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Positive-unlabeled (PU) learning aims to train a classifier using the data containing only labeled-positive instances and unlabeled instances. However, existing PU learning methods are generally hard to achieve satisfactory performance on trifurcate data, where the positive instances distribute on both sides of the negative instances. To address this issue, firstly we propose a PU classifier with asymmetric loss (PUAL), by introducing a structure of asymmetric loss on positive instances into the objective function of the global and local learning classifier. Then we develop a kernel-based algorithm to enable PUAL to obtain non-linear decision boundary. We show that, through experiments on both simulated and real-world datasets, PUAL can achieve satisfactory classification on trifurcate data., Comment: 24 pages, 6 figures

Dimension reduction plays a pivotal role in analysing high-dimensional data. However, observations with missing values present serious difficulties in directly applying standard dimension reduction techniques. As a large number of dimension reduction approaches are based on the Gram matrix, we first investigate the effects of missingness on dimension reduction by studying the statistical properties of the Gram matrix with or without missingness, and then we present a bias-corrected Gram matrix with nice statistical properties under heterogeneous missingness. Extensive empirical results, on both simulated and publicly available real datasets, show that the proposed unbiased Gram matrix can significantly improve a broad spectrum of representative dimension reduction approaches., Comment: Accepted for the 37th Conference on Uncertainty in Artificial Intelligence (UAI 2021)

This paper proposes a dual-supervised uncertainty inference (DS-UI) framework for improving Bayesian estimation-based uncertainty inference (UI) in deep neural network (DNN)-based image recognition. In the DS-UI, we combine the classifier of a DNN, i.e., the last fully-connected (FC) layer, with a mixture of Gaussian mixture models (MoGMM) to obtain an MoGMM-FC layer. Unlike existing UI methods for DNNs, which only calculate the means or modes of the DNN outputs' distributions, the proposed MoGMM-FC layer acts as a probabilistic interpreter for the features that are inputs of the classifier to directly calculate the probability density of them for the DS-UI. In addition, we propose a dual-supervised stochastic gradient-based variational Bayes (DS-SGVB) algorithm for the MoGMM-FC layer optimization. Unlike conventional SGVB and optimization algorithms in other UI methods, the DS-SGVB not only models the samples in the specific class for each Gaussian mixture model (GMM) in the MoGMM, but also considers the negative samples from other classes for the GMM to reduce the intra-class distances and enlarge the inter-class margins simultaneously for enhancing the learning ability of the MoGMM-FC layer in the DS-UI. Experimental results show the DS-UI outperforms the state-of-the-art UI methods in misclassification detection. We further evaluate the DS-UI in open-set out-of-domain/-distribution detection and find statistically significant improvements. Visualizations of the feature spaces demonstrate the superiority of the DS-UI.

Due to lack of data, overfitting ubiquitously exists in real-world applications of deep neural networks (DNNs). We propose advanced dropout, a model-free methodology, to mitigate overfitting and improve the performance of DNNs. The advanced dropout technique applies a model-free and easily implemented distribution with parametric prior, and adaptively adjusts dropout rate. Specifically, the distribution parameters are optimized by stochastic gradient variational Bayes in order to carry out an end-to-end training. We evaluate the effectiveness of the advanced dropout against nine dropout techniques on seven computer vision datasets (five small-scale datasets and two large-scale datasets) with various base models. The advanced dropout outperforms all the referred techniques on all the datasets.We further compare the effectiveness ratios and find that advanced dropout achieves the highest one on most cases. Next, we conduct a set of analysis of dropout rate characteristics, including convergence of the adaptive dropout rate, the learned distributions of dropout masks, and a comparison with dropout rate generation without an explicit distribution. In addition, the ability of overfitting prevention is evaluated and confirmed. Finally, we extend the application of the advanced dropout to uncertainty inference, network pruning, text classification, and regression. The proposed advanced dropout is also superior to the corresponding referred methods. Codes are available at https://github.com/PRIS-CV/AdvancedDropout., Comment: Accepted by IEEE TPAMI, 2021

Metric learning aims to learn a distance metric such that semantically similar instances are pulled together while dissimilar instances are pushed away. Many existing methods consider maximizing or at least constraining a distance margin in the feature space that separates similar and dissimilar pairs of instances to guarantee their generalization ability. In this paper, we advocate imposing an adversarial margin in the input space so as to improve the generalization and robustness of metric learning algorithms. We first show that, the adversarial margin, defined as the distance between training instances and their closest adversarial examples in the input space, takes account of both the distance margin in the feature space and the correlation between the metric and triplet constraints. Next, to enhance robustness to instance perturbation, we propose to enlarge the adversarial margin through minimizing a derived novel loss function termed the perturbation loss. The proposed loss can be viewed as a data-dependent regularizer and easily plugged into any existing metric learning methods. Finally, we show that the enlarged margin is beneficial to the generalization ability by using the theoretical technique of algorithmic robustness. Experimental results on 16 datasets demonstrate the superiority of the proposed method over existing state-of-the-art methods in both discrimination accuracy and robustness against possible noise., Comment: 27 pages

Few-shot meta-learning has been recently reviving with expectations to mimic humanity's fast adaption to new concepts based on prior knowledge. In this short communication, we give a concise review on recent representative methods in few-shot meta-learning, which are categorized into four branches according to their technical characteristics. We conclude this review with some vital current challenges and future prospects in few-shot meta-learning., Comment: 7 pages

This paper discusses a new type of discriminant analysis based on the orthogonal projection of data onto a generalized difference subspace (GDS). In our previous work, we have demonstrated that GDS projection works as the quasi-orthogonalization of class subspaces, which is an effective feature extraction for subspace based classifiers. Interestingly, GDS projection also works as a discriminant feature extraction through a similar mechanism to the Fisher discriminant analysis (FDA). A direct proof of the connection between GDS projection and FDA is difficult due to the significant difference in their formulations. To avoid the difficulty, we first introduce geometrical Fisher discriminant analysis (gFDA) based on a simplified Fisher criterion. Our simplified Fisher criterion is derived from a heuristic yet practically plausible principle: the direction of the sample mean vector of a class is in most cases almost equal to that of the first principal component vector of the class, under the condition that the principal component vectors are calculated by applying the principal component analysis (PCA) without data centering. gFDA can work stably even under few samples, bypassing the small sample size (SSS) problem of FDA. Next, we prove that gFDA is equivalent to GDS projection with a small correction term. This equivalence ensures GDS projection to inherit the discriminant ability from FDA via gFDA. Furthermore, to enhance the performances of gFDA and GDS projection, we normalize the projected vectors on the discriminant spaces. Extensive experiments using the extended Yale B+ database and the CMU face database show that gFDA and GDS projection have equivalent or better performance than the original FDA and its extensions.

Heat demand prediction is a prominent research topic in the area of intelligent energy networks. It has been well recognized that periodicity is one of the important characteristics of heat demand. Seasonal-trend decomposition based on LOESS (STL) algorithm can analyze the periodicity of a heat demand series, and decompose the series into seasonal and trend components. Then, predicting the seasonal and trend components respectively, and combining their predictions together as the heat demand prediction is a possible way to predict heat demand. In this paper, STL-ENN-ARIMA (SEA), a combined model, was proposed based on the combination of the Elman neural network (ENN) and the autoregressive integrated moving average (ARIMA) model, which are commonly applied to heat demand prediction. ENN and ARIMA are used to predict seasonal and trend components, respectively. Experimental results demonstrate that the proposed SEA model has a promising performance.

A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be a Dirichlet distribution. With the Bayes rule, searching for the optimal parameters is equivalent to finding the mode of the posterior distribution. In order to explicitly characterize the nonnegative L1-norm constraint of the parameters, we further approximate the true posterior distribution by a Dirichlet distribution. We estimate the statistics of the approximating Dirichlet posterior distribution by sampling methods. Four sampling methods have been introduced. With the estimated posterior distributions, the original parameters can be effectively reconstructed in polynomial fitting problems, and the BALSON framework is found to perform better than conventional methods.

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian distributed, the conventional principal component analysis (PCA) cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations.