Knowledge Tracing (KT) aims to trace changes in students' knowledge states throughout their entire learning process by analyzing their historical learning data and predicting their future learning performance. Existing forgetting curve theory based knowledge tracing models only consider the general forgetting caused by time intervals, ignoring the individualization of students and the causal relationship of the forgetting process. To address these problems, we propose a Concept-driven Personalized Forgetting knowledge tracing model (CPF) which integrates hierarchical relationships between knowledge concepts and incorporates students' personalized cognitive abilities. First, we integrate the students' personalized capabilities into both the learning and forgetting processes to explicitly distinguish students' individual learning gains and forgetting rates according to their cognitive abilities. Second, we take into account the hierarchical relationships between knowledge points and design a precursor-successor knowledge concept matrix to simulate the causal relationship in the forgetting process, while also integrating the potential impact of forgetting prior knowledge points on subsequent ones. The proposed personalized forgetting mechanism can not only be applied to the learning of specifc knowledge concepts but also the life-long learning process. Extensive experimental results on three public datasets show that our CPF outperforms current forgetting curve theory based methods in predicting student performance, demonstrating CPF can better simulate changes in students' knowledge status through the personalized forgetting mechanism.

When faced with accomplishing a task, human experts exhibit intentional behavior. Their unique intents shape their plans and decisions, resulting in experts demonstrating diverse behaviors to accomplish the same task. Due to the uncertainties encountered in the real world and their bounded rationality, experts sometimes adjust their intents, which in turn influences their behaviors during task execution. This paper introduces IDIL, a novel imitation learning algorithm to mimic these diverse intent-driven behaviors of experts. Iteratively, our approach estimates expert intent from heterogeneous demonstrations and then uses it to learn an intent-aware model of their behavior. Unlike contemporary approaches, IDIL is capable of addressing sequential tasks with high-dimensional state representations, while sidestepping the complexities and drawbacks associated with adversarial training (a mainstay of related techniques). Our empirical results suggest that the models generated by IDIL either match or surpass those produced by recent imitation learning benchmarks in metrics of task performance. Moreover, as it creates a generative model, IDIL demonstrates superior performance in intent inference metrics, crucial for human-agent interactions, and aptly captures a broad spectrum of expert behaviors.

In this paper, we show how mixed-integer conic optimization can be used to combine feature subset selection with holistic generalized linear models to fully automate the model selection process. Concretely, we directly optimize for the Akaike and Bayesian information criteria while imposing constraints designed to deal with multicollinearity in the feature selection task. Specifically, we propose a novel pairwise correlation constraint that combines the sign coherence constraint with ideas from classical statistical models like Ridge regression and the OSCAR model.

This work introduces a new method for selecting the number of components in finite mixture models (FMMs) using variational Bayes, inspired by the large-sample properties of the Evidence Lower Bound (ELBO) derived from mean-field (MF) variational approximation. Specifically, we establish matching upper and lower bounds for the ELBO without assuming conjugate priors, suggesting the consistency of model selection for FMMs based on maximizing the ELBO. As a by-product of our proof, we demonstrate that the MF approximation inherits the stable behavior (benefited from model singularity) of the posterior distribution, which tends to eliminate the extra components under model misspecification where the number of mixture components is over-specified. This stable behavior also leads to the $n^{-1/2}$ convergence rate for parameter estimation, up to a logarithmic factor, under this model overspecification. Empirical experiments are conducted to validate our theoretical findings and compare with other state-of-the-art methods for selecting the number of components in FMMs.

The field of Knowledge Tracing aims to understand how students learn and master knowledge over time by analyzing their historical behaviour data. To achieve this goal, many researchers have proposed Knowledge Tracing models that use data from Intelligent Tutoring Systems to predict students' subsequent actions. However, with the development of Intelligent Tutoring Systems, large-scale datasets containing long-sequence data began to emerge. Recent deep learning based Knowledge Tracing models face obstacles such as low efficiency, low accuracy, and low interpretability when dealing with large-scale datasets containing long-sequence data. To address these issues and promote the sustainable development of Intelligent Tutoring Systems, we propose a LSTM BERT-based Knowledge Tracing model for long sequence data processing, namely LBKT, which uses a BERT-based architecture with a Rasch model-based embeddings block to deal with different difficulty levels information and an LSTM block to process the sequential characteristic in students' actions. LBKT achieves the best performance on most benchmark datasets on the metrics of ACC and AUC. Additionally, an ablation study is conducted to analyse the impact of each component of LBKT's overall performance. Moreover, we used t-SNE as the visualisation tool to demonstrate the model's embedding strategy. The results indicate that LBKT is faster, more interpretable, and has a lower memory cost than the traditional deep learning based Knowledge Tracing methods.

While deep neural networks (DNNs) based personalized federated learning (PFL) is demanding for addressing data heterogeneity and shows promising performance, existing methods for federated learning (FL) suffer from efficient systematic uncertainty quantification. The Bayesian DNNs-based PFL is usually questioned of either over-simplified model structures or high computational and memory costs. In this paper, we introduce FedSI, a novel Bayesian DNNs-based subnetwork inference PFL framework. FedSI is simple and scalable by leveraging Bayesian methods to incorporate systematic uncertainties effectively. It implements a client-specific subnetwork inference mechanism, selects network parameters with large variance to be inferred through posterior distributions, and fixes the rest as deterministic ones. FedSI achieves fast and scalable inference while preserving the systematic uncertainties to the fullest extent. Extensive experiments on three different benchmark datasets demonstrate that FedSI outperforms existing Bayesian and non-Bayesian FL baselines in heterogeneous FL scenarios.

Multi-label Recognition (MLR) involves the identification of multiple objects within an image. To address the additional complexity of this problem, recent works have leveraged information from vision-language models (VLMs) trained on large text-images datasets for the task. These methods learn an independent classifier for each object (class), overlooking correlations in their occurrences. Such co-occurrences can be captured from the training data as conditional probabilities between a pair of classes. We propose a framework to extend the independent classifiers by incorporating the co-occurrence information for object pairs to improve the performance of independent classifiers. We use a Graph Convolutional Network (GCN) to enforce the conditional probabilities between classes, by refining the initial estimates derived from image and text sources obtained using VLMs. We validate our method on four MLR datasets, where our approach outperforms all state-of-the-art methods.

Learning and understanding car-following (CF) behaviors are crucial for microscopic traffic simulation. Traditional CF models, though simple, often lack generalization capabilities, while many data-driven methods, despite their robustness, operate as "black boxes" with limited interpretability. To bridge this gap, this work introduces a Bayesian Matrix Normal Mixture Regression (MNMR) model that simultaneously captures feature correlations and temporal dynamics inherent in CF behaviors. This approach is distinguished by its separate learning of row and column covariance matrices within the model framework, offering an insightful perspective into the human driver decision-making processes. Through extensive experiments, we assess the model's performance across various historical steps of inputs, predictive steps of outputs, and model complexities. The results consistently demonstrate our model's adeptness in effectively capturing the intricate correlations and temporal dynamics present during CF. A focused case study further illustrates the model's outperforming interpretability of identifying distinct operational conditions through the learned mean and covariance matrices. This not only underlines our model's effectiveness in understanding complex human driving behaviors in CF scenarios but also highlights its potential as a tool for enhancing the interpretability of CF behaviors in traffic simulations and autonomous driving systems.

In many applications, ranging from logistics to engineering, a designer is faced with a sequence of optimization tasks for which the objectives are in the form of black-box functions that are costly to evaluate. For example, the designer may need to tune the hyperparameters of neural network models for different learning tasks over time. Rather than evaluating the objective function for each candidate solution, the designer may have access to approximations of the objective functions, for which higher-fidelity evaluations entail a larger cost. Existing multi-fidelity black-box optimization strategies select candidate solutions and fidelity levels with the goal of maximizing the information accrued about the optimal value or solution for the current task. Assuming that successive optimization tasks are related, this paper introduces a novel information-theoretic acquisition function that balances the need to acquire information about the current task with the goal of collecting information transferable to future tasks. The proposed method includes shared inter-task latent variables, which are transferred across tasks by implementing particle-based variational Bayesian updates. Experimental results across synthetic and real-world examples reveal that the proposed provident acquisition strategy that caters to future tasks can significantly improve the optimization efficiency as soon as a sufficient number of tasks is processed.

We propose a neural operator framework, termed mixture density nonlinear manifold decoder (MD-NOMAD), for stochastic simulators. Our approach leverages an amalgamation of the pointwise operator learning neural architecture nonlinear manifold decoder (NOMAD) with mixture density-based methods to estimate conditional probability distributions for stochastic output functions. MD-NOMAD harnesses the ability of probabilistic mixture models to estimate complex probability and the high-dimensional scalability of pointwise neural operator NOMAD. We conduct empirical assessments on a wide array of stochastic ordinary and partial differential equations and present the corresponding results, which highlight the performance of the proposed framework.