Multiple methods of finding the vertices belonging to a planted dense subgraph in a random dense $G(n, p)$ graph have been proposed, with an emphasis on planted cliques. Such methods can identify the planted subgraph in polynomial time, but are all limited to several subgraph structures. Here, we present PYGON, a graph neural network-based algorithm, which is insensitive to the structure of the planted subgraph. This is the first algorithm that uses advanced learning tools for recovering dense subgraphs. We show that PYGON can recover cliques of sizes $\Theta\left(\sqrt{n}\right)$, where $n$ is the size of the background graph, comparable with the state of the art. We also show that the same algorithm can recover multiple other planted subgraphs of size $\Theta\left(\sqrt{n}\right)$, in both directed and undirected graphs. We suggest a conjecture that no polynomial time PAC-learning algorithm can detect planted dense subgraphs with size smaller than $O\left(\sqrt{n}\right)$, even if in principle one could find dense subgraphs of logarithmic size.

Bitcoin is one of the decentralized cryptocurrencies powered by a peer-to-peer blockchain network. Parties who trade in the bitcoin network are not required to disclose any personal information. Such property of anonymity, however, precipitates potential malicious transactions to a certain extent. Indeed, various illegal activities such as money laundering, dark network trading, and gambling in the bitcoin network are nothing new now. While a proliferation of work has been developed to identify malicious bitcoin transactions, the behavior analysis and classification of bitcoin addresses are largely overlooked by existing tools. In this paper, we propose BAClassifier, a tool that can automatically classify bitcoin addresses based on their behaviors. Technically, we come up with the following three key designs. First, we consider casting the transactions of the bitcoin address into an address graph structure, of which we introduce a graph node compression technique and a graph structure augmentation method to characterize a unified graph representation. Furthermore, we leverage a graph feature network to learn the graph representations of each address and generate the graph embeddings. Finally, we aggregate all graph embeddings of an address into the address-level representation, and engage in a classification model to give the address behavior classification. As a side contribution, we construct and release a large-scale annotated dataset that consists of over 2 million real-world bitcoin addresses and concerns 4 types of address behaviors. Experimental results demonstrate that our proposed framework outperforms state-of-the-art bitcoin address classifiers and existing classification models, where the precision and F1-score are 96% and 95%, respectively. Our implementation and dataset are released, hoping to inspire others.

Skillful streamflow forecasts can inform decisions in various areas of water policy and management. We integrate numerical weather prediction ensembles, distributed hydrological model and machine learning to generate ensemble streamflow forecasts at medium-range lead times (1 - 7 days). We demonstrate a case study for machine learning applications in postprocessing ensemble streamflow forecasts in the Upper Susquehanna River basin in the eastern United States. Our results show that the machine learning postprocessor can improve streamflow forecasts relative to low complexity forecasts (e.g., climatological and temporal persistence) as well as standalone hydrometeorological modeling and neural network. The relative gain in forecast skill from postprocessor is generally higher at medium-range timescales compared to shorter lead times; high flows compared to low-moderate flows, and warm-season compared to cool ones. Overall, our results highlight the benefits of machine learning in many aspects for improving both the skill and reliability of streamflow forecasts.

A recent goal in the theory of deep learning is to identify how neural networks can escape the "lazy training," or Neural Tangent Kernel (NTK) regime, where the network is coupled with its first order Taylor expansion at initialization. While the NTK is minimax optimal for learning dense polynomials (Ghorbani et al, 2021), it cannot learn features, and hence has poor sample complexity for learning many classes of functions including sparse polynomials. Recent works have thus aimed to identify settings where gradient based algorithms provably generalize better than the NTK. One such example is the "QuadNTK" approach of Bai and Lee (2020), which analyzes the second-order term in the Taylor expansion. Bai and Lee (2020) show that the second-order term can learn sparse polynomials efficiently; however, it sacrifices the ability to learn general dense polynomials. In this paper, we analyze how gradient descent on a two-layer neural network can escape the NTK regime by utilizing a spectral characterization of the NTK (Montanari and Zhong, 2020) and building on the QuadNTK approach. We first expand upon the spectral analysis to identify "good" directions in parameter space in which we can move without harming generalization. Next, we show that a wide two-layer neural network can jointly use the NTK and QuadNTK to fit target functions consisting of a dense low-degree term and a sparse high-degree term -- something neither the NTK nor the QuadNTK can do on their own. Finally, we construct a regularizer which encourages our parameter vector to move in the "good" directions, and show that gradient descent on the regularized loss will converge to a global minimizer, which also has low test error. This yields an end to end convergence and generalization guarantee with provable sample complexity improvement over both the NTK and QuadNTK on their own.

Word feature vectors have been proven to improve many NLP tasks. With recent advances in unsupervised learning of these feature vectors, it became possible to train it with much more data, which also resulted in better quality of learned features. Since it learns joint probability of latent features of words, it has the advantage that we can train it without any prior knowledge about the goal task we want to solve. We aim to evaluate the universal applicability property of feature vectors, which has been already proven to hold for many standard NLP tasks like part-of-speech tagging or syntactic parsing. In our case, we want to understand the topical focus of text documents and design an efficient representation suitable for discriminating different topics. The discriminativeness can be evaluated adequately on text categorisation task. We propose a novel method to extract discriminative keywords from documents. We utilise word feature vectors to understand the relations between words better and also understand the latent topics which are discussed in the text and not mentioned directly but inferred logically. We also present a simple way to calculate document feature vectors out of extracted discriminative words. We evaluate our method on the four most popular datasets for text categorisation. We show how different discriminative metrics influence the overall results. We demonstrate the effectiveness of our approach by achieving state-of-the-art results on text categorisation task using just a small number of extracted keywords. We prove that word feature vectors can substantially improve the topical inference of documents' meaning. We conclude that distributed representation of words can be used to build higher levels of abstraction as we demonstrate and build feature vectors of documents.

Gaussian smoothing (GS) is a derivative-free optimization (DFO) algorithm that estimates the gradient of an objective using perturbations of the current parameters sampled from a standard normal distribution. We generalize it to sampling perturbations from a larger family of distributions. Based on an analysis of DFO for non-convex functions, we propose to choose a distribution for perturbations that minimizes the mean squared error (MSE) of the gradient estimate. We derive three such distributions with provably smaller MSE than Gaussian smoothing. We conduct evaluations of the three sampling distributions on linear regression, reinforcement learning, and DFO benchmarks in order to validate our claims. Our proposal improves on GS with the same computational complexity, and are usually competitive with and often outperform Guided ES and Orthogonal ES, two computationally more expensive algorithms that adapt the covariance matrix of normally distributed perturbations.

Most existing fuzzy set methods use points as their input, which is the finest granularity from the perspective of granular computing. Consequently, these methods are neither efficient nor robust to label noise. Therefore, we propose a frame-work called granular-ball fuzzy set by introducing granular-ball computing into fuzzy set. The computational framework is based on the granular-balls input rather than points; therefore, it is more efficient and robust than traditional fuzzy methods, and can be used in various fields of fuzzy data processing according to its extensibility. Furthermore, the framework is extended to the classifier fuzzy support vector machine (FSVM), to derive the granular ball fuzzy SVM (GBFSVM). The experimental results demonstrate the effectiveness and efficiency of GBFSVM.

With the rapid development of information technologies, centralized data processing is subject to many limitations, such as computational overheads, communication delays, and data privacy leakage. Decentralized data processing over networked terminal nodes becomes an important technology in the era of big data. Dictionary learning is a powerful representation learning method to exploit the low-dimensional structure from the high-dimensional data. By exploiting the low-dimensional structure, the storage and the processing overhead of data can be effectively reduced. In this paper, we propose a novel decentralized complete dictionary learning algorithm, which is based on $\ell^{4}$-norm maximization. Compared with existing decentralized dictionary learning algorithms, comprehensive numerical experiments show that the novel algorithm has significant advantages in terms of per-iteration computational complexity, communication cost, and convergence rate in many scenarios. Moreover, a rigorous theoretical analysis shows that the dictionaries learned by the proposed algorithm can converge to the one learned by a centralized dictionary learning algorithm at a linear rate with high probability under certain conditions.

Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ) devices and usage for solving all types of machine learning problems. Kernel methods rely on the notion of similarity between points in a higher (possibly infinite) dimensional feature space. For machine learning, the notion of similarity assumes that points close in the feature space should be close in the machine learning task space. In this paper, we discuss the use of variational quantum kernels with task-specific quantum metric learning to generate optimal quantum embeddings (a.k.a. quantum feature encodings) that are specific to machine learning tasks. Such task-specific optimal quantum embeddings, implicitly supporting feature selection, are valuable not only to quantum kernel methods in improving the latter's performance, but they can also be valuable to non-kernel QML methods based on parameterized quantum circuits (PQCs) as pretrained embeddings and for transfer learning. This further demonstrates the quantum utility, and quantum advantage (with classically-intractable quantum embeddings), of quantum kernel methods.

This paper presents a computationally efficient variant of gradient boosting for multi-class classification and multi-output regression tasks. Standard gradient boosting uses a 1-vs-all strategy for classifications tasks with more than two classes. This strategy translates in that one tree per class and iteration has to be trained. In this work, we propose the use of multi-output regressors as base models to handle the multi-class problem as a single task. In addition, the proposed modification allows the model to learn multi-output regression problems. An extensive comparison with other multi-ouptut based gradient boosting methods is carried out in terms of generalization and computational efficiency. The proposed method showed the best trade-off between generalization ability and training and predictions speeds.