tail asymptotics of sums of heavy-tailed risks.
result Obtained asymptotic expansions for Value-at-Risk of aggregate risk.
Paper studies robust MDPs, improving sample complexity and asymptotic performance.
problem Optimal robust policy and value function in robust MDPs with generative models.
method Improves prior results on non-asymptotic and asymptotic performances of robust MDPs, considering various uncertainty sets.
result Improved sample complexity and asymptotic normality of optimal robust value function.
Method uses DNNs to approximate functions with specific asymptotic behavior.
problem Approximating functions with given asymptotic behavior.
method Specifically constructed terms combined with unconstrained DNN.
result Enforcing asymptotic behavior leads to better approximation and faster convergence.
Gradient flows of neural networks converge to optimal values or diverge, with thresholds and asymptotic behaviors.
problem Understanding the convergence and divergence of gradient flows in neural networks.
method Analysis of gradient flows on loss landscapes of neural networks using o-minimal structures.
result Gradient flows either converge to optimal values or diverge to infinity, with thresholds and asymptotic behaviors.
The study proves properties of intersections of horospheres in harmonic spaces.
problem Properties of intersections of horospheres in harmonic spaces.
method Constructing volume preserving mappings using Busemann functions.
result Upper bound of the volume of intersection of horospheres is independent of Busemann function differences.
We investigate statistical uncertainty quantification for reinforcement learning (RL) and its implications in exploration policy. Despite ever-growing literature on RL applications, fundamental questions about inference and error quantification, such as large-sample behaviors, appear to remain quite open. In this paper…
We consider an agent who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost. The utility function considered is power utility. We provide a heuristic and a rigorous derivation of the asymptotic ex…
The paper solves heat kernel asymptotics on non-degenerate CR manifolds.
problem Existence of small-time asymptotics for the heat kernel of the Kohn Laplacian on CR manifolds.
method Analytic methods and spectral theory for CR manifolds.
result Established small-time asymptotics for the heat kernel and analytic torsion on non-degenerate CR manifolds.
We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small non-linear price impact. In our model cross-impacts between assets are allowed. In the limit for small price impact, we determine the asymptotic expansion of the value function around …
In [16], a new family of vector-valued risk measures called multivariate expectiles is introduced. In this paper, we focus on the asymptotic behavior of these measures in a multivariate regular variations context. For models with equivalent tails, we propose an estimator of these multivariate asymptotic expectiles, in …
We discuss a variant of Thompson sampling for nonparametric reinforcement learning in a countable classes of general stochastic environments. These environments can be non-Markov, non-ergodic, and partially observable. We show that Thompson sampling learns the environment class in the sense that (1) asymptotically its …
Paper improves risk estimation for extreme events.
problem Estimating extreme risks accurately.
method Modified Bayes risk for expectiles, asymptotic expansions, efficient estimators.
result Asymptotic normality of estimators proved.
The paper calculates the value of information in high-dimensional decision making.
problem Determining the value of acquiring new information in high-dimensional decision problems.
method Using tools from sub-Gaussian processes and generic chaining for asymptotic analysis.
result Asymptotic results on the expected value of information as dimensionality increases.
A new estimator for evaluating policies in unknown environments.
problem Evaluating policies when both logging policy and value function are unknown.
method Doubly-Robust (DR) off-policy evaluation (OPE) estimator, DRUnknown, that estimates both the logging policy and value function.
result DRUnknown achieves the smallest asymptotic variance and is optimal when both models are correctly specified.
Study on random representations of surface groups into SU(n), focusing on asymptotic expansions.
problem Understanding random representations of surface groups into special unitary groups.
method Use of a symplectic form on moduli space, establishing asymptotic expansions for trace values.
result Existence of large n asymptotic expansions for expected values of trace of elements under random representations.
We price a contingent claim liability using the utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of positive proportional transaction cost in two c…
Extreme value theory enhances statistical learning extrapolation for rare events.
problem Challenges in traditional machine learning methods for extreme data.
method Asymptotic theory and statistical tools for tail behavior.
result Effective extrapolation methods for extreme quantiles and anomalies.
Study investigates non-existence of bounded solutions on curved spaces.
problem Non-existence of bounded solutions to semi-linear elliptic equations on Cartan-Hadamard manifolds.
method Novel comparison technique using convex hypersurfaces.
result Extends previous results to curved spaces, highlighting curvature's role.
Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.
problem Capturing higher-order tail behavior and dependence effects in risk measures.
method Second-order asymptotic expansions using extreme value theory and regular variation theory.
result Second-order approximations reduce approximation errors, especially at extreme confidence levels.
In this paper we prove a universal inequality describing the asymptotic behavior of support points for planar continuous curves. As corollaries we get an analogous result for tangent points of differentiable planar curves and some (partially known) assertions on the asymptotic of the mean value points for various class…
Develops a new risk measure for Markov chains' asymptotic behavior.
problem Lack of risk measures for asymptotic regimes of Markov chains.
method Simulation-based approach using large deviations theory, density estimation, and stochastic approximation.
result Developed Asymptotic CVaR (ACVaR) for Markov chains.
Paper approximates risk measures using SGD with Langevin dynamics.
problem Approximating arbitrary law invariant risk measures.
method Stochastic Gradient Langevin Dynamics (SGD-Langevin) for general risk measures.
result Non-asymptotic convergence rates of the approximation algorithm.
Sharp inequalities for J functional on Kahler metrics.
problem Asymptotic behavior of J functional on Kahler metrics. method Sharp inequalities derived for d1 metric. result Sharp inequalities between J functional asymptotics. The paper solves a specific Dirichlet problem for constant mean curvature surfaces in a particular manifold.
problem Existence and uniqueness of constant mean curvature graphs with prescribed asymptotic values.
method Defined a new product compactification for the homogeneous manifold and proved the existence of entire H-graphs.
result Existence and uniqueness of entire H-graphs with prescribed asymptotic values.
An optimal algorithm for multi-armed bandits with constraints.
problem Optimizing decisions in constrained multi-armed bandit problems.
method An index-based deterministic algorithm using Locatelli's anytime thresholding under known optimal value assumption.
result The algorithm achieves asymptotic optimality with probability approaching 1.
Solves complex equation for specific geometric solitons.
problem Solving complex Monge-Ampère equation for specific geometric solitons.
method Aubin continuity path and continuity method.
result Initial value of the path parameter has a solution and is open to all.
We show that the limit at infinity of the vector-valued Brown-York-type quasi-local mass along any coordinate exhaustion of an asymptotically hyperbolic 3-manifold satisfying the relevant energy condition on the scalar curvature has the conjectured causal character. Our proof uses spinors and relies on a Witten-type …
Federated learning method improves covariate shift adaptation for missing target values.
problem Missing target values in federated learning.
method Federated covariate shift adaptation algorithm for missing target output values.
result Asymptotically unbiased and efficient algorithm for federated learning.
Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a recent proposal by Wasserman and Roeder (2008) which splits the data into two pa…
We present an optimal investment theorem for a currency exchange model with random and possibly discontinuous proportional transaction costs. The investor's preferences are represented by a multivariate utility function, allowing for simultaneous consumption of any prescribed selection of the currencies at a given term…
We present a classification of SU(2) instantons on T2×R2 according to their asymptotic behaviour. We then study the existence of such instantons for different values of the asymptotic parameters, describing explicitly the moduli space for unit charge.
This work analyzes self-attention matrices using random matrix theory.
problem Understanding the theoretical behavior of self-attention layers in neural networks.
method Asymptotic spectral analysis of the attention matrix, Gaussian equivalence, and linearization.
result The singular value distribution of the attention matrix is asymptotically characterized by a linear model.
We study asymptotically harmonic manifolds of negative curvature, without any cocompactness or homogeneity assumption. We show that asymptotic harmonicity provides a lot of information on the asymptotic geometry of these spaces: in particular, we determine the volume entropy, the spectrum and the relative densities of …
The paper studies heat kernel asymptotics for Kohn Laplacians on CR manifolds.
problem Analyzing heat kernel asymptotics for Kohn Laplacians on CR manifolds.
method Establishing asymptotics of heat kernels and equivariant heat kernels on CR manifolds.
result Heat kernel asymptotics for Kohn Laplacians on CR manifolds are derived.
The paper defines a new condition for Fano manifolds and shows its implications on their asymptotic behavior.
problem Understanding the asymptotic behavior of Fano manifolds.
method Introducing the asymptotically Mittag-Leffler condition and proving its implications on the J-function. result The J-function of a Fano manifold exhibits exponential growth if it is asymptotically Mittag-Leffler. Study a market with uncertain informed traders, finding price impact depends on both asset value and informed trader count distribution.
problem Uncertain participation of informed traders in a market with limit orders.
method Characterized equilibrium by a fixed point integral equation, analyzed large order asymptotics, solved numerically.
result Equilibrium price impact depends on both asset value and distribution of informed traders, not just expected number of informed traders.
The paper examines extreme value statistics of high-dimensional sample covariances, with applications in finance and image analysis.
problem Statistical validation of normal conditions in high-dimensional time series data.
method Generalizes the maximal deviation of sample autocovariances to high dimensions and applies Gumbel-type extreme value asymptotics.
result Gumbel-type extreme value asymptotics holds true for high-dimensional sample covariances.
We study the asymptotic behaviour of 1-parameter subgroups with respect to Hofer's metric when the underlying symplectic manifold is an open surface of infinite area. We prove that, depending on the topology of the level sets of the Hamiltonian H, the distance either is bounded or behaves asymptotically linear. Moreove…
We study the portfolio selection problem of a long-run investor who is maximising the asymptotic growth rate of her expected utility. We show that, somewhat surprisingly, it is essentially not affected by introduction of a floor constraint which requires the wealth process to dominate a given benchmark at all times. We…
We find the entropy's infinite-size behavior in complex manifold sections.
problem Determining entropy behavior in complex manifold sections.
method Analyzing entanglement entropy in tensor powers of hermitian line bundles.
result Asymptotic formula for expected entanglement entropy.
Study Vassiliev invariants and periodic orbits of Axiom A flows.
problem Calculating Vassiliev invariants and writhe for periodic orbits of Axiom A flows.
method Asymptotic analysis of Vassiliev invariants and writhe.
result Obtained asymptotics for Vassiliev invariants and writhe of periodic orbits.
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…
Improved singular value approximation for convolutional layers.
problem Improving accuracy of singular value approximation for linear convolutional layers.
method Developed a new spectral density matrix method for singular value approximation with improved accuracy and reduced computational complexity.
result Obtained moderate improvement in singular value distribution compared to circular approximation.
The paper uses EVT to improve tail risk measures under ambiguity sets.
problem Misspecification of tail risk measures leads to inflated risk estimates.
method Applies Extreme Value Theory to derive worst-case tail risk under ambiguity sets.
result Proposes a tail-calibrated ambiguity design that preserves nominal tail asymptotic scaling.