Calibrated Disambiguation for Partial Multi-label Learning

Partial multi-label learning (PML) models the scenario where each training instance is annotated with a set of candidate labels, and only some of the labels are relevant. The PML problem is practical in real-world scenarios, as it is difficult and even impossible to obtain precisely labeled samples. Several PML solutions have been proposed to combat with the prone misled by the irrelevant labels concealed in the candidate labels, but they generally focus on the smoothness assumption in feature space or low-rank assumption in label space, while ignore the negative information between features and labels. Specifically, if two instances have largely overlapped candidate labels, irrespective of their feature similarity, their ground-truth labels should be similar; while if they are dissimilar in the feature and candidate label space, their ground-truth labels should be dissimilar with each other. To achieve a credible predictor on PML data, we propose a novel approach called PML-LFC (Partial Multi-label Learning with Label and Feature Collaboration). PML-LFC estimates the confidence values of relevant labels for each instance using the similarity from both the label and feature spaces, and trains the desired predictor with the estimated confidence values. PML-LFC achieves the predictor and the latent label matrix in a reciprocal reinforce manner by a unified model, and develops an alternative optimization procedure to optimize them. Extensive empirical study on both synthetic and real-world datasets demonstrates the superiority of PML-LFC.

Partial multi-label learning (PML) deals with problems where each instance is assigned with a candidate label set, which contains multiple relevant labels and some noisy labels. Recent studies usually solve PML problems with the disambiguation strategy, which recovers ground-truth labels from the candidate label set by simply assuming that the noisy labels are generated randomly. In real applications, however, noisy labels are usually caused by some ambiguous contents of the example. Based on this observation, we propose a partial multi-label learning approach to simultaneously recover the ground-truth information and identify the noisy labels. The two objectives are formalized in a unified framework with trace norm and ℓ1 norm regularizers. Under the supervision of the observed noise-corrupted label matrix, the multi-label classifier and noisy label identifier are jointly optimized by incorporating the label correlation exploitation and feature-induced noise model. Extensive experiments on synthetic as well as real-world data sets validate the effectiveness of the proposed approach.

Partial multi-label feature selection based on label disambiguation and double-regularized sparse regression

Noisy label tolerance: A new perspective of Partial Multi-Label Learning

Partial multi-label learning via specific label disambiguation

This paper presents an optimal weighted least squares (WLS) method for designing low-complexity all-pass variable fractional-delay (VFD) digital filters. Instead of using a fixed range for the VFD parameter p and same-order constant-coefficient filters (subfilters), both the VFD parameter range p isin [p Min,p Max] and subfilter orders are optimized such that a low-complexity all-pass VFD filter can be achieved for the LS design. To suppress the peak errors of variable frequency response, weighting functions are adopted and optimized such that the boundary peak errors can be further reduced but without noticeably increasing the total error energy (integral of squared error) of variable frequency response. After optimizing the variable range of the VFD parameter, weighting functions, and subfilter orders, an all-pass VFD filter can be designed by using a generalized noniterative WLS method, which yields a closed-form solution. Design examples are given to illustrate that utilizing different-order subfilters, along with the optimal range and optimal weighting functions, can yield an all-pass VFD filter with significantly reduced complexity and design errors as compared with existing ones.

Optimal Control of the Grinding Process Based on the Filtering and Prediction Theory

Extrapolation of scattering amplitudes IV. Extrapolation off a part of the boundary to the rest of the boundary

Pollution error is a well known source of inaccuracies in continuous or discontinuous FE approaches to solve the Helmholtz equation. This topic is widely studied in a large number of papers, e.g., (Ihlenburg and Babuska, Comput Math Appl 30(9):9–37, 1995; Ihlenburg, Finite element analysis of acoustic scattering applied mathematical sciences, vol 132. Springer, New York, 1998). Robust methodologies for structured square meshes have been developed in recent years. This work seeks to develop a methodology based on Petrov–Galerkin discontinuous formulation, to minimize phase error for Helmholtz equation for both structured and unstructured meshes. A Petrov–Galerkin finite element formulation is introduced for the Helmholtz problem in two dimensions using polynomial weighting functions. At each node of the triangular mesh, a global basis function for the weighting space is obtained, adding bilinear $$C^0$$ Lagrangian weighting function linear combinations. The optimal weighting functions, with the same support of the corresponding global test functions, are obtained after computing the coefficients of these linear combinations attending to optimal criteria. This is done numerically through a preprocessing technique that is naturally applied to non-uniform and unstructured meshes. In particular, for uniform meshes a quasi optimal interior stencil of the same order of the quasi-stabilized finite element method stencil derived by (Babuska et al., Comput Meth Appl Mech Eng 128:325–359, 1995) is obtained. The numerical results indicate a better performance in relation to the classic discontinuous Galerkin method.

Partial multilabel learning (PML) aims to learn from training data, where each instance is associated with a set of candidate labels, among which only a part is correct. The common strategy to deal with such a problem is disambiguation, that is, identifying the ground-truth labels from the given candidate labels. However, the existing PML approaches always focus on leveraging the instance relationship to disambiguate the given noisy label space, while the potentially useful information in label space is not effectively explored. Meanwhile, the existence of noise and outliers in training data also makes the disambiguation operation less reliable, which inevitably decreases the robustness of the learned model. In this article, we propose a prior label knowledge regularized self-representation PML approach, called PAKS, where the self-representation scheme and prior label knowledge are jointly incorporated into a unified framework. Specifically, we introduce a self-representation model with a low-rank constraint, which aims to learn the subspace representations of distinct instances and explore the high-order underlying correlation among different instances. Meanwhile, we incorporate prior label knowledge into the above self-representation model, where the prior label knowledge is regarded as the complement of features to obtain an accurate self-representation matrix. The core of PAKS is to take advantage of the data membership preference, which is derived from the prior label knowledge, to purify the discovered membership of the data and accordingly obtain more representative feature subspace for model induction. Enormous experiments on both synthetic and real-world datasets show that our proposed approach can achieve superior or comparable performance to state-of-the-art approaches.

Last year, we reported a new disparity effect on optic-flow perception. It occurs when a flow field of radially moving random dots is transparently superimposed by a unidirectional motion pattern. Subjects asked to locate the centre of the expansion pattern perceive it shifted away from its true position (Duffy and Wurtz, 1993 Vision Research33 1481 – 1490). The magnitude of this shift depends on binocular disparity between the two superimposed patterns: presenting the translation in front of the expansion causes a massive reduction of the shift, presenting it behind the expansion yields only a slight reduction. To determine possible mechanisms for this interaction, we tried to model our results by modifying a previously developed neural model for optic-flow processing (Lappe and Rauschecker, 1995 Vision Research35 1619 – 1631). We compared three possible mechanisms of disparity influence. The first was based on the assumption that the absolute distance of the stimuli from the observer was known. The second was based on a disparity-based spatial integration, as found in ‘tuned’ neurons in primate visual area MT. Neither could account for our data. Finally we included a disparity-dependent weighting function in the model, assuming that distant flow vectors contribute more strongly than near ones to the processing of optic flow. This reproduced the experimental findings. Surprisingly, the optimal weighting function was similar to the disparity-dependence of the so-called ‘far-neurons’ in area MT. We conclude that the visual system uses disparity in optic-flow processing by putting special emphasis on distant flow vectors, and that far-neurons in MT might serve as a neuronal substrate for this.

Partial Multi-label Learning with a Few Accurately Labeled Data

QCD sum rules of Shifman, Vainstein and Zakharov are investigated from the point of view of analytical extrapolations: in the weighted sum rule the analyticity connects the low energy hadron parameters with the high energy QCD parameters (coupling constant, quark masses, condensate parameters). It is shown that the optimal weight function in the sum rule is prescribed by the errors of the input information. The optimal tests of analyticity are proposed and applied (under some simplifying assumptions) to the vector and pseudoscalar charmonium channels.

Evaluation of real-time digital pulse shapers with various HPGe and silicon radiation detectors

Learning to rank has been intensively studied and has shown great value in many fields, such as web search, question answering and recommender systems. This paper focuses on listwise document ranking, where all documents associated with the same query in the training data are used as the input. We propose a novel ranking method, referred to as WassRank, under which the problem of listwise document ranking boils down to the task of learning the optimal ranking function that achieves the minimum Wasserstein distance. Specifically, given the query level predictions and the ground truth labels, we first map them into two probability vectors. Analogous to the optimal transport problem, we view each probability vector as a pile of relevance mass with peaks indicating higher relevance. The listwise ranking loss is formulated as the minimum cost (the Wasserstein distance) of transporting (or reshaping) the pile of predicted relevance mass so that it matches the pile of ground-truth relevance mass. The smaller the Wasserstein distance is, the closer the prediction gets to the ground-truth. To better capture the inherent relevance-based order information among documents with different relevance labels and lower the variance of predictions for documents with the same relevance label, ranking-specific cost matrix is imposed. To validate the effectiveness of WassRank, we conduct a series of experiments on two benchmark collections. The experimental results demonstrate that: compared with four non-trivial listwise ranking methods (i.e., LambdaRank, ListNet, ListMLE and ApxNDCG), WassRank can achieve substantially improved performance in terms of nDCG and ERR across different rank positions. Specifically, the maximum improvements of WassRank over LambdaRank, ListNet, ListMLE and ApxNDCG in terms of nDCG@1 are 15%, 5%, 7%, 5%, respectively.