The paper introduces new 4D twists and exotic families from a plug, with applications to knot surgeries.
problem Exploring new 4-dimensional twists and exotic families from a plug.
method Defined an infinite order plug ( P , φ ) (P,\varphi) ( P , φ ) and used it to create families Y n Y_n Y n , Z n Z_n Z n of exotic enlargements. result Introduced a new method to produce 2-bridge knot or link surgeries.
Every exotic pair in 4-dimension is obtained each other by twisting a {\it cork} or {\it plug} which are codimension 0 submanifolds embedded in the 4-manifolds. The twist was an involution on the boundary of the submanifold. We define cork (or plug) with order p ∈ N ∪ { ∞ } p\in {\Bbb N}\cup \{\infty\} p ∈ N ∪ { ∞ } and show there exists a plug…
Develops robust estimators for high-frequency data with market microstructure noise.
problem Estimating prices in the presence of market microstructure noise.
method Plug-in versions of existing estimators, using raw price and limit order book data.
result Noise-robust estimators can be applied to various high-frequency data problems.
New estimator for estimating derivatives in nonparametric regression.
problem Estimating derivatives of regression functions.
method Plug-in kernel ridge regression (KRR) estimator.
result Plug-in property for derivatives estimation, optimal rate of convergence.
C-Learner improves stability of plug-in estimators for causal inference.
problem Limited overlap between treatment and control groups leads to unstable estimates.
method Constrained learning framework that achieves stability and asymptotic properties.
result Constrained learning produces stable estimates with desirable asymptotic properties.
It is known that every exotic smooth structure on a simply connected closed 4-manifold is determined by a codimention zero compact contractible Stein submanifold and an involution on its boundary. Such a pair is called a cork. In this paper, we construct infinitely many knotted imbeddings of corks in 4-manifolds such t…
Semiparametric method removes bias in functional bilevel gradient estimation.
problem First-order bias in plug-in hypergradient when lower-level problem is nonparametric.
method Semiparametric debiasing theory based on efficient influence function leads to cross-fitted orthogonal hypergradient estimator.
result Asymptotic normality and uniform control over outer parameter established for the estimator.
SLIM efficiently solves overidentified models in a scalable manner.
problem Overidentified models with many moment conditions.
method Stochastic approximation framework using mini-batches and unbiased updates.
result SLIM solves overidentified models in under 1.4 hours, compared to 18 hours for full-sample GMM.
We discuss corks, and introduce new objects which we call plugs. Though plugs are fundamentally different objects, they also detect exotic smooth structures in 4-manifolds like corks. We discuss relation between corks, plugs and rational blow-downs. We show how to detect corks and plugs inside of some exotic manifolds.…
Transformers approximate Bayesian posteriors but not exactly.
problem Bayesian accounts of in-context learning face challenges due to task-preserving order changes in transformers.
method Showed that excess prequential code length is exactly cumulative predictive KL, decomposing expected regret into order-averaged predictor and order-averaging gain.
result Transformers approximate Bayesian posteriors but not exactly, priced by log loss.
The paper proves statistical consistency and fairness guarantees for a plug-in algorithm.
problem Establishing statistical guarantees for fairness-aware binary classification.
method Proves statistical consistency and derives finite sample guarantees for the plug-in algorithm.
result The plug-in algorithm is statistically consistent and guarantees fairness and differential privacy.
Constructed genus zero PALF structures on Akbulut-Yasui plugs.
problem Creating PALF structures on specific 3-manifolds.
method Positive factorization in mapping class groups.
result Described monodromies of PALFs on Akbulut-Yasui plugs.
Learn to automatically plug domain-specific modules into a common network.
problem Learning inflexibility and computational intensiveness in multi-domain learning.
method Neural Architecture Search (NAS) for data-driven adapter plugging and structure design.
result NAS-driven MDL model achieves comparable performance to existing approaches.
Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic quantities as test statistics, that is, as quantities obtained from empirical data, p…
Optimal sample complexity analysis for plug-in approach in average-reward MDPs.
problem Learning optimal policies in average-reward MDPs with a generative model.
method Plug-in approach that constructs a model estimate and computes an optimal policy.
result Optimal sample complexities for the plug-in approach without prior knowledge of problem parameters.
New algorithm for optimizing statistical utilities in bandits.
problem Optimizing statistical functionals of long-run reward distributions.
method Influence-function calculus for stochastic gradient estimation, entropic mirror-ascent algorithm.
result Regret bounds that separate optimization and estimation errors.
Estimates change point in high dimensional time series models.
problem Change point estimation in high dimensional time series.
method Plug-in least squares estimator with sufficient conditions for adaptivity.
result Optimal rate of convergence O p ( ξ − 2 ) O_p(ξ^{-2}) O p ( ξ − 2 ) in integer scale. Infinite order loose corks created.
problem Creating loose corks of infinite order.
method Constructing an infinite order loose cork.
result Demonstrated construction of an infinite order loose cork.
Simplified plug-in loss approximates EDL for reliable uncertainty estimation.
problem Efficient and reliable uncertainty estimation in real-world sensor-based learning systems.
method Approximate Dirichlet expected objectives with plug-in losses evaluated at the Dirichlet mean.
result Plug-in losses provide comparable predictive accuracy and selective prediction performance to classical EDL, while being simpler to implement.
Centered plug-in estimators reduce bias in Wasserstein distance estimation.
problem Conservative bias in plug-in estimators of Wasserstein distances.
method Centering procedure based on linear combinations to reduce bias.
result Centered plug-in estimators provide informative upper and lower bounds on Wasserstein distances.
Study minimax off-policy evaluation in multi-armed bandits with known and unknown behavior policies.
problem Evaluate policies in multi-armed bandits with unknown behavior policies.
method Develop minimax rate-optimal procedures for known and unknown behavior policies, including the Switch estimator and Chebyshev polynomial-based estimator.
result Plug-in estimator achieves optimal competitive ratio up to a logarithmic factor when behavior policy is unknown.
Concrete description of infinite order cork automorphism.
problem Describing the infinite order loose-cork automorphism.
method Concatenating the defining ribbon disk by an infinite order isotopy.
result Concrete description of the infinite order cork automorphism.
Every infinite order mapping class has an infinite order action on the homology of some finite cover.
problem Proving every infinite order mapping class has an infinite order action on the homology of some finite cover.
method Theory of homological shadows and Fourier analysis.
result There exists a finite solvable cover and a lift of an infinite order mapping class with an infinite order action on the homology.
Develops a new method for statistical optimal allocation problems.
problem Statistical optimal allocation problems with constraints.
method Functional differentiability approach and Hadamard differentiability of value functions.
result Validates margin assumption for fast convergence rate of plug-in methods.
The Conway knot can't be smoothly tied to any other knot an infinite number of times.
problem Understanding the concordance order of knots.
method Rasmussen invariant, satellite operations, null-homologous twists.
result The Conway knot has infinite concordance order.
Develops a robust method for image reconstruction from limited data.
problem Inference of unknown images from few measurements, often ill-posed.
method Introduces DPnP, a diffusion plug-and-play method combining likelihood and score-based samplers.
result Establishes performance guarantees for DPnP, demonstrating robustness and efficiency.
The paper analyzes rates of convergence for optimal transport map estimators using barycentric projections.
problem Estimating optimal transport maps from data sampled according to two distributions.
method Comprehensive analysis of rates of convergence for plug-in estimators defined via barycentric projections.
result New stability estimate for barycentric projections under minimal smoothness assumptions.
Two new covariance estimators for ROOT-SGD improve statistical inference.
problem Uncertainty measurement for ROOT-SGD's normal distribution estimator.
method Developed two covariance estimators: plug-in and Hessian-free.
result Hessian-free estimator is asymptotically consistent and Hessian-free.
New infinite order corks found that cannot twist exotic 4-manifolds.
problem Finding new infinite order corks to twist exotic 4-manifolds.
method Proved necessary conditions for generating 4-manifolds by infinite order corks and found non-contractible examples.
result First example of infinite order corks not generating exotic 4-manifolds.
We construct a new aperiodic symplectic plug and hence new smooth counterexamples to the Hamiltonian Seifert conjecture in R^{2n} for n>2. In other words, we develop an alternative procedure, to those of V. L. Ginzburg and M. Herman, for constructing smooth Hamiltonian flows, on the standard symplectic R^{2n} for n>2, …
Optimally estimates a functional using nuisance function tuning and sample splitting.
problem Estimating optimal rates for a doubly robust functional.
method Combines nuisance function tuning and sample splitting strategies.
result Shows optimal rates of convergence for various estimators.
Contact forms with large systolic ratios found in arbitrary dimensions.
problem Finding contact forms with large systolic ratios in arbitrary dimensions.
method Generalized plug construction and Liouville open books.
result Every co-orientable contact structure admits a contact form with arbitrarily large systolic ratio.
Plug-and-play L-GM-AMP improves CS recovery for any i.i.d. source prior.
problem Efficiently recovering signals from compressed measurements with unknown priors.
method Deep learning with Gaussian-mixture model to approximate source prior, combined with learned denoising.
result L-GM-AMP achieves state-of-the-art performance without prior knowledge of source distribution.
New method improves online covariance estimation for SGD.
problem Improving online covariance estimation for SGD.
method Proposes a de-biased covariance estimator that eliminates second-order derivatives.
result Achieves a convergence rate of n ( α − 1 ) / 2 log n n^{(α-1)/2} \sqrt{\log n} n ( α − 1 ) /2 log n , outperforming existing methods. Infinite Klein bottles with 4-fold meridians found.
problem Finding indecomposable Klein bottles with specific meridian orders.
method Exhibited an infinite family of Klein bottles in 4-sphere.
result Infinite family of indecomposable Klein bottles with order-4 meridians.
New handle diagrams show infinite order corks in 4-manifolds.
problem Existence of infinite order corks in 4-manifolds.
method Translated earlier proof into handle diagrams and conditions on torus twists.
result First handle diagrams of infinite order corks.
Infinite order elements found in symplectic mapping class groups.
problem Understanding infinite order elements in symplectic mapping class groups.
method Analyzing symplectically embedded ( − 1 ) (-1) ( − 1 ) -tori. result Infinite order elements exist and are shown to be non-trivial.
New invariant detects infinite order cabled knots.
problem Detecting infinite order knots in the concordance group.
method Involutive knot Floer homology and cabling techniques.
result Infinite family of knots with infinite order in concordance group.
New PnP algorithm converges with relaxed proximal gradient descent.
problem Convergence issues in PnP methods with deep denoisers.
method Relaxed proximal gradient descent for PnP with weakly convex regularization.
result Proposed PnP- α \alpha α PGD converges for a wider range of regularization parameters. Develops non-standard analysis for coherent risk estimation.
problem Estimating coherent risk measures in financial contexts.
method Non-standard analysis, hyperfinite representations, discrete Kusuoka formulae, plug-in asymptotics.
result Uniform almost sure consistency and asymptotic normality of spectral plug-in estimators.
Infinite order corks are described with detailed handle decompositions.
problem Understanding the structure of infinite order corks in 4-manifolds.
method Detailed handle decompositions and embeddings of corks in E ( n ) E(n) E ( n ) . result The twisted doubles of infinite order corks are Gluck twists and log transforms of S 4 S^4 S 4 . Plug-in method improves performative prediction accuracy.
problem Learning under performative feedback with slow convergence rates.
method Plug-in performative optimization using models.
result Plug-in method can be superior to model-agnostic strategies.
We prove new fast learning rates for the one-vs-all multiclass plug-in classifiers trained either from exponentially strongly mixing data or from data generated by a converging drifting distribution. These are two typical scenarios where training data are not iid. The learning rates are obtained under a multiclass vers…
A new method debiases multiple target parameters without IFs.
problem Debiasing multiple target parameters in nonparametric models.
method Kernel Debiased Plug-in Estimation (KDPE) using TMLE and reproducing kernel Hilbert spaces.
result KDPE simultaneously debiases all pathwise differentiable target parameters.
We use the Heegaard Floer obstructions defined by Grigsby, Ruberman, and Strle to show that forty-six of the sixty-seven knots through eleven crossings whose concordance orders were previously unknown have infinite concordance order.
The paper addresses supervised learning with censored data, proposing a method to estimate risk.
problem Learning from censored data in regression problems.
method Proposes a plug-in estimate of the true risk based on a Kaplan-Meier estimator of the censorship distribution.
result The learning rate of minimizers of the proposed risk functional is of order \(O_{\mathbb{P}}(\sqrt{\log(n)/n})\).
Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex X of W. We consider many special cases, including W word hyperbolic, and X with isolated flats. We establish tha…
This paper provides a method for noise-calibrated inference from DP synthetic data.
problem Inference from DP synthetic data is often miscalibrated and lacks principled uncertainty quantification.
method Release DP sufficient statistics, perform noise-calibrated likelihood-based inference, and optional synthetic data generation.
result Asymptotic normality and valid confidence intervals for the plug-in DP MLE.