Lei Shi

Zhuoqing Song, Weijian Li, Kexin Jin et al.

Decentralized optimization is an emerging paradigm in distributed learning in which agents achieve network-wide solutions by peer-to-peer communication without the central server. Since communication tends to be slower than computation, when each agent communicates with only a few neighboring agents per iteration, they can complete iterations faster than with more agents or a central server. However, the total number of iterations to reach a network-wide solution is affected by the speed at which the agents' information is ``mixed'' by communication. We found that popular communication topologies either have large maximum degrees (such as stars and complete graphs) or are ineffective at mixing information (such as rings and grids). To address this problem, we propose a new family of topologies, EquiTopo, which has an (almost) constant degree and a network-size-independent consensus rate that is used to measure the mixing efficiency. In the proposed family, EquiStatic has a degree of $Θ(\ln(n))$, where $n$ is the network size, and a series of time-dependent one-peer topologies, EquiDyn, has a constant degree of 1. We generate EquiDyn through a certain random sampling procedure. Both of them achieve an $n$-independent consensus rate. We apply them to decentralized SGD and decentralized gradient tracking and obtain faster communication and better convergence, theoretically and empirically. Our code is implemented through BlueFog and available at \url{https://github.com/kexinjinnn/EquiTopo}

Zhen Lei, Lei Shi, Chenyu Zeng

Implementing deep neural networks for learning the solution maps of parametric partial differential equations (PDEs) turns out to be more efficient than using many conventional numerical methods. However, limited theoretical analyses have been conducted on this approach. In this study, we investigate the expressive power of deep rectified quadratic unit (ReQU) neural networks for approximating the solution maps of parametric PDEs. The proposed approach is motivated by the recent important work of G. Kutyniok, P. Petersen, M. Raslan and R. Schneider (Gitta Kutyniok, Philipp Petersen, Mones Raslan, and Reinhold Schneider. A theoretical analysis of deep neural networks and parametric pdes. Constructive Approximation, pages 1-53, 2021), which uses deep rectified linear unit (ReLU) neural networks for solving parametric PDEs. In contrast to the previously established complexity-bound $\mathcal{O}\left(d^3\log_{2}^{q}(1/ ε) \right)$ for ReLU neural networks, we derive an upper bound $\mathcal{O}\left(d^3\log_{2}^{q}\log_{2}(1/ ε) \right)$ on the size of the deep ReQU neural network required to achieve accuracy $ε>0$, where $d$ is the dimension of reduced basis representing the solutions. Our method takes full advantage of the inherent low-dimensionality of the solution manifolds and better approximation performance of deep ReQU neural networks. Numerical experiments are performed to verify our theoretical result.

Zheng-Chu Guo, Andreas Christmann, Lei Shi

In this paper, we study an online learning algorithm with a robust loss function $\mathcal{L}_σ$ for regression over a reproducing kernel Hilbert space (RKHS). The loss function $\mathcal{L}_σ$ involving a scaling parameter $σ>0$ can cover a wide range of commonly used robust losses. The proposed algorithm is then a robust alternative for online least squares regression aiming to estimate the conditional mean function. For properly chosen $σ$ and step size, we show that the last iterate of this online algorithm can achieve optimal capacity independent convergence in the mean square distance. Moreover, if additional information on the underlying function space is known, we also establish optimal capacity dependent rates for strong convergence in RKHS. To the best of our knowledge, both of the two results are new to the existing literature of online learning.

Xin Guo, Zheng-Chu Guo, Lei Shi

This article provides convergence analysis of online stochastic gradient descent algorithms for functional linear models. Adopting the characterizations of the slope function regularity, the kernel space capacity, and the capacity of the sampling process covariance operator, significant improvement on the convergence rates is achieved. Both prediction problems and estimation problems are studied, where we show that capacity assumption can alleviate the saturation of the convergence rate as the regularity of the target function increases. We show that with properly selected kernel, capacity assumptions can fully compensate for the regularity assumptions for prediction problems (but not for estimation problems). This demonstrates the significant difference between the prediction problems and the estimation problems in functional data analysis.

Yuan Mao, Lei Shi, Zheng-Chu Guo

In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on the coefficients and kernels are assumed to be indefinite. The algorithm involves two stages of sampling, the first stage sample consists of distributions and the second stage sample is obtained from these distributions. Asymptotic behaviors of the algorithm in different regularity ranges of the regression function are comprehensively studied and learning rates are derived via integral operator techniques. We get the optimal rates under some mild conditions, which matches the one-stage sampled minimax optimal rate. Compared with the kernel methods for distribution regression in the literature, the algorithm under consideration does not require the kernel to be symmetric and positive semi-definite and hence provides a simple paradigm for designing indefinite kernel methods, which enriches the theme of the distribution regression. To the best of our knowledge, this is the first result for distribution regression with indefinite kernels, and our algorithm can improve the saturation effect.

Matteo Bortoletto, Constantin Ruhdorfer, Lei Shi et al.

We propose MToMnet - a Theory of Mind (ToM) neural network for predicting beliefs and their dynamics during human social interactions from multimodal input. ToM is key for effective nonverbal human communication and collaboration, yet, existing methods for belief modelling have not included explicit ToM modelling or have typically been limited to one or two modalities. MToMnet encodes contextual cues (scene videos and object locations) and integrates them with person-specific cues (human gaze and body language) in a separate MindNet for each person. Inspired by prior research on social cognition and computational ToM, we propose three different MToMnet variants: two involving fusion of latent representations and one involving re-ranking of classification scores. We evaluate our approach on two challenging real-world datasets, one focusing on belief prediction, while the other examining belief dynamics prediction. Our results demonstrate that MToMnet surpasses existing methods by a large margin while at the same time requiring a significantly smaller number of parameters. Taken together, our method opens up a highly promising direction for future work on artificial intelligent systems that can robustly predict human beliefs from their non-verbal behaviour and, as such, more effectively collaborate with humans.

Guanhang Lei, Lei Shi

Regularized pairwise ranking with Gaussian kernels is one of the cutting-edge learning algorithms. Despite a wide range of applications, a rigorous theoretical demonstration still lacks to support the performance of such ranking estimators. This work aims to fill this gap by developing novel oracle inequalities for regularized pairwise ranking. With the help of these oracle inequalities, we derive fast learning rates of Gaussian ranking estimators under a general box-counting dimension assumption on the input domain combined with the noise conditions or the standard smoothness condition. Our theoretical analysis improves the existing estimates and shows that a low intrinsic dimension of input space can help the rates circumvent the curse of dimensionality.

Susanne Hindennach, Lei Shi, Filip Miletić et al.

When users perceive AI systems as mindful, independent agents, they hold them responsible instead of the AI experts who created and designed these systems. So far, it has not been studied whether explanations support this shift in responsibility through the use of mind-attributing verbs like "to think". To better understand the prevalence of mind-attributing explanations we analyse AI explanations in 3,533 explainable AI (XAI) research articles from the Semantic Scholar Open Research Corpus (S2ORC). Using methods from semantic shift detection, we identify three dominant types of mind attribution: (1) metaphorical (e.g. "to learn" or "to predict"), (2) awareness (e.g. "to consider"), and (3) agency (e.g. "to make decisions"). We then analyse the impact of mind-attributing explanations on awareness and responsibility in a vignette-based experiment with 199 participants. We find that participants who were given a mind-attributing explanation were more likely to rate the AI system as aware of the harm it caused. Moreover, the mind-attributing explanation had a responsibility-concealing effect: Considering the AI experts' involvement lead to reduced ratings of AI responsibility for participants who were given a non-mind-attributing or no explanation. In contrast, participants who read the mind-attributing explanation still held the AI system responsible despite considering the AI experts' involvement. Taken together, our work underlines the need to carefully phrase explanations about AI systems in scientific writing to reduce mind attribution and clearly communicate human responsibility.

Huijie Guo, Ying Ba, Jie Hu et al.

Self-Supervised Learning (SSL) methods harness the concept of semantic invariance by utilizing data augmentation strategies to produce similar representations for different deformations of the same input. Essentially, the model captures the shared information among multiple augmented views of samples, while disregarding the non-shared information that may be beneficial for downstream tasks. To address this issue, we introduce a module called CompMod with Meta Comprehensive Regularization (MCR), embedded into existing self-supervised frameworks, to make the learned representations more comprehensive. Specifically, we update our proposed model through a bi-level optimization mechanism, enabling it to capture comprehensive features. Additionally, guided by the constrained extraction of features using maximum entropy coding, the self-supervised learning model learns more comprehensive features on top of learning consistent features. In addition, we provide theoretical support for our proposed method from information theory and causal counterfactual perspective. Experimental results show that our method achieves significant improvement in classification, object detection and instance segmentation tasks on multiple benchmark datasets.

Zhaoxing Li, Vahid Yazdanpanah, Jindi Wang et al.

The integration of AI in education offers significant potential to enhance learning efficiency. Large Language Models (LLMs), such as ChatGPT, Gemini, and Llama, allow students to query a wide range of topics, providing unprecedented flexibility. However, LLMs face challenges, such as handling varying content relevance and lack of personalization. To address these challenges, we propose TutorLLM, a personalized learning recommender LLM system based on Knowledge Tracing (KT) and Retrieval-Augmented Generation (RAG). The novelty of TutorLLM lies in its unique combination of KT and RAG techniques with LLMs, which enables dynamic retrieval of context-specific knowledge and provides personalized learning recommendations based on the student's personal learning state. Specifically, this integration allows TutorLLM to tailor responses based on individual learning states predicted by the Multi-Features with Latent Relations BERT-based KT (MLFBK) model and to enhance response accuracy with a Scraper model. The evaluation includes user assessment questionnaires and performance metrics, demonstrating a 10% improvement in user satisfaction and a 5\% increase in quiz scores compared to using general LLMs alone.

Jinhui Bai, Andreas Christmann, Lei Shi

In this paper, we propose a novel kernel stochastic gradient descent (SGD) algorithm for large-scale supervised learning with general losses. Compared to traditional kernel SGD, our algorithm improves efficiency and scalability through an innovative regularization strategy. By leveraging the infinite series expansion of spherical radial basis functions, this strategy projects the stochastic gradient onto a finite-dimensional hypothesis space, which is adaptively scaled according to the bias-variance trade-off, thereby enhancing generalization performance. Based on a new estimation of the spectral structure of the kernel-induced covariance operator, we develop an analytical framework that unifies optimization and generalization analyses. We prove that both the last iterate and the suffix average converge at minimax-optimal rates, and we further establish optimal strong convergence in the reproducing kernel Hilbert space. Our framework accommodates a broad class of classical loss functions, including least-squares, Huber, and logistic losses. Moreover, the proposed algorithm significantly reduces computational complexity and achieves optimal storage complexity by incorporating coordinate-wise updates from linear SGD, thereby avoiding the costly pairwise operations typical of kernel SGD and enabling efficient processing of streaming data. Finally, extensive numerical experiments demonstrate the efficiency of our approach.

Jialin Yu, Laila Alrajhi, Anoushka Harit et al.

Massive Open Online Courses (MOOCs) have become a popular choice for e-learning thanks to their great flexibility. However, due to large numbers of learners and their diverse backgrounds, it is taxing to offer real-time support. Learners may post their feelings of confusion and struggle in the respective MOOC forums, but with the large volume of posts and high workloads for MOOC instructors, it is unlikely that the instructors can identify all learners requiring intervention. This problem has been studied as a Natural Language Processing (NLP) problem recently, and is known to be challenging, due to the imbalance of the data and the complex nature of the task. In this paper, we explore for the first time Bayesian deep learning on learner-based text posts with two methods: Monte Carlo Dropout and Variational Inference, as a new solution to assessing the need of instructor interventions for a learner's post. We compare models based on our proposed methods with probabilistic modelling to its baseline non-Bayesian models under similar circumstances, for different cases of applying prediction. The results suggest that Bayesian deep learning offers a critical uncertainty measure that is not supplied by traditional neural networks. This adds more explainability, trust and robustness to AI, which is crucial in education-based applications. Additionally, it can achieve similar or better performance compared to non-probabilistic neural networks, as well as grant lower variance.

Lei Shi, Alexandra I. Cristea, Armando M. Toda et al.

Massive Open Online Courses (MOOCs) exhibit a remarkable heterogeneity of students. The advent of complex "big data" from MOOC platforms is a challenging yet rewarding opportunity to deeply understand how students are engaged in MOOCs. Past research, looking mainly into overall behavior, may have missed patterns related to student diversity. Using a large dataset from a MOOC offered by FutureLearn, we delve into a new way of investigating hidden patterns through both machine learning and statistical modelling. In this paper, we report on clustering analysis of student activities and comparative analysis on both behavioral patterns and demographical patterns between student subpopulations in the MOOC. Our approach allows for a deeper understanding of how MOOC students behave and achieve. Our findings may be used to design adaptive strategies towards an enhanced MOOC experience

Lei Shi, Alexandra I. Cristea, Armando M. Toda et al.

Massive Open Online Courses (MOOCs) continue to see increasing enrolment, but only a small percent of enrolees completes the MOOCs. Whilst a lot of research has focused on predicting completion, there is little research analysing the ostensible contradiction between the MOOC's popularity and the apparent disengagement of learners. Specifically, it is important to analyse engagement not just in learning, but also from a social perspective. This is especially crucial, as MOOCs offer a growing amount of activities, which can be classified as social interactions. Thus, this study is particularly concerned with how learners interact with peers, along with their study progression in MOOCs. Additionally, unlike most existing studies that are mainly focused on learning outcomes, this study adopts a fine-grained temporal approach to exploring how learners progress within a MOOC. The study was conducted on the less explored FutureLearn platform, which employs a social constructivist approach and promotes collaborative learning. The preliminary results suggest potential interesting fine-grained predictive models for learner behaviour, involving weekly monitoring of social, non-social behaviour of active students (further classified as completers and non-completers).

Lei Shi, Alexandra Cristea, Ahmad Alamri et al.

An exploratory study on social interactions of MOOC students in FutureLearn was conducted, to answer "how can we cluster students based on their social interactions?" Comments were categorized based on how students interacted with them, e.g., how a student's comment received replies from peers. Statistical modelling and machine learning were used to analyze comment categorization, resulting in 3 strong and stable clusters.

Linh Nguyen, Jaime Valls Miro, Lei Shi et al.

Rapidly estimating the remaining wall thickness (RWT) is paramount for the non-destructive condition assessment evaluation of large critical metallic pipelines. A robotic vehicle with embedded magnetism-based sensors has been developed to traverse the inside of a pipeline and conduct inspections at the location of a break. However its sensing speed is constrained by the magnetic principle of operation, thus slowing down the overall operation in seeking dense RWT mapping. To ameliorate this drawback, this work proposes the partial scanning of the pipe and then employing Gaussian Processes (GPs) to infer RWT at the unseen pipe sections. Since GP prediction assumes to have normally distributed input data - which does correspond with real RWT measurements - Gaussian mixture (GM) models are proven in this work as fitting marginal distributions to effectively capture the probability of any RWT value in the inspected data. The effectiveness of the proposed approach is extensively validated from real-world data collected in collaboration with a water utility from a cast iron water main pipeline in Sydney, Australia.