This paper introduces an unsupervised method to estimate the class separability of text datasets from a topological point of view. Using persistent homology, we demonstrate how tracking the evolution of embedding manifolds during training can inform about class separability. More specifically, we show how this technique can be applied to detect when the training process stops improving the separability of the embeddings. Our results, validated across binary and multi-class text classification tasks, show that the proposed method's estimates of class separability align with those obtained from supervised methods. This approach offers a novel perspective on monitoring and improving the fine-tuning of sentence transformers for classification tasks, particularly in scenarios where labeled data is scarce. We also discuss how tracking these quantities can provide additional insights into the properties of the trained classifier.
相關內容
This paper is about the recent notion of computably probably approximately correct learning, which lies between the statistical learning theory where there is no computational requirement on the learner and efficient PAC where the learner must be polynomially bounded. Examples have recently been given of hypothesis classes which are PAC learnable but not computably PAC learnable, but these hypothesis classes are unnatural or non-canonical in the sense that they depend on a numbering of proofs, formulas, or programs. We use the on-a-cone machinery from computability theory to prove that, under mild assumptions such as that the hypothesis class can be computably listable, any natural hypothesis class which is learnable must be computably learnable. Thus the counterexamples given previously are necessarily unnatural.
Applying differential privacy (DP) by means of the DP-SGD algorithm to protect individual data points during training is becoming increasingly popular in NLP. However, the choice of granularity at which DP is applied is often neglected. For example, neural machine translation (NMT) typically operates on the sentence-level granularity. From the perspective of DP, this setup assumes that each sentence belongs to a single person and any two sentences in the training dataset are independent. This assumption is however violated in many real-world NMT datasets, e.g. those including dialogues. For proper application of DP we thus must shift from sentences to entire documents. In this paper, we investigate NMT at both the sentence and document levels, analyzing the privacy/utility trade-off for both scenarios, and evaluating the risks of not using the appropriate privacy granularity in terms of leaking personally identifiable information (PII). Our findings indicate that the document-level NMT system is more resistant to membership inference attacks, emphasizing the significance of using the appropriate granularity when working with DP.
The aim of this paper is to provide a coherent framework for transforming boundary pairs of digital images from one resolution to another without knowledge of the full images. It is intended to facilitate the simultaneous usage of multiresolution processing and boundary reduction, primarily for algorithms in computational dynamics and computational control theory.
This study proposes a unified theory and statistical learning approach for traffic conflict detection, addressing the long-existing call for a consistent and comprehensive methodology to evaluate the collision risk emerging in road user interactions. The proposed theory assumes context-dependent probabilistic collision risk and frames conflict detection as assessing this risk by statistical learning of extreme events in daily interactions. Experiments using real-world trajectory data are conducted in this study, where a unified metric of conflict is trained with lane-changing interactions on German highways and applied to near-crash events from the 100-Car Naturalistic Driving Study in the U.S. Results of the experiments demonstrate that the trained metric provides effective collision warnings, generalises across distinct datasets and traffic environments, covers a broad range of conflicts, and delivers a long-tailed distribution of conflict intensity. Reflecting on these results, the unified theory ensures consistent evaluation by a generic formulation that encompasses varying assumptions of traffic conflicts; the statistical learning approach then enables a comprehensive consideration of influencing factors such as motion states of road users, environment conditions, and participant characteristics. Therefore, the theory and learning approach jointly provide an explainable and adaptable methodology for conflict detection among different road users and across various interaction scenarios. This promises to reduce accidents and improve overall traffic safety, by enhanced safety assessment of traffic infrastructures, more effective collision warning systems for autonomous driving, and a deeper understanding of road user behaviour in different traffic conditions.
Bayesian optimization (BO) is a principled approach to molecular design tasks. In this paper we explain three pitfalls of BO which can cause poor empirical performance: an incorrect prior width, over-smoothing, and inadequate acquisition function maximization. We show that with these issues addressed, even a basic BO setup is able to achieve the highest overall performance on the PMO benchmark for molecule design (Gao et al 2022). These results suggest that BO may benefit from more attention in the machine learning for molecules community.
This paper considers a joint survival and mixed-effects model to explain the survival time from longitudinal data and high-dimensional covariates. The longitudinal data is modeled using a nonlinear effects model, where the regression function serves as a link function incorporated into a Cox model as a covariate. In that way, the longitudinal data is related to the survival time at a given time. Additionally, the Cox model takes into account the inclusion of high-dimensional covariates. The main objectives of this research are two-fold: first, to identify the relevant covariates that contribute to explaining survival time, and second, to estimate all unknown parameters of the joint model. For that purpose, we consider the maximization of a Lasso penalized likelihood. To tackle the optimization problem, we implement a pre-conditioned stochastic gradient to handle the latent variables of the nonlinear mixed-effects model associated with a proximal operator to manage the non-differentiability of the penalty. We provide relevant simulations that showcase the performance of the proposed variable selection and parameters' estimation method in the joint modeling of a Cox and logistic model.
The aim of this paper is to present three construction methods for quasi-copulas based on recent developments: a representation of multivariate quasi-copulas by means of infima and suprema of copulas, an extension of a classical result on shuffles of min to the setting of quasi-copulas, and a construction method for quasi-copulas obeying a given signed mass pattern on a patch.
In this paper, a two-dimensional Dirichlet-to-Neumann (DtN) finite element method (FEM) is developed to analyze the scattering of SH guided waves due to an interface delamination in a bi-material plate. During the finite element analysis, it is necessary to determine the far-field DtN conditions at virtual boundaries where both displacements and tractions are unknown. In this study, firstly, the scattered waves at the virtual boundaries are represented by a superposition of guided waves with unknown scattered coefficients. Secondly, utilizing the mode orthogonality, the unknown tractions at virtual boundaries are expressed in terms of the unknown scattered displacements at virtual boundaries via scattered coefficients. Thirdly, this relationship at virtual boundaries can be finally assembled into the global DtN-FEM matrix to solve the problem. This method is simple and elegant, which has advantages on dimension reduction and needs no absorption medium or perfectly matched layer to suppress the reflected waves compared to traditional FEM. Furthermore, the reflection and transmission coefficients of each guided mode can be directly obtained without post-processing. This proposed DtN-FEM will be compared with boundary element method (BEM), and finally validated for several benchmark problems.
This paper develops a novel Bayesian approach for nonlinear regression with symmetric matrix predictors, often used to encode connectivity of different nodes. Unlike methods that vectorize matrices as predictors that result in a large number of model parameters and unstable estimation, we propose a Bayesian multi-index regression method, resulting in a projection-pursuit-type estimator that leverages the structure of matrix-valued predictors. We establish the model identifiability conditions and impose a sparsity-inducing prior on the projection directions for sparse sampling to prevent overfitting and enhance interpretability of the parameter estimates. Posterior inference is conducted through Bayesian backfitting. The performance of the proposed method is evaluated through simulation studies and a case study investigating the relationship between brain connectivity features and cognitive scores.
Extreme value theory has constructed asymptotic properties of the sample maximum. This study concerns probability distribution estimation of the sample maximum. The traditional approach is parametric fitting to the limiting distribution -- the generalized extreme value distribution; however, the model in non-limiting cases is misspecified to a certain extent. We propose a plug-in type of nonparametric estimator that does not need model specification. Asymptotic properties of the distribution estimator are derived. The simulation study numerically investigates the relative performance in finite-sample cases. This study assumes that the underlying distribution of the original sample belongs to one of the Hall class, the Weibull class or the bounded class, whose types of the limiting distributions are all different: the Frechet, Gumbel or Weibull. It is proven that the convergence rate of the parametric fitting estimator depends on both the extreme value index and the second-order parameter and gets slower as the extreme value index tends to zero. On the other hand, the rate of the nonparametric estimator is proven to be independent of the extreme value index under certain conditions. The numerical performances of the parametric fitting estimator and the nonparametric estimator are compared, which shows that the nonparametric estimator performs better, especially for the extreme value index close to zero. Finally, we report two real case studies: the Potomac River peak stream flow (cfs) data and the Danish Fire Insurance data.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191