This paper aims to explore the application of machine learning in forecasting Chinese macroeconomic variables. Specifically, it employs various machine learning models to predict the quarterly real GDP growth of China, and analyzes the factors contributing to the performance differences among these models. Our findings indicate that the average forecast errors of machine learning models are generally lower than those of traditional econometric models or expert forecasts, particularly in periods of economic stability. However, during certain inflection points, although machine learning models still outperform traditional econometric models, expert forecasts may exhibit greater accuracy in some instances due to experts' more comprehensive understanding of the macroeconomic environment and real-time economic variables. In addition to macroeconomic forecasting, this paper employs interpretable machine learning methods to identify the key attributive variables from different machine learning models, aiming to enhance the understanding and evaluation of their contributions to macroeconomic fluctuations.

Analyzing time-series data that may contain personal information, particularly in the medical field, presents serious privacy concerns. Sensitive health data from patients is often used to train machine-learning models for diagnostics and ongoing care. Assessing the privacy risk of such models is crucial to making knowledgeable decisions on whether to use a model in production, share it with third parties, or deploy it in patients' homes. Membership Inference Attacks (MIA) are a key method for this kind of evaluation, however time-series prediction models have not been thoroughly studied in this context. We explore existing MIA techniques on time-series models, and introduce new features, focusing on the seasonality and trend components of the data. Seasonality is estimated using a multivariate Fourier transform, and a low-degree polynomial is used to approximate trends. We applied these techniques to various types of time-series models, using datasets from the health domain. Our results demonstrate that these new features enhance the effectiveness of MIAs in identifying membership, improving the understanding of privacy risks in medical data applications.

The growing success of deep learning in various domains has prompted investigations into its application to tabular data, where deep models have shown promising results compared to traditional tree-based methods. In this paper, we revisit Neighborhood Component Analysis (NCA), a classic tabular prediction method introduced in 2004, designed to learn a linear projection that captures semantic similarities between instances. We find that minor modifications, such as adjustments to the learning objectives and the integration of deep learning architectures, significantly enhance NCA's performance, enabling it to surpass most modern deep tabular models. Additionally, we introduce a stochastic neighbor sampling strategy that improves both the efficiency and predictive accuracy of our proposed ModernNCA -- sampling only a subset of neighbors during training, while utilizing the entire neighborhood during inference. Extensive experiments demonstrate that our ModernNCA achieves state-of-the-art results in both classification and regression tasks across various tabular datasets, outperforming both tree-based and other deep tabular models, while also reducing training time and model size.

In the age of big data and advanced computational methods, the prediction of large-scale social behaviors, reminiscent of Isaac Asimov's fictional science of Psychohistory, is becoming increasingly feasible. This paper consists of a theoretical exploration of the integration of computational power and mathematical frameworks, particularly through Topological Data Analysis (TDA) (Carlsson, Vejdemo-Johansson, 2022) and Artificial Intelligence (AI), to forecast societal trends through social media data analysis. By examining social media as a reflective surface of collective human behavior through the systematic behaviorist approach (Glenn, et al., 2016), I argue that these tools provide unprecedented clarity into the dynamics of large communities. This study dialogues with Asimov's work, drawing parallels between his visionary concepts and contemporary methodologies, illustrating how modern computational techniques can uncover patterns and predict shifts in social behavior, contributing to the emerging field of digital sociology -- or even, Psychohistory itself.

Explainable Artificial Intelligence (XAI) has become a widely discussed topic, the related technologies facilitate better understanding of conventional black-box models like Random Forest, Neural Networks and etc. However, domain-specific applications of XAI are still insufficient. To fill this gap, this research analyzes various machine learning models to the tasks of binary and multi-class classification for intrusion detection from network traffic on the same dataset using occlusion sensitivity. The models evaluated include Linear Regression, Logistic Regression, Linear Support Vector Machine (SVM), K-Nearest Neighbors (KNN), Random Forest, Decision Trees, and Multi-Layer Perceptrons (MLP). We trained all models to the accuracy of 90\% on the UNSW-NB15 Dataset. We found that most classifiers leverage only less than three critical features to achieve such accuracies, indicating that effective feature engineering could actually be far more important for intrusion detection than applying complicated models. We also discover that Random Forest provides the best performance in terms of accuracy, time efficiency and robustness. Data and code available at https://github.com/pcwhy/XML-IntrusionDetection.git

Optimization algorithms is crucial in training physics-informed neural networks (PINNs), unsuitable methods may lead to poor solutions. Compared to the common gradient descent algorithm, implicit gradient descent (IGD) outperforms it in handling some multi-scale problems. In this paper, we provide convergence analysis for the implicit gradient descent for training over-parametrized two-layer PINNs. We first demonstrate the positive definiteness of Gram matrices for general smooth activation functions, like sigmoidal function, softplus function, tanh function and so on. Then the over-parameterization allows us to show that the randomly initialized IGD converges a globally optimal solution at a linear convergence rate. Moreover, due to the different training dynamics, the learning rate of IGD can be chosen independent of the sample size and the least eigenvalue of the Gram matrix.

Graph Neural Networks (GNNs), especially message-passing-based models, have become prominent in top-k recommendation tasks, outperforming matrix factorization models due to their ability to efficiently aggregate information from a broader context. Although GNNs are evaluated with ranking-based metrics, e.g. NDCG@k and Recall@k, they remain largely trained with proxy losses, e.g. the BPR loss. In this work we explore the use of ranking loss functions to directly optimize the evaluation metrics, an area not extensively investigated in the GNN community for collaborative filtering. We take advantage of smooth approximations of the rank to facilitate end-to-end training of GNNs and propose a Personalized PageRank-based negative sampling strategy tailored for ranking loss functions. Moreover, we extend the evaluation of GNN models for top-k recommendation tasks with an inductive user-centric protocol, providing a more accurate reflection of real-world applications. Our proposed method significantly outperforms the standard BPR loss and more advanced losses across four datasets and four recent GNN architectures while also exhibiting faster training.

Recent research has shown that quasar-convexity can be found in applications such as identification of linear dynamical systems and generalized linear models. Such observations have in turn spurred exciting developments in design and analysis algorithms that exploit quasar-convexity. In this work, we study the online stochastic quasar-convex optimization problems in a dynamic environment. We establish regret bounds of online gradient descent in terms of cumulative path variation and cumulative gradient variance for losses satisfying quasar-convexity and strong quasar-convexity. We then apply the results to generalized linear models (GLM) when the underlying parameter is time-varying. We establish regret bounds of online gradient descent when applying to GLMs with leaky ReLU activation function, logistic activation function, and ReLU activation function. Numerical results are presented to corroborate our findings.

A vertex exchange method is proposed for solving the strongly convex quadratic program subject to the generalized simplex constraint. We conduct rigorous convergence analysis for the proposed algorithm and demonstrate its essential roles in solving some important classes of constrained convex optimization. To get a feasible initial point to execute the algorithm, we also present and analyze a highly efficient semismooth Newton method for computing the projection onto the generalized simplex. The excellent practical performance of the proposed algorithms is demonstrated by a set of extensive numerical experiments. Our theoretical and numerical results further motivate the potential applications of the considered model and the proposed algorithms.

In this paper, we present an information-theoretic method for clustering mixed-type data, that is, data consisting of both continuous and categorical variables. The method is a variant of the Deterministic Information Bottleneck algorithm which optimally compresses the data while retaining relevant information about the underlying structure. We compare the performance of the proposed method to that of three well-established clustering methods (KAMILA, K-Prototypes, and Partitioning Around Medoids with Gower's dissimilarity) on simulated and real-world datasets. The results demonstrate that the proposed approach represents a competitive alternative to conventional clustering techniques under specific conditions.