Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.
problem Adversarial online nonparametric regression with general convex losses.
method Parameter-free learning algorithm leveraging chaining trees to compete against H{ö}lder functions, dynamically tracking and adapting to local smoothness variations.
result First computationally efficient algorithm with locally adaptive optimal rates for online regression in an adversarial setting.
Study approximates unknown function levels with queries.
problem Approximating unknown function levels through sequential queries.
method Introduce Bisect and Approximate algorithms to reduce to local function approximation.
result Rate-optimal sample complexity guarantees for H{ö}lder functions.
The purpose of these notes is to explain parts of Gromov's survey of Carnot-Carathedory spaces, in the light of subsequent results of M. Rumin. Among the rich material provided by Gromov, most of which pertains to analysis on metric spaces, we choose to concentrate on the H{ö}lder equivalence problem for Carnot manifol…
A variant of Gromov's H{ö}lder-equivalence problem, motivated by a pinching problem in Riemannian geometry, is discussed. A partial result is given. The main tool is a general coarea inequality satisfied by packing energies of maps.
We study finite energy classes of quasiplurisubharmonic (qpsh) functions in the setting of toric compact K{ä}hler manifolds. We characterize toric qpsh functions and give necessary and sufficient conditions for them to have finite (weighted) energy, both in terms of the associated convex function in R n , and through t…
Let S be a closed oriented surface of genus at least 2, and denote by T(S) its Teichm{ü}ller space. For any isotopy class of closed curves γ, we compute the first three derivatives of the length function ℓ_γ:T(S)→R_+ in the shearing coordinates associated to a maxim…
In the context of stochastic continuum-armed bandits, we present an algorithm that adapts to the unknown smoothness of the objective function. We exhibit and compute a polynomial cost of adaptation to the H{ö}lder regularity for regret minimization. To do this, we first reconsider the recent lower bound of Locatelli an…
We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a non-constructive fashion by Rakhlin and Sridharan (2014). Our regret bound is expre…
In this paper we provide an alternative framework to tackle the first-best Principal-Agent problem under CARA utilities. This framework leads to both a proof of existence and uniqueness of the solution to the Risk-Sharing problem under very general assumptions on the underlying contract space. Our analysis relies on an…
Validates economic scenarios using statistical tests on stochastic processes.
problem Ensuring the accuracy of real-world economic scenario models.
method Applies Chevyrev and Oberhauser's (2022) signature and maximum mean distance test to various stochastic processes.
result Demonstrates the test's effectiveness across different path properties relevant to financial modeling.
We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature conditions we consider include 2-non-negative and weakly $\t…
New algorithms for interactive learning match minimax bounds efficiently.
problem Interactive learning in the realizable setting with computational efficiency.
method General framework, computationally efficient algorithms, Monte Carlo hit-and-run sampling.
result Sample complexities quantifiable in terms of combinatorial quantities, computationally efficient.
Study shows zero-shot super-resolution in neural operators is impossible in many cases.
problem Understanding the theoretical limits of zero-shot super-resolution in neural operators.
method Systematic theoretical study including information-theoretic and generalization bounds analysis.
result Zero-shot super-resolution is information-theoretically impossible in many settings.
Introduces a space of almost complex structures for complex Lie group bundles.
problem Integrability of almost complex structures on complex Lie group bundles.
method Introduces a space of bundle almost complex structures and studies their properties.
result Locally pseudo-holomorphic sections exist if and only if the obstruction form is zero.
Efficient algorithms for contextual bandits with smooth regret in continuous action spaces.
problem Efficient learning in large or continuous action spaces.
method Smooth regret notion and efficient algorithms for general function approximation.
result Statistically and computationally efficient algorithms for contextual bandits with smooth regret.
General lower bounds on neural network approximation in L^p norm.
problem Fundamental limits of neural network expressivity.
method General lower bound proof on approximation in L^p norm, applied to feed-forward neural networks.
result Neural networks can't approximate certain functions as well as previously thought.
This paper selects features in deep neural networks with theoretical guarantees.
problem Feature selection in deep neural networks with unknown nonlinear functions.
method Reformulate neural networks as index models, estimate feature sets using Stein's formula, and apply screening-and-selection mechanism.
result Consistent feature selection with theoretical guarantees, even in high-dimensional settings.
Classifies manifolds with dense conjugacy classes in their mapping class groups.
problem Classifying manifolds based on conjugacy classes in their mapping class groups.
method Analyzing connected orientable 2-manifolds and their mapping class groups.
result Mapping class groups of certain manifolds have dense conjugacy classes.
This paper tackles worst-class error rate in classification tasks.
problem Minimizing worst-class error rate in classification tasks, especially in medical image classification.
method Designing a boosting approach to bound the worst-class error rate using Deep Neural Networks (DNNs).
result The proposed boosting approach lowers worst-class test error rates while avoiding overfitting.
New method learns multi-class from single-class data with confidences.
problem Learning multi-class from single-class data without additional data.
method Empirical risk minimization framework for multi-class classification.
result Method achieves Bayes-consistency with noisy confidences.
Paper constructs a cohomology class related to McDuff's secondary class, proving it transgresses to the Euler class of foliated sphere bundles.
problem Finding higher-dimensional analogs of the Calabi invariant and its transgression to the Euler class.
method Constructing a cohomology class of volume-preserving diffeomorphisms and proving transgression to the Euler class of foliated sphere bundles.
result The cohomology class transgresses to the Euler class of foliated sphere bundles.
One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinali…
The paper proves inequalities for orbifold second Chern classes in Fujiki's class.
problem Inequalities for orbifold second Chern classes of compact normal analytic varieties.
method Generic nefness theorems for tangent and cotangent sheaves, and an orbifold Bogomolov--Gieseker inequality for mixed polarizations.
result Semipositivity of the orbifold second Chern class for varieties with nef anti-canonical divisor.
Study on characteristic classes for foliation deformations.
problem Characterizing and understanding characteristic classes for foliation deformations.
method Introduced a differential graded algebra (DGA) to recover Bott vanishing and formulae, and discussed properties of its cohomology.
result Discovered new classes that cannot be described by existing classes like Godbillon--Vey and Fuks--Lodder--Kotschick.
The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping class group of a punctured sphere. The more general family of superelliptic mapping…
CILF learns adaptive embeddings for class-incremental learning with novel class detection and model update.
problem Handling unknown classes and model update in streaming data with new classes.
method CILF uses decoupled prototype based loss for intra-class and inter-class structure improvement, and a learnable curriculum clustering operator for adaptive embedding.
result CILF effectively detects multiple novel classes and mitigates embedding confusion, while updating the model without catastrophic forgetting.
In this paper we give explicit formulas of differential characteristic classes of principal G-bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes, differential Pontryagin classes and differential Euler class. Furthermore, we show that…
A new method identifies class-specific covariates in multi-class prediction tasks.
problem Identifying covariates specifically associated with one or more outcome classes in multi-class prediction tasks.
method Introducing multi forests (MuFs) with multi-way and binary splits to measure class-associated discriminatory ability.
result The multi-class VIM specifically ranks class-associated covariates highly, unlike conventional VIMs.
Study of conjugacy classes in infinite-type surfaces' mapping class groups.
problem Characterizing conjugacy classes in infinite-type surfaces' mapping class groups.
method Model-theoretic methods developed by Kechris, Rosendal, and Truss.
result Detailed classification of conjugacy classes in mapping class groups of infinite-type surfaces.
The paper classifies dense conjugacy classes in mapping class groups of locally finite graphs.
problem Identifying which mapping class groups have dense conjugacy classes.
method Developed flux homomorphisms and combinatorial criteria for stability.
result A complete classification for self-similar locally finite graphs and a criterion for stability.
We give a complete description of conjugacy classes of finite subgroups of the mapping class group of the sphere with r marked points. As a corollary we obtain a description of conjugacy classes of maximal finite subgroups of the hyperelliptic mapping class group. In particular, we prove that for a fixed genus g there …
We present a simple generative framework for learning to predict previously unseen classes, based on estimating class-attribute-gated class-conditional distributions. We model each class-conditional distribution as an exponential family distribution and the parameters of the distribution of each seen/unseen class are d…
SWRLDA improves LDA for multi-class classification with edge classes.
problem LDA's vulnerability to edge classes causing biased mean and large distances.
method Self-weighted robust LDA with l21-norm distance criterion.
result SWRLDA outperforms other methods on synthetic and real-world datasets.
For a local Lie group M we define odd order cohomology classes. The first class is an obstruction to globalizability of the local Lie group. The third class coincides with Godbillon-Vey class in a particular case. These classes are secondary as they emerge when curvature vanishes.
This paper proposes a novel generic one-class feature learning method based on intra-class splitting. In one-class classification, feature learning is challenging, because only samples of one class are available during training. Hence, state-of-the-art methods require reference multi-class datasets to pretrain feature …
This research sets limits on how complex multi-class learning problems can be.
problem Understanding the complexity of multi-class classification problems.
method Established upper bounds on Natarajan dimensions for specific function classes.
result Upper bounds on Natarajan dimensions for multi-class decision trees, random forests, and neural networks.
Infinitely many unique ways to generate a surface's mapping class group.
problem Identifying unique ways to generate mapping class groups.
method Analyzing Nielsen equivalence classes of two-element generators.
result There are infinitely many unique ways to generate a surface's mapping class group.
Characteristic classes of oriented vector bundles can be identified with cohomology classes of the disjoint union of classifying spaces BSO_n of special orthogonal groups SO_n with n=0,1,... A characteristic class is stable if it extends to a cohomology class of a homotopy colimit BSO of classifying spaces BSO_n. Simil…
Study rigid classes on hyperkahler manifolds, showing general ones are rigid.
problem Characterize rigid classes on compact hyperkahler manifolds.
method Analyze eigenvectors of hyperbolic automorphisms and use BBF form.
result General parabolic classes on hyperkahler manifolds are rigid.
Defines kappa classes on KSBA spaces, generalizing classes on curves.
problem Generalizing Miller-Morita-Mumford classes to KSBA stable varieties and pairs.
method Defining kappa classes on KSBA moduli spaces and computing them in specific cases.
result Computed kappa classes on Campedelli surfaces, including finding the Chow ring of a specific GIT quotient.
By analyzing how the Borel regulator classes vanish on various groups related to GL(n,Z), we define three series of secondary characteristic classes for subgroups of automorphism groups of free groups. The first case is the IA-automorphism groups and we show that our classes coincide with…
DRAGON improves learning for rare classes in unbalanced datasets using class descriptions.
problem Learning rare classes in unbalanced datasets with deep models.
method DRAGON is a late-fusion architecture that corrects bias towards frequent classes and fuses class-descriptions to improve tail-class accuracy.
result DRAGON outperforms state-of-the-art models on new benchmarks for long-tail learning with class descriptors.
Gen1S learns novel classes with 1-shot data using residual space and generative models.
problem Learning new classes with limited data in a growing dataset.
method Mapping embeddings to a residual space, using generative models to learn multi-modal distribution, and applying it as a structural prior.
result Consistent improvement over state-of-the-art methods in recognizing novel classes.
We study types of mapping classes which arise as a product of a given mapping class and powers of certain pure mapping classes. We derive an explicit constant depending only on a surface such that almost all above pure mapping classes give rise to pseudo-Anosov type whenever their powers are larger than the constant. F…
New classes defined for manifold pseudogroups, linking to cohomology and bundle structures.
problem Characterizing pseudogroups of diffeomorphisms using characteristic classes.
method Defined Godbillon-Vey-Losik and first Chern-Losik classes via de Rham cohomology and frame bundles.
result Explicit expressions and geometric representations for the new classes.
Paper tackles many-class few-shot learning with class hierarchy, improving accuracy.
problem Many-class few-shot learning problem in practical applications.
method Leverages class hierarchy to train a coarse-to-fine classifier using memory-augmented hierarchical-classification network (MahiNet).
result MahiNet outperforms state-of-the-art models on MCFS problems in both supervised and meta-learning settings.
Solutions to Strominger system found for square of Kähler class.
problem Finding solutions to Strominger system with specific balanced classes.
method Deforming Calabi-Yau and Hermitian-Yang-Mills metrics.
result Classes that are squares of Kähler metrics admit solutions.
Continuous epimorphisms between certain mapping class groups are induced by homeomorphisms.
problem Understanding continuous epimorphisms between specific mapping class groups.
method Analyzing subgroups of mapping class groups of infinite-genus 2-manifolds with no planar ends.
result Continuous epimorphisms are induced by homeomorphisms for the specified subgroups.