Most theoretical studies explaining the regularization effect in deep learning have only focused on gradient descent with a sufficient small learning rate or even gradient flow (infinitesimal learning rate). Such researches, however, have neglected a reasonably large learning rate applied in most practical applications. In this work, we characterize the implicit bias effect of deep linear networks for binary classification using the logistic loss in the large learning rate regime, inspired by the seminal work by Lewkowycz et al. [26] in a regression setting with squared loss. They found a learning rate regime with a large stepsize named the catapult phase, where the loss grows at the early stage of training and eventually converges to a minimum that is flatter than those found in the small learning rate regime. We claim that depending on the separation conditions of data, the gradient descent iterates will converge to a flatter minimum in the catapult phase. We rigorously prove this claim under the assumption of degenerate data by overcoming the difficulty of the non-constant Hessian of logistic loss and further characterize the behavior of loss and Hessian for non-separable data. Finally, we demonstrate that flatter minima in the space spanned by non-separable data along with the learning rate in the catapult phase can lead to better generalization empirically.

We describe mechanisms for the allocation of a scarce resource among multiple users in a way that is efficient, fair, and strategy-proof, but when users do not know their resource requirements. The mechanism is repeated for multiple rounds and a user's requirements can change on each round. At the end of each round, users provide feedback about the allocation they received, enabling the mechanism to learn user preferences over time. Such situations are common in the shared usage of a compute cluster among many users in an organisation, where all teams may not precisely know the amount of resources needed to execute their jobs. By understating their requirements, users will receive less than they need and consequently not achieve their goals. By overstating them, they may siphon away precious resources that could be useful to others in the organisation. We formalise this task of online learning in fair division via notions of efficiency, fairness, and strategy-proofness applicable to this setting, and study this problem under three types of feedback: when the users' observations are deterministic, when they are stochastic and follow a parametric model, and when they are stochastic and nonparametric. We derive mechanisms inspired by the classical max-min fairness procedure that achieve these requisites, and quantify the extent to which they are achieved via asymptotic rates. We corroborate these insights with an experimental evaluation on synthetic problems and a web-serving task.

The main aim in ensemble learning is using multiple individual classifiers outputs rather than one classifier output to aggregate them for more accurate classification. Generating an ensemble classifier generally is composed of three steps: selecting the base classifier, applying a sampling strategy to generate different individual classifiers and aggregation the classifiers outputs. This paper focuses on the classifiers outputs aggregation step and presents a new interval-based aggregation modeling using bagging resampling approach and Interval Agreement Approach (IAA) in ensemble learning. IAA is an interesting and practical aggregation approach in decision making which was introduced to combine decision makers opinions when they present their opinions by intervals. In this paper, in addition to implementing a new aggregation approach in ensemble learning, we designed some experiments to encourage researchers to use interval modeling in ensemble learning because it preserves more uncertainty and this leads to more accurate classification. For this purpose, we compared the results of implementing the proposed method to the majority vote as the most common and successful aggregation function in the literature on 10 medical data sets to show the better performance of the interval modeling and the proposed interval-based aggregation function in binary classification when it comes to ensemble learning. The results confirm the good performance of our proposed approach.

Expressivity plays a fundamental role in evaluating deep neural networks, and it is closely related to understanding the limit of performance improvement. In this paper, we propose a three-pipeline training framework based on critical expressivity, including global model contraction, weight evolution, and link's weight rewiring. Specifically, we propose a pyramidal-like skeleton to overcome the saddle points that affect information transfer. Then we analyze the reason for the modularity (clustering) phenomenon in network topology and use it to rewire potential erroneous weighted links. We conduct numerical experiments on node classification and the results confirm that the proposed training framework leads to a significantly improved performance in terms of fast convergence and robustness to potential erroneous weighted links. The architecture design on GNNs, in turn, verifies the expressivity of GNNs from dynamics and topological space aspects and provides useful guidelines in designing more efficient neural networks.

Most deep neural networks are considered to be black boxes, meaning their output is hard to interpret. In contrast, logical expressions are considered to be more comprehensible since they use symbols that are semantically close to natural language instead of distributed representations. However, for high-dimensional input data such as images, the individual symbols, i.e. pixels, are not easily interpretable. We introduce the concept of first-order convolutional rules, which are logical rules that can be extracted using a convolutional neural network (CNN), and whose complexity depends on the size of the convolutional filter and not on the dimensionality of the input. Our approach is based on rule extraction from binary neural networks with stochastic local search. We show how to extract rules that are not necessarily short, but characteristic of the input, and easy to visualize. Our experiments show that the proposed approach is able to model the functionality of the neural network while at the same time producing interpretable logical rules.

Classification of quantum data is essential for quantum machine learning and near-term quantum technologies. In this paper, we propose a new hybrid quantum-classical framework for supervised quantum learning, which we call Variational Shadow Quantum Learning (VSQL). Our method in particular utilizes the classical shadows of quantum data, which fundamentally represent the side information of quantum data with respect to certain physical observables. Specifically, we first use variational shadow quantum circuits to extract classical features in a convolution way and then utilize a fully-connected neural network to complete the classification task. We show that this method could sharply reduce the number of parameters and thus better facilitate quantum circuit training. Simultaneously, less noise will be introduced since fewer quantum gates are employed in such shadow circuits. Moreover, we show that the Barren Plateau issue, a significant gradient vanishing problem in quantum machine learning, could be avoided in VSQL. Finally, we demonstrate the efficiency of VSQL in quantum classification via numerical experiments on the classification of quantum states and the recognition of multi-labeled handwritten digits. In particular, our VSQL approach outperforms existing variational quantum classifiers in the test accuracy in the binary case of handwritten digit recognition and notably requires much fewer parameters.

Systematic literature reviews (SLRs) are at the heart of evidence-based research, setting the foundation for future research and practice. However, producing good quality timely contributions is a challenging and highly cognitive endeavor, which has lately motivated the exploration of automation and support in the SLR process. In this paper we address an often overlooked phase in this process, that of planning literature reviews, and explore under the lenses of cognitive process augmentation how to overcome its most salient challenges. In doing so, we report on the insights from 24 SLR authors on planning practices, its challenges as well as feedback on support strategies inspired by recent advances in cognitive computing.

With the continuous development of NoSQL databases, more and more developers choose to use semi-structured data for development and data management, which puts forward requirements for schema management of semi-structured data stored in NoSQL databases. Schema extraction plays an important role in understanding schemas, optimizing queries, and validating data consistency. Therefore, in this survey we investigate structural methods based on tree and graph and statistical methods based on distributed architecture and machine learning to extract schemas. The schemas obtained by the structural methods are more interpretable, and the statistical methods have better applicability and generalization ability. Moreover, we also investigate tools and systems for schemas extraction. Schema extraction tools are mainly used for spark or NoSQL databases, and are suitable for small datasets or simple application environments. The system mainly focuses on the extraction and management of schemas in large data sets and complex application scenarios. Furthermore, we also compare these techniques to facilitate data managers' choice.

Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues (resp. singular values) and eigenvectors (resp. singular vectors) of some properly designed matrices constructed from data. A diverse array of applications have been found in machine learning, data science, and signal processing. Due to their simplicity and effectiveness, spectral methods are not only used as a stand-alone estimator, but also frequently employed to initialize other more sophisticated algorithms to improve performance. While the studies of spectral methods can be traced back to classical matrix perturbation theory and methods of moments, the past decade has witnessed tremendous theoretical advances in demystifying their efficacy through the lens of statistical modeling, with the aid of non-asymptotic random matrix theory. This monograph aims to present a systematic, comprehensive, yet accessible introduction to spectral methods from a modern statistical perspective, highlighting their algorithmic implications in diverse large-scale applications. In particular, our exposition gravitates around several central questions that span various applications: how to characterize the sample efficiency of spectral methods in reaching a target level of statistical accuracy, and how to assess their stability in the face of random noise, missing data, and adversarial corruptions? In addition to conventional $\ell_2$ perturbation analysis, we present a systematic $\ell_{\infty}$ and $\ell_{2,\infty}$ perturbation theory for eigenspace and singular subspaces, which has only recently become available owing to a powerful "leave-one-out" analysis framework.

Analysis of water and environmental data is an important aspect of many intelligent water and environmental system applications where inference from such analysis plays a significant role in decision making. Quite often these data that are collected through sensible sensors can be anomalous due to different reasons such as systems breakdown, malfunctioning of sensor detectors, and more. Regardless of their root causes, such data severely affect the results of the subsequent analysis. This paper demonstrates data cleaning and preparation for time-series data and further proposes cost-sensitive machine learning algorithms as a solution to detect anomalous data points in time-series data. The following models: Logistic Regression, Random Forest, Support Vector Machines have been modified to support the cost-sensitive learning which penalizes misclassified samples thereby minimizing the total misclassification cost. Our results showed that Random Forest outperformed the rest of the models at predicting the positive class (i.e anomalies). Applying predictive model improvement techniques like data oversampling seems to provide little or no improvement to the Random Forest model. Interestingly, with recursive feature elimination, we achieved a better model performance thereby reducing the dimensions in the data. Finally, with Influxdb and Kapacitor the data was ingested and streamed to generate new data points to further evaluate the model performance on unseen data, this will allow for early recognition of undesirable changes in the drinking water quality and will enable the water supply companies to rectify on a timely basis whatever undesirable changes abound.