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Exponents and logarithms are fundamental components in many important applications such as logistic regression, maximum likelihood, relative entropy, and so on. Since the exponential cone can be viewed as the epigraph of perspective of the natural exponential function or the hypograph of perspective of the natural logarithm function, many mixed-integer convex programs involving exponential or logarithm functions can be recast as mixed-integer exponential conic programs (MIECPs). However, unlike mixed-integer linear programs (MILPs) and mixed-integer second-order conic programs (MISOCPs), MIECPs are still under development. To harvest the past efforts on MILPs and MISOCPs, this paper presents second-order conic (SOC) and polyhedral approximation schemes for the exponential cone with application to MIECPs. To do so, we first extend and generalize existing SOC approximation approaches in the extended space, propose new scaling and shifting methods, prove approximation accuracies, and derive lower bounds of approximations. We then study the polyhedral outer approximation of the exponential cones in the original space using gradient inequalities, show its approximation accuracy, and derive a lower bound of the approximation. When implementing SOC approximations, we suggest learning the approximation pattern by testing smaller cases and then applying it to the large-scale ones; and for the polyhedral approximation, we suggest using the branch and cut method for MIECPs. Our numerical study shows that the proposed methods show speed-ups over solver MOSEK for MIECPs, and the scaling, shifting, and polyhedral outer approximation methods work very well., Comment: 37 pages, 9 figures

Arrhythmia is a cardiovascular disease that manifests irregular heartbeats. In arrhythmia detection, the electrocardiogram (ECG) signal is an important diagnostic technique. However, manually evaluating ECG signals is a complicated and time-consuming task. With the application of convolutional neural networks (CNNs), the evaluation process has been accelerated and the performance is improved. It is noteworthy that the performance of CNNs heavily depends on their architecture design, which is a complex process grounded on expert experience and trial-and-error. In this paper, we propose a novel approach, Heart-Darts, to efficiently classify the ECG signals by automatically designing the CNN model with the differentiable architecture search (i.e., Darts, a cell-based neural architecture search method). Specifically, we initially search a cell architecture by Darts and then customize a novel CNN model for ECG classification based on the obtained cells. To investigate the efficiency of the proposed method, we evaluate the constructed model on the MIT-BIH arrhythmia database. Additionally, the extensibility of the proposed CNN model is validated on two other new databases. Extensive experimental results demonstrate that the proposed method outperforms several state-of-the-art CNN models in ECG classification in terms of both performance and generalization capability.

Bitcoin, one of the major cryptocurrencies, presents great opportunities and challenges with its tremendous potential returns accompanying high risks. The high volatility of Bitcoin and the complex factors affecting them make the study of effective price forecasting methods of great practical importance to financial investors and researchers worldwide. In this paper, we propose a novel approach called MRC-LSTM, which combines a Multi-scale Residual Convolutional neural network (MRC) and a Long Short-Term Memory (LSTM) to implement Bitcoin closing price prediction. Specifically, the Multi-scale residual module is based on one-dimensional convolution, which is not only capable of adaptive detecting features of different time scales in multivariate time series, but also enables the fusion of these features. LSTM has the ability to learn long-term dependencies in series, which is widely used in financial time series forecasting. By mixing these two methods, the model is able to obtain highly expressive features and efficiently learn trends and interactions of multivariate time series. In the study, the impact of external factors such as macroeconomic variables and investor attention on the Bitcoin price is considered in addition to the trading information of the Bitcoin market. We performed experiments to predict the daily closing price of Bitcoin (USD), and the experimental results show that MRC-LSTM significantly outperforms a variety of other network structures. Furthermore, we conduct additional experiments on two other cryptocurrencies, Ethereum and Litecoin, to further confirm the effectiveness of the MRC-LSTM in short-term forecasting for multivariate time series of cryptocurrencies.

In educational applications, Knowledge Tracing (KT), the problem of accurately predicting students' responses to future questions by summarizing their knowledge states, has been widely studied for decades as it is considered a fundamental task towards adaptive online learning. Among all the proposed KT methods, Deep Knowledge Tracing (DKT) and its variants are by far the most effective ones due to the high flexibility of the neural network. However, DKT often ignores the inherent differences between students (e.g. memory skills, reasoning skills, ...), averaging the performances of all students, leading to the lack of personalization, and therefore was considered insufficient for adaptive learning. To alleviate this problem, in this paper, we proposed Leveled Attentive KNowledge TrAcing (LANA), which firstly uses a novel student-related features extractor (SRFE) to distill students' unique inherent properties from their respective interactive sequences. Secondly, the pivot module was utilized to dynamically reconstruct the decoder of the neural network on attention of the extracted features, successfully distinguishing the performance between students over time. Moreover, inspired by Item Response Theory (IRT), the interpretable Rasch model was used to cluster students by their ability levels, and thereby utilizing leveled learning to assign different encoders to different groups of students. With pivot module reconstructed the decoder for individual students and leveled learning specialized encoders for groups, personalized DKT was achieved. Extensive experiments conducted on two real-world large-scale datasets demonstrated that our proposed LANA improves the AUC score by at least 1.00% (i.e. EdNet 1.46% and RAIEd2020 1.00%), substantially surpassing the other State-Of-The-Art KT methods., Comment: EDM2021

As an important problem in modern data analytics, classification has witnessed varieties of applications from different domains. Different from conventional classification approaches, fair classification concerns the issues of unintentional biases against the sensitive features (e.g., gender, race). Due to high nonconvexity of fairness measures, existing methods are often unable to model exact fairness, which can cause inferior fair classification outcomes. This paper fills the gap by developing a novel unified framework to jointly optimize accuracy and fairness. The proposed framework is versatile and can incorporate different fairness measures studied in literature precisely as well as can be applicable to many classifiers including deep classification models. Specifically, in this paper, we first prove Fisher consistency of the proposed framework. We then show that many classification models within this framework can be recast as mixed-integer convex programs, which can be solved effectively by off-the-shelf solvers when the instance sizes are moderate and can be used as benchmarks to compare the efficiency of approximation algorithms. We prove that in the proposed framework, when the classification outcomes are known, the resulting problem, termed "unbiased subdata selection," is strongly polynomial-solvable and can be used to enhance the classification fairness by selecting more representative data points. This motivates us to develop an iterative refining strategy (IRS) to solve the large-scale instances, where we improve the classification accuracy and conduct the unbiased subdata selection in an alternating fashion. We study the convergence property of IRS and derive its approximation bound. More broadly, this framework can be leveraged to improve classification models with unbalanced data by taking F1 score into consideration., Comment: 42 pages, 4 Figures