New method for private learning with public features improves convergence rates.
problem Private estimation with public features under local differential privacy.
method Semi-feature LDP, HistOfTree estimator.
result HistOfTree reaches mini-max optimal convergence rate.
New method uses public data to achieve optimal nonparametric classification with privacy constraints.
problem Optimal nonparametric classification under local differential privacy constraints.
method Locally differentially private classification tree with data-driven pruning.
result Achieves mini-max optimal convergence rate with public data.
We propose a new indicator for technical analysis. The indicator emphasizes maximums and minimums in price series with inherent smoothing and has a potential to be useful in both mechanical trading rules and chart pattern analysis.
This paper analyzes divide-and-conquer estimators for functional linear regression without assuming target function in the RKHS.
problem Functional linear regression without target function in RKHS.
method Integral operator approach to establish upper bounds and prove asymptotic optimality.
result Sharp finite sample upper bounds and asymptotic optimality of divide-and-conquer estimators.
The paper explores heat flow and constants on graphs, proving properties and proposing new concepts.
problem Analyzing heat flow and constants on graphs.
method Introducing concepts, recalling graph theory, and proposing new discrete Morse flows.
result Weak discrete Morse flows for heat flow on finite graphs under suitable assumptions.
Standard adversarial training involves two agents, namely a generator and a discriminator, playing a mini-max game. However, even if the players converge to an equilibrium, the generator may only recover a part of the target data distribution, in a situation commonly referred to as mode collapse. In this work, we prese…
Novel unsupervised MIG detectors improve signal detection in cluttered environments.
problem Signal detection in nonhomogeneous clutter environments.
method Developed novel discriminative MIG detectors using HPD matrices and geometric measures.
result Improved signal detection performance compared to conventional methods.
This work analyzes how overparameterization aids GANs in reaching global saddle points.
problem Understanding the role of overparameterization in GANs for convergence to global saddle points.
method Theoretical and empirical analysis of overparameterized GANs with various architectures and datasets.
result GDA converges to a global saddle point in overparameterized GANs with certain assumptions.
SGD improves DR by solving two-stage sampling problems.
problem Improving the learning properties of SGD for distribution regression.
method Applying SGD to two-stage sampling problems in distribution regression.
result Theoretical guarantees for SGD's performance in DR, with optimal bounds.
We consider the off-policy estimation problem of estimating the expected reward of a target policy using samples collected by a different behavior policy. Importance sampling (IS) has been a key technique to derive (nearly) unbiased estimators, but is known to suffer from an excessively high variance in long-horizon pr…
We present a new algorithm to train a robust neural network against adversarial attacks. Our algorithm is motivated by the following two ideas. First, although recent work has demonstrated that fusing randomness can improve the robustness of neural networks (Liu 2017), we noticed that adding noise blindly to all the la…
New algorithm improves bandit with graph feedback by decomposing regret.
problem Improving performance in bandit problems with graph feedback.
method Partition-based algorithm framework using regret decomposition.
result Improved and optimal regret bounds on various graph families.
GAN approach optimizes investment under market uncertainty.
problem Maximizing worst-case outcomes in uncertain markets.
method Generative adversarial network (GAN) to solve robust utility optimization.
result Outperforms other strategies in realistic market settings.
Active learning aims to develop label-efficient algorithms by sampling the most representative queries to be labeled by an oracle. We describe a pool-based semi-supervised active learning algorithm that implicitly learns this sampling mechanism in an adversarial manner. Unlike conventional active learning algorithms, o…
Outlier detection is an important topic in machine learning and has been used in a wide range of applications. In this paper, we approach outlier detection as a binary-classification issue by sampling potential outliers from a uniform reference distribution. However, due to the sparsity of data in high-dimensional spac…
The paper studies adversarial training for linear regression models.
problem Understanding the tradeoffs between robust and standard accuracy in adversarial training.
method Characterizes the fundamental tradeoff and specific adversarial training approach for linear regression with Gaussian features.
result Precise characterization of the standard and robust accuracy tradeoff in high-dimensional settings.
In binary classification problems, mainly two approaches have been proposed; one is loss function approach and the other is uncertainty set approach. The loss function approach is applied to major learning algorithms such as support vector machine (SVM) and boosting methods. The loss function represents the penalty of …
Proves weak convergence equals mean convergence in GGC.
problem Proving convergence in GGC distributions.
method Using generalized gamma convolution (GGC) and expected utility maximization.
result Weak convergence implies mean convergence in GGC.
This is an intuitive survey of extrinsic and intrinsic notions of convergence of manifolds complete with pictures of key examples and a discussion of the properties associated with each notion. We begin with a description of three extrinsic notions which have been applied to study sequences of submanifolds in Euclidean…
The abstract discusses convergence properties of Lipschitz functions and sets defined by equations.
problem Convergence of Lipschitz functions and sets defined by equations.
method Painlevé-Kuratowski convergence applied to Lipschitz functions and sets defined by equations.
result Generalizations and reverses of classical theorems on convergence of functions and sets.
Study shows intrinsic timed Hausdorff convergence leads to Gromov-Hausdorff and big bang convergence.
problem Distance between Lorentzian manifolds.
method Intrinsic timed Hausdorff convergence.
result Intrinsic timed Hausdorff convergence implies Gromov-Hausdorff and big bang convergence.
Studied SGD convergence under weak conditions.
problem Convergence of SGD in nonconvex optimization.
method Analyzed biased nonconvex SGD under mild conditions.
result Provided convergence rates and complexities.
Study on convergence rate of Q Q Q -curvature flow in 6 dimensions.
problem Analyzing the convergence rate of Q Q Q -curvature flow in 6 dimensions. method Provided an example of a slowly converging Q 6 Q_6 Q 6 -curvature flow in dimension 6. result The Q Q Q -curvature flow in 6 dimensions does not always converge exponentially, unlike in 2 dimensions. The objective of this paper is to introduce the notion of generalized almost statistical (briefly, GAS) convergence of bounded real sequences, which generalizes the notion of almost convergence as well as statistical convergence of bounded real sequences. As a special kind of Banach limit functional, we also introduce …
Establishes geometric convergence of iterative optimization algorithms.
problem Analyzes convergence of iterative optimization algorithms under general assumptions.
method General framework for iterative optimization algorithms, proving asymptotic geometric convergence and providing convergence rates.
result Asymptotic geometric convergence of iterative optimization algorithms with exact rate.
Uniform counting formulas for orthogeodesics in Kleinian groups converge.
problem Counting orthogeodesics in Kleinian groups converging to a limit.
method Spectral gap of the limit manifold and geodesic flow mixing property.
result Asymptotically uniform counting formulas for orthogeodesics.
The paper explores null distance convergence for warped product spacetimes.
problem Defining convergence for sequences of spacetimes as metric spaces.
method Using the null distance to define convergence of spacetimes.
result Optimal convergence theorem for warped product spacetimes.
New quasi-Newton method guarantees global superlinear convergence.
problem Global convergence and superlinear convergence of quasi-Newton methods.
method Hybrid proximal extragradient method with online learning for Hessian approximation.
result First globally convergent quasi-Newton method with explicit superlinear convergence rate.
We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.
problem Achieving decoupled convergence in nonlinear two-time-scale stochastic approximation.
method Nested local linearity assumption, suitable step size selection, convergence analysis of matrix cross term, fourth-order moment convergence rates.
result Finite-time decoupled convergence rates can be achieved in nonlinear two-time-scale stochastic approximation with proper step size selection.
The article introduces a new convergence concept for Lorentzian spaces and applies it to generalized cones.
problem Stability of curvature bounds in generalized Lorentzian cones.
method Introduces ℓ \ell ℓ -convergence for Lorentzian pre-length spaces, applies it to generalized cones, and proves stability of curvature bounds. result Sharp timelike curvature and curvature-dimension bounds for generalized cones are established.
AdaBoost's classifier and margins converge to a known value.
problem Convergence properties of AdaBoost algorithm.
method Formal proofs of convergence properties of AdaBoost's classifier and margins.
result AdaBoost's classifier and margins converge to a known value.
Study shows gap between uniform convergence and test error in random feature models.
problem Understanding the gap between uniform convergence and test error in random feature models.
method Analytical expressions for uniform convergence over norm balls, interpolators, and minimum norm interpolator risk derived and proved.
result Uniform convergence over interpolators still gives a non-trivial bound of test error even when classical uniform convergence is vacuous.
The Sinkhorn-Knopp derivatives converge with linear rate.
problem Optimal transport problem with entropic regularization.
method Iterative proportional fitting procedure.
result Derivatives converge with linear rate.
The paper examines convergence of distances in Lipschitz structures on manifolds.
problem Convergence of distances in Lipschitz vector fields and norms on manifolds.
method Analysis of convergence of distances associated to converging structures of Lipschitz vector fields and norms.
result Under mild controllability assumption, distances converge locally uniformly to the limit Carnot-Carathéodory distance.
New approach to geometric quantization for symplectic manifolds.
problem Quantization of symplectic manifolds with non-singular Lagrangian fibrations.
method Using spectral convergence of metric measure spaces, the authors develop a new geometric quantization approach.
result Spectral and quantum Hilbert space convergence results for Kähler and almost Kähler quantizations.
We introduce a natural definition of L p L^p L p -convergence of maps, p ≥ 1 p \ge 1 p ≥ 1 , in the case where the domain is a convergent sequence of measured metric space with respect to the measured Gromov-Hausdorff topology and the target is a Gromov-Hausdorff convergent sequence. With the L p L^p L p -convergence, we establish a theory of …
We prove a criterion of convergence in the augmented Teichmueller space that can be phrased in terms of convergence of the hyperbolic metrics or of quasiconformal convergence away from the nodes.
Sharp convergence theorem for sphere submanifolds proved.
problem Sphere submanifolds in spheres.
method Proved a sharp convergence theorem.
result New differentiable sphere theorem for submanifolds in spheres.
DCDC calculates convergence rates for Markov chains using neural networks.
problem Computing precise convergence rates for Markov chains is hard.
method Developed a neural network-based algorithm (DCDC) to bound convergence rates in Wasserstein distance.
result Demonstrated effective convergence bounds for real-world Markov chains.
Proves curvature tensor convergence for smoothable spaces.
problem Curvature tensor behavior in smoothable Alexandrov spaces.
method Weak convergence of curvature tensors in noncollapsing sequences.
result Proves convergence of curvature tensors in smoothable Alexandrov spaces.
Develops clustering methods based on likelihood and convergence proved.
problem Hard clustering based on likelihood.
method k-MLE, k-Bregman, k-VARs approaches.
result Convergence proved for clustering methods.
Study utility maximization with costs, proving convergence and strategies.
problem Utility maximization with proportional transaction costs.
method Extended weak convergence theory and Meyer--Zheng topology.
result Prove convergence of utility maximization problems and optimal trading strategies.
New technique explains convergence in ML models with data modifications.
problem Understanding convergence of ML models under data changes.
method Analogue of Fatou's lemma and gamma-convergence.
result Relevance and applications in general ML tasks and domain adaptation.
Characterizes problems solvable via linear convergence algorithms.
problem Optimization problems solvable with linear convergence.
method Riemannian gradient descent.
result Characterized problems solvable via linear convergence.
Equivalence shown between two mathematical concepts for hyperbolic surfaces.
problem None explicitly stated, but related to mathematical equivalence of concepts.
method Benjamini-Schramm convergence and zeta functions equivalence demonstration.
result Equivalence of Benjamini-Schramm convergence and zeta functions for compact hyperbolic surfaces.
The paper provides convergence guarantees for multicalibration gradient boosting.
problem Understanding the convergence properties of multicalibration gradient boosting.
method Computational guarantees for multicalibration gradient boosting algorithms, including adaptive variants.
result The magnitude of successive prediction updates decays at O ( 1 / T ) O(1/\sqrt{T}) O ( 1/ T ) , leading to convergence in empirical multicalibration error. Study Gromov-Hausdorff convergence of metric pairs and tuples.
problem Understanding convergence in metric spaces.
method Prove equivalence of definitions, embedding, completeness, and compactness theorems.
result Relative version of Fukaya's theorem and finiteness theorem for stratified spaces.
Study on convergence rate of Bergman metrics on Kähler manifolds.
problem Analyzing convergence rate of Bergman metrics on Kähler manifolds.
method Using Tian's peak section method to show uniform C 1 , α C^{1,α} C 1 , α convergence. result Uniform C 1 , α C^{1,α} C 1 , α convergence of Bergman metrics is demonstrated.