Extends topological theorems to new mapping families.
problem Limitations of existing topological theorems.
method Replaces large subset requirements with smaller subset requirements.
result Extends theorems to m-sphere to n-space mappings with m<n.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
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48 results for “milder form”
Geodesic X-ray transform proves injective for smooth one-forms on gas giant manifolds.
problem Injectivity of geodesic X-ray transform for one-forms on specific manifolds.
method Pestov identity and asymptotic analysis of short geodesics.
result Geodesic X-ray transform is solenoidally injective for smooth one-forms on gas giant manifolds.
Improved analysis shows milder over-parameterization for deep neural networks.
problem Ensuring global convergence of over-parameterized deep neural networks.
method Improved analysis of gradient descent for training deep neural networks.
result Milder over-parameterization condition than previous work.
Ensemble learning improves anomaly detection for milder symptoms.
problem Difficulty in detecting incipient anomalies due to similarity to normal conditions.
method Utilize uncertainty information from ensemble learning to identify misclassified incipient anomalies.
result Ensemble learning methods show improved performance on incipient anomaly detection.
For a density on , a {\it high-density cluster} is any connected component of , for some . The set of all high-density clusters forms a hierarchy called the {\it cluster tree} of . We present two procedures for estimating the cluster tree given samples from . The first…
Paper introduces new Finsler metrics preserved under projective transformations.
problem Developing new projective invariant in Finsler geometry.
method Formulated weakly generalized Douglas-Weyl equation to generalize Finsler metrics.
result Introduces new subclasses of Finsler metrics: generalized weakly-Weyl and generalized -metrics.
Logistic regression gets a new, simpler uniform bound.
problem Finding a uniform bound for logistic regression's empirical risk.
method PAC-Bayes approach with second-order expansion and Rademacher-complexity bounds.
result Provides a dimension-free uniform concentration bound.
Efficiently learns a single neuron with adversarial noise, improving on prior work.
problem Learning a single neuron with adversarial label noise.
method Efficient algorithm using local error bounds from optimization theory.
result Approximates optimal -error within a constant factor.
We examine the squared error loss landscape of shallow linear neural networks. We show---with significantly milder assumptions than previous works---that the corresponding optimization problems have benign geometric properties: there are no spurious local minima and the Hessian at every saddle point has at least one ne…
Study bubbling Kahler metrics using algebraic geometry.
problem Analyzing the degeneration of Kahler metrics with Euclidean volume growth.
method Algebraic construction of birational modifications to simplify degenerations, comparing with analytic constructions.
result Provide a framework to compare algebraic and analytic approaches to bubbling phenomena.
Paper improves classification rates for private data.
problem Classifying data with privacy constraints and relaxed assumptions.
method Introduced a novel approach for classification under privacy constraints, relaxing the strong density assumption.
result Achieved minimax optimal convergence rates without strong density assumption.
This work addresses various open questions in the theory of active learning for nonparametric classification. Our contributions are both statistical and algorithmic: -We establish new minimax-rates for active learning under common \textit{noise conditions}. These rates display interesting transitions -- due to the inte…
We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups . In particular, such subgroups are quasiconvex in . In addition, we identify a milder cond…
Gradient methods learn a single neuron under mild assumptions.
problem Learning a single neuron with gradient methods under realistic conditions.
method Gradient methods applied to a single neuron model.
result Positive guarantees achieved under mild assumptions, beyond previous literature.
Dynamic angles estimated from noisy measurements over time with smoothness constraints.
problem Recovering angles from noisy pairwise measurements over time.
method Three algorithms for joint estimation of angles under smoothness constraints.
result MSE converges to zero as increases under milder conditions.
Unified analysis of SGD and GD convergence rates.
problem Analyzing convergence rates of SGD and GD methods.
method Unified proof for convergence of SGD on μ-convex functions under mild smoothness assumptions.
result Convergence rates match best known iteration complexities up to constants.
This paper addresses a gap in the classifcation of Codazzi tensors with exactly two eigenfunctions on a Riemannian manifold of dimension three or higher. Derdzinski proved that if the trace of such a tensor is constant and the dimension of one of the the eigenspaces is , then the metric is a warped product where t…
We propose a communication-efficient distributed estimation method for sparse linear discriminant analysis (LDA) in the high dimensional regime. Our method distributes the data of size into machines, and estimates a local sparse LDA estimator on each machine using the data subset of size . After the distri…
Simplified SGD interpretation as Ito process for broader applicability.
problem Lack of generality in current SGD interpretation.
method Introduced a simplified scheme for discrete-time approximation of Ito process.
result Flexibly interprets SGD and SGLD, providing insights into their asymptotic properties.
In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that contain information of the cluster structure in high-dimensional space. Based on this …
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation of the sum of an approximately) low rank matrix with a second matrix endowed with a complementary …
Study on fair learning under differential privacy constraints.
problem Creating fair models without sensitive attribute data.
method Two algorithms: one using explicit group membership, the other not.
result Tradeoffs between fairness, accuracy, and privacy.
We analyze a negative-parameter variant of the diversity-weighted portfolio studied by Fernholz, Karatzas, and Kardaras (Finance Stoch 9(1):1-27, 2005), which invests in each company a fraction of wealth inversely proportional to the company's market weight (the ratio of its capitalization to that of the entire market)…
Super-Linear Convergence of Dual Augmented-Lagrangian Algorithm for Sparsity Regularized Estimationstat.ML
We analyze the convergence behaviour of a recently proposed algorithm for regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is based on a new interpretation of DAL as a proximal minimization algorithm. We theoretically show under some conditions that DAL converges super-linearly in a non-asymp…
Ensemble models struggle with detecting mild faults.
problem Difficulty in detecting Intermediate-Severity faults due to their resemblance to normal conditions.
method Extensive experiments with ensemble models to identify and address common pitfalls.
result Designing more effective ensemble models for IS fault detection and diagnosis.
Improved anomaly detection for incipient faults using ensemble learning.
problem Difficulty in detecting milder anomalies due to similarity to normal conditions.
method Utilize uncertainty information from ensemble learning to identify misclassified incipient anomalies.
result Ensemble learning improves performance on incipient anomaly detection.
We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical Gaussian components, where the clusters are distinguished by only a few relevant dimens…
In the mixture models problem it is assumed that there are distributions and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances with their generating distributions, or to identify the parameters of the hidden distribu…
Paper corrects Max-Margin loss for multi-label tasks.
problem Max-Margin loss inconsistency in multi-label classification.
method Introduced Restricted-Max-Margin loss.
result Consistent loss for multi-label tasks under milder conditions.
We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings minimise, providing an intuitive understanding of the embeddings and a justificatio…
The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps (1979). In the context of optimal portfolio selection with expected utility preferences this question has been a focus of considerable attention over the last twenty years. We…
Complex performance measures, beyond the popular measure of accuracy, are increasingly being used in the context of binary classification. These complex performance measures are typically not even decomposable, that is, the loss evaluated on a batch of samples cannot typically be expressed as a sum or average of losses…
Deep learning framework for kernel methods using RKHM and Perron-Frobenius operators.
problem Kernel methods in deep learning with potential overfitting issues.
method Combining RKHM and Perron-Frobenius operator to derive a new Rademacher bound and analyze deep kernel methods.
result Theoretical interpretation of benign overfitting and milder dependency on output dimension.
The paper computes torsion invariants for groups acting on complexes.
problem Computing torsion invariants for groups acting on complexes.
method Analyzes residually finite groups acting cocompactly on contractible complexes with specific stabilizers.
result Torsion limits to the torsion of the boundary subcomplex, independent of the chain of subgroups.
We theoretically investigate the convergence rate and support consistency (i.e., correctly identifying the subset of non-zero coefficients in the large sample limit) of multiple kernel learning (MKL). We focus on MKL with block-l1 regularization (inducing sparse kernel combination), block-l2 regularization (inducing un…
1-Lipschitz networks are as accurate as classical networks and offer robustness.
problem Misconceptions about 1-Lipschitz neural networks and their properties.
method Analysis of 1-Lipschitz neural networks' accuracy, robustness, and generalization.
result 1-Lipschitz neural networks are as accurate as classical networks and can fit arbitrarily difficult boundaries.
In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting. Our first main result studies the sparsistency, or consistency in sparsity pattern recovery, properties of a forward-backward greedy algorithm as applied to general statistical model…
New method identifies Gaussian SEMs with varying error variances.
problem Identify Gaussian SEMs with both homogeneous and heterogeneous error variances.
method Exploits error variances and edge weights; provides a statistically consistent and feasible structure learning algorithm.
result Proves identifiability of Gaussian SEMs with both homogeneous and heterogeneous unknown error variances.
Improved Analysis of the Accelerated Noisy Power Method with Applications to Decentralized PCAstat.ML
Improved analysis of accelerated noisy power method for PCA.
problem Inexact matrix-vector products in PCA settings.
method Improved analysis of Accelerated Noisy Power Method under milder perturbation conditions.
result Worst-case optimal convergence rate with relaxed noise conditions.
In topic modeling, many algorithms that guarantee identifiability of the topics have been developed under the premise that there exist anchor words -- i.e., words that only appear (with positive probability) in one topic. Follow-up work has resorted to three or higher-order statistics of the data corpus to relax the an…
Paper develops KMS Wasserstein for high-dimensional data reduction.
problem Optimal transport's curse of dimensionality in high-dimensional data.
method Kernel max-sliced (KMS) Wasserstein distance for dimensionality reduction.
result Sharp finite-sample guarantees for KMS -Wasserstein distance.
Develops a Best-of-Both-Worlds algorithm for linear contextual bandits with Tsallis entropy.
problem Linear contextual bandits with i.i.d. contexts.
method Follow-The-Regularized-Leader (FTRL) with Tsallis entropy.
result Achieves $O\left(\log(T)^{\frac{1+β}{2+β}}T^{\frac{1}{2+β}}
ight)$ regret under margin condition.
T-SCI improves Cox-MLP's guaranteed coverage for censored data.
problem Losing guaranteed coverage when relaxing linear assumption with neural networks.
method Two-stage conformal inference algorithm with non-conformity score.
result T-SCI provides guaranteed coverage under milder assumptions.
New bounds on generalization error using information density moments.
problem Bounding the generalization error of randomized learning algorithms.
method Derives bounds on average and tail probabilities of generalization error using mth central moments of the information density.
result Explicit bounds on generalization error are derived, showing better dependence on confidence level with higher-order information density moments.
New method identifies shared components from unpaired multimodal mixtures.
problem Identify shared components from unpaired multimodal mixtures.
method Distribution divergence minimization-based loss with sufficient conditions for identifiability.
result Sufficient conditions for shared component identifiability from unaligned multimodal mixtures.
Paper proposes efficient offline neural bandit method.
problem Offline policy learning with neural networks.
method Provable efficient offline contextual bandit with neural network function approximation.
result Method provably generalizes over unseen contexts.
New algorithm trains ReLU gates provably in linear time.
problem Training ReLU gates in realizable settings with mild conditions.
method Iterative stochastic algorithm with moment assumptions.
result First recovery of true labels under data-poisoning attacks.
Improves SGM convergence bounds in W2-distance without strict assumptions.
problem Convergence bounds for SGMs in W2-distance require stringent assumptions.
method Novel framework using the OU process and PDE analysis.
result Log-concavity evolves from weak to strong over time.