In this work we consider active local learning: given a query point $x$, and active access to an unlabeled training set $S$, output the prediction $h(x)$ of a near-optimal $h \in H$ using significantly fewer labels than would be needed to actually learn $h$ fully. In particular, the number of label queries should be independent of the complexity of $H$, and the function $h$ should be well-defined, independent of $x$. This immediately also implies an algorithm for distance estimation: estimating the value $opt(H)$ from many fewer labels than needed to actually learn a near-optimal $h \in H$, by running local learning on a few random query points and computing the average error. For the hypothesis class consisting of functions supported on the interval $[0,1]$ with Lipschitz constant bounded by $L$, we present an algorithm that makes $O(({1 / \epsilon^6}) \log(1/\epsilon))$ label queries from an unlabeled pool of $O(({L / \epsilon^4})\log(1/\epsilon))$ samples. It estimates the distance to the best hypothesis in the class to an additive error of $\epsilon$ for an arbitrary underlying distribution. We further generalize our algorithm to more than one dimensions. We emphasize that the number of labels used is independent of the complexity of the hypothesis class which depends on $L$. Furthermore, we give an algorithm to locally estimate the values of a near-optimal function at a few query points of interest with number of labels independent of $L$. We also consider the related problem of approximating the minimum error that can be achieved by the Nadaraya-Watson estimator under a linear diagonal transformation with eigenvalues coming from a small range. For a $d$-dimensional pointset of size $N$, our algorithm achieves an additive approximation of $\epsilon$, makes $\tilde{O}({d}/{\epsilon^2})$ queries and runs in $\tilde{O}({d^2}/{\epsilon^{d+4}}+{dN}/{\epsilon^2})$ time.

Name disambiguation aims to identify unique authors with the same name. Existing name disambiguation methods always exploit author attributes to enhance disambiguation results. However, some discriminative author attributes (e.g., email and affiliation) may change because of graduation or job-hopping, which will result in the separation of the same author's papers in digital libraries. Although these attributes may change, an author's co-authors and research topics do not change frequently with time, which means that papers within a period have similar text and relation information in the academic network. Inspired by this idea, we introduce Multi-view Attention-based Pairwise Recurrent Neural Network (MA-PairRNN) to solve the name disambiguation problem. We divided papers into small blocks based on discriminative author attributes and blocks of the same author will be merged according to pairwise classification results of MA-PairRNN. MA-PairRNN combines heterogeneous graph embedding learning and pairwise similarity learning into a framework. In addition to attribute and structure information, MA-PairRNN also exploits semantic information by meta-path and generates node representation in an inductive way, which is scalable to large graphs. Furthermore, a semantic-level attention mechanism is adopted to fuse multiple meta-path based representations. A Pseudo-Siamese network consisting of two RNNs takes two paper sequences in publication time order as input and outputs their similarity. Results on two real-world datasets demonstrate that our framework has a significant and consistent improvement of performance on the name disambiguation task. It was also demonstrated that MA-PairRNN can perform well with a small amount of training data and have better generalization ability across different research areas.

The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular values of a matrix to obtain a low-rank matrix. However, calculating singular values can be very expensive for large matrices. The second type of algorithm replaces the low-rank matrix as the multiplication of two small matrices. They are faster than the first type because no singular value decomposition (SVD) is required. However, the rank of the low-rank matrix is required, and an accurate rank estimation is needed to obtain a reasonable solution. In this paper, we propose algorithms that combine both types. Our proposed algorithms require an upper bound of the rank and SVD on small matrices. First, they are faster than the first type because the cost of SVD on small matrices is negligible. Second, they are more robust than the second type because an upper bound of the rank instead of the exact rank is required. Furthermore, we apply the Gauss-Newton method to increase the speed of our algorithms. Numerical experiments show the better performance of our proposed algorithms.

Over the past two decades, Support Vector Machine (SVM) has been a popular supervised machine learning model, and plenty of distinct algorithms are designed separately based on different KKT conditions of SVM model for classification/regression with the different losses, including the convex loss or non-convex loss. In this paper, we propose an algorithm that can train different SVM models in a \emph{unified} scheme. Firstly, we introduce a definition of the \emph{LS-DC} (least squares type of difference of convex) loss and show that the most commonly used losses in the SVM community are LS-DC loss or can be approximated by LS-DC loss. Then based on DCA (difference of convex algorithm), we propose a unified algorithm, called \emph{UniSVM} that can solve the SVM model with any convex or non-convex LS-DC loss, in which only a vector is computed especially by the specifically chosen loss. Particularly, for training robust SVM models with non-convex losses, UniSVM has a dominant advantage over all the existing algorithms, because it has a closed-form solution per iteration while the existing ones always need to solve an L1/L2-SVM per iteration. Furthermore, by the low-rank approximation of the kernel matrix, UniSVM can solve the large-scale nonlinear problems with efficiency. To verify the efficacy and feasibility of the proposed algorithm, experiments on large benchmark data sets with/without outliers for classification and regression are investigated. UniSVM can be easily grasped by users or researchers because its core code in Matlab is less than 10 lines.

EW sensor technologies have contributed to the advent of "big data" in biomedicine, of which signal data are for example, saliency methods help visualize the activation of an important modality. From one-dimensional electrocardiography individual input features [5], while attribution methods like and electroencephalography signals from the heart and LIME [6] and SHAP [7] quantify the impact of each feature brain, to two-dimensional tissue images of tumor histology, to on the output predictions. However, these post hoc techniques three-dimensional magnetic resonance images, these consist are inadequate for developing simpler models. of sequential measures of an observable along one or more With regard to relevancy, studies report that people favor independent axes such as time, distance, or frequency. Signal explanations that are short, contrast instances with different data differ from structured forms of data in that the meaning outcomes, and highlight abnormal causes [8]. In other words, of each independent variable is not as distinctively and intuitively we seek to understand which features are important, and definable. Informative features must be extracted from how these affect the outcome. Data scientists often pursue these raw data using signal processing and machine learning these goals through feature selection, in addition to feature (ML) techniques before useful patterns can be detected and extraction, to ensure that their conclusions are based on leveraged to make predictions.

A common goal in network modeling is to uncover the latent community structure present among nodes. For many real-world networks, observed connections consist of events arriving as streams, which are then aggregated to form edges, ignoring the temporal dynamic component. A natural way to take account of this temporal dynamic component of interactions is to use point processes as the foundation of the network models for community detection. Computational complexity hampers the scalability of such approaches to large sparse networks. To circumvent this challenge, we propose a fast online variational inference algorithm for learning the community structure underlying dynamic event arrivals on a network using continuous-time point process latent network models. We provide regret bounds on the loss function of this procedure, giving theoretical guarantees on performance. The proposed algorithm is illustrated, using both simulation studies and real data, to have comparable performance in terms of community structure in terms of community recovery to non-online variants. Our proposed framework can also be readily modified to incorporate other popular network structures.

Along with the analysis of time-to-event data, it is common to assume that only partial information is given at hand. In the presence of right-censored data with covariates, the conditional Kaplan-Meier estimator (also referred as the Beran estimator) is known to propose a consistent estimate for the lifetimes conditional survival function. However, a necessary condition is the clear knowledge of whether each individual is censored or not, although, this information might be incomplete or even totally absent in practice. We thus propose a study on the Beran estimator when the censoring indicator is not clearly specified. From this, we provide a new estimator for the conditional survival function and establish its asymptotic normality under mild conditions. We further study the supervised learning problem where the conditional survival function is to be predicted with no censorship indicators. To this aim, we investigate various approaches estimating the conditional expectation for the censoring indicator. Along with the theoretical results, we illustrate how the estimators work for small samples by means of a simulation study and show their practical applicability with the analysis of synthetic data and the study of real data for the prognosis of monoclonal gammopathy.

Unsupervised graph representation learning aims to learn low-dimensional node embeddings without supervision while preserving graph topological structures and node attributive features. Previous graph neural networks (GNN) require a large number of labeled nodes, which may not be accessible in real-world graph data. In this paper, we present a novel cluster-aware graph neural network (CAGNN) model for unsupervised graph representation learning using self-supervised techniques. In CAGNN, we perform clustering on the node embeddings and update the model parameters by predicting the cluster assignments. Moreover, we observe that graphs often contain inter-class edges, which mislead the GNN model to aggregate noisy information from neighborhood nodes. We further refine the graph topology by strengthening intra-class edges and reducing node connections between different classes based on cluster labels, which better preserves cluster structures in the embedding space. We conduct comprehensive experiments on two benchmark tasks using real-world datasets. The results demonstrate the superior performance of the proposed model over existing baseline methods. Notably, our model gains over 7% improvements in terms of accuracy on node clustering over state-of-the-arts.

Multi Task Learning (MTL) efficiently leverages useful information c ontained in multiple related tasks to help improve the generalization performance of all tasks. This article conducts a large dimensional analysis of a simple but, as we shall see, extremely powerful when carefully tuned, Least Square Support Vector Machine (LSS VM) version of MTL, in the regime where the dimension p of the data and their number n grow large at the same rate. Under mild assumptions on the input data, the theoretical analysis o f the MTL-LSSVM algorithm first reveals the "sufficient statistics" exploited by the alg orithm and their interaction at work. These results demonstrate, as a striking consequ ence, that the standard approach to MTL-LSSVM is largely suboptimal, can lead to severe effe cts of negative transfer but that these impairments are easily corrected. These correctio ns are turned into an improved MTL-LSSVM algorithm which can only benefit from additional data, and the theoretical performance of which is also analyzed. As evidenced and theoretically sustained in numerous recent works, these large dimensional results are robust to broad ranges of data distributions, w hich our present experiments corroborate. Specifically, the article reports a systematic ally close behavior between theoretical and empirical performances on popular datasets, wh ich is strongly suggestive of the applicability of the proposed carefully tuned MTL-LSSVM method to real data. This fine-tuning is fully based on the theoretical analysis and does not in p articular require any cross validation procedure. Besides, the reported performance s on real datasets almost systematically outperform much more elaborate and less intuitive state -of-the-art multi-task and transfer learning methods.

Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic-clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These features defy any theoretical treatment that requires local or global quasi-uniformity of distribution of data sites. Incorporating a recently-developed application of integral operator theory in machine learning, we propose and study in the current article a new framework to analyze kernel interpolation of high dimensional data, which features bounding stochastic approximation error by a hybrid (discrete and continuous) $K$-functional tied to the spectrum of the underlying kernel matrix. Both theoretical analysis and numerical simulations show that spectra of kernel matrices are reliable and stable barometers for gauging the performance of kernel-interpolation methods for high dimensional data.