This study presents a novel framework to evaluate the usability and user experience of e-learning platforms, focusing on the Duolingo language learning app. By integrating advanced Natural Language Processing (NLP) techniques such as Large Language Models (LLMs), Latent Dirichlet Allocation (LDA), and sentence embedding models, we identified thirteen key usability and user experience topics from a large dataset of user reviews. Our findings reveal that Duolingo is highly rated since users value its enjoyable learning experiences and effectiveness. However, technical issues, lack of explanations, and frustrating features were identified as areas for improvement. The study demonstrates the effectiveness of our framework in analyzing user feedback at scale, offering valuable insights for improving user experience in e-learning platforms and other domains.

Conditional Stochastic Optimization (CSO) is a powerful modelling paradigm for optimization under uncertainty. The existing literature on CSO is mainly based on the independence assumption of data, which shows that the solution of CSO is asymptotically consistent and enjoys a finite sample guarantee. The independence assumption, however, does not typically hold in many important applications with dependence patterns, such as time series analysis, operational control, and reinforcement learning. In this paper, we aim to fill this gap and consider a Sample Average Approximation (SAA) for CSO with dependent data. Leveraging covariance inequalities and independent block sampling technique, we provide theoretical guarantees of SAA for CSO with dependent data. In particular, we show that SAA for CSO retains asymptotic consistency and a finite sample guarantee under mild conditions. In addition, we establish the sample complexity $O(d / \varepsilon^4)$ of SAA for CSO, which is shown to be of the same order as independent cases. Through experiments on several applications, we verify the theoretical results and demonstrate that dependence does not degrade the performance of the SAA approach in real data applications.

The regularized clustering (RC) framework based on the fusion penalty has attracted extensive attention in the last decade because it does not require the prior knowledge of the number of clusters. Although the ground truth connections and weights among samples are beneficial for clustering, the performance of RC could be distorted by the omnipresent spurious connections in real-world data sets. To effectively address the issue, this letter constructs an enhanced regularized clustering model by incorporating a spurious connection detection mechanism into the objective function of the RC framework. The proposed model can effectively reduce the damage caused by spurious connections through adaptively identifying the importance of each connection. Furthermore, an alternating minimization algorithm is developed with detailed convergence analysis. Experimental results validate its effectiveness against several state-of-the-art RC methods

$\ell _{1}$-norm quantile regression is a common choice if there exists outlier or heavy-tailed error in high-dimensional data sets. However, it is computationally expensive to solve this problem when the feature size of data is ultra high. As far as we know, existing screening rules can not speed up the computation of the$\ell _{1}$-norm quantile regression, which dues to the non-differentiability of the quantile function/pinball loss. In this paper, we introduce the dual circumscribed sphere technique and propose a novel$\ell _{1}$-norm quantile regression screening rule. Our rule is expressed as the closed-form function of given data and eliminates inactive features with a low computational cost. Numerical experiments on some simulation and real data sets show that this screening rule can be used to eliminate almost all inactive features. Moreover, this rule can help to reduce up to 23 times of computational time, compared with the computation without our screening rule.

To deal with outliers or heavy-tailed random errors in common high-dimensional data sets, robust regressions are preferable selections and Rank Lasso is a notable model among them. However, the large-scaled feature size in data set increases the computational cost of solving Rank Lasso. In this paper, we build up a safe feature screening rule for Rank Lasso, which can effectively and safely identify inactive features in data sets and reduce the computation time of this model. The advantage of our screening rule is that it can be expressed as the closed-form function of given data and is easily implemented. The proposed screening rule is evaluated on some simulation and real data sets, which show that it can safely discard inactive features with a small computational cost and reduce the time for solving Rank Lasso.

Quadratic compressive sensing, as a nonlinear extension of compressive sensing, has attracted considerable attention in optical image, X-ray crystallography, transmission electron microscopy, etc. We introduce the concept of uniform s-regularity to study the uniqueness in quadratic compressive sensing and propose a greedy algorithm for the corresponding numerical optimization. Moreover, we prove the convergence of the proposed algorithm under the uniform s-regularity condition. Finally, we present numerical results to demonstrate the efficiency of the proposed method.