Structural learning, which aims to learn directed acyclic graphs (DAGs) from observational data, is foundational to causal reasoning and scientific discovery. Recent advancements formulate structural learning into a continuous optimization problem; however, DAG learning remains a highly non-convex problem, and there has not been much work on leveraging well-developed convex optimization techniques for causal structural learning. We fill this gap by proposing a data-adaptive linear approach for causal structural learning from time series data, which can be conveniently cast into a convex optimization problem using a recently developed monotone operator variational inequality (VI) formulation. Furthermore, we establish non-asymptotic recovery guarantee of the VI-based approach and show the superior performance of our proposed method on structure recovery over existing methods via extensive numerical experiments.

Dialogue acts (DAs) can represent conversational actions of tutors or students that take place during tutoring dialogues. Automating the identification of DAs in tutoring dialogues is significant to the design of dialogue-based intelligent tutoring systems. Many prior studies employ machine learning models to classify DAs in tutoring dialogues and invest much effort to optimize the classification accuracy by using limited amounts of training data (i.e., low-resource data scenario). However, beyond the classification accuracy, the robustness of the classifier is also important, which can reflect the capability of the classifier on learning the patterns from different class distributions. We note that many prior studies on classifying educational DAs employ cross entropy (CE) loss to optimize DA classifiers on low-resource data with imbalanced DA distribution. The DA classifiers in these studies tend to prioritize accuracy on the majority class at the expense of the minority class which might not be robust to the data with imbalanced ratios of different DA classes. To optimize the robustness of classifiers on imbalanced class distributions, we propose to optimize the performance of the DA classifier by maximizing the area under the ROC curve (AUC) score (i.e., AUC maximization). Through extensive experiments, our study provides evidence that (i) by maximizing AUC in the training process, the DA classifier achieves significant performance improvement compared to the CE approach under low-resource data, and (ii) AUC maximization approaches can improve the robustness of the DA classifier under different class imbalance ratios.

We study mean-field variational Bayesian inference using the TAP approach, for Z2-synchronization as a prototypical example of a high-dimensional Bayesian model. We show that for any signal strength $\lambda > 1$ (the weak-recovery threshold), there exists a unique local minimizer of the TAP free energy functional near the mean of the Bayes posterior law. Furthermore, the TAP free energy in a local neighborhood of this minimizer is strongly convex. Consequently, a natural-gradient/mirror-descent algorithm achieves linear convergence to this minimizer from a local initialization, which may be obtained by a constant number of iterates of Approximate Message Passing (AMP). This provides a rigorous foundation for variational inference in high dimensions via minimization of the TAP free energy. We also analyze the finite-sample convergence of AMP, showing that AMP is asymptotically stable at the TAP minimizer for any $\lambda > 1$, and is linearly convergent to this minimizer from a spectral initialization for sufficiently large $\lambda$. Such a guarantee is stronger than results obtainable by state evolution analyses, which only describe a fixed number of AMP iterations in the infinite-sample limit. Our proofs combine the Kac-Rice formula and Sudakov-Fernique Gaussian comparison inequality to analyze the complexity of critical points that satisfy strong convexity and stability conditions within their local neighborhoods.

Physics-informed neural networks (PINNs) have proven a suitable mathematical scaffold for solving inverse ordinary (ODE) and partial differential equations (PDE). Typical inverse PINNs are formulated as soft-constrained multi-objective optimization problems with several hyperparameters. In this work, we demonstrate that inverse PINNs can be framed in terms of maximum-likelihood estimators (MLE) to allow explicit error propagation from interpolation to the physical model space through Taylor expansion, without the need of hyperparameter tuning. We explore its application to high-dimensional coupled ODEs constrained by differential algebraic equations that are common in transient chemical and biological kinetics. Furthermore, we show that singular-value decomposition (SVD) of the ODE coupling matrices (reaction stoichiometry matrix) provides reduced uncorrelated subspaces in which PINNs solutions can be represented and over which residuals can be projected. Finally, SVD bases serve as preconditioners for the inversion of covariance matrices in this hyperparameter-free robust application of MLE to ``kinetics-informed neural networks''.

In this paper, we propose a novel Fine-Tuned attribute Weighted Na\"ive Bayes (FT-WNB) classifier to identify the Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) for UltraWide Bandwidth (UWB) signals in an Indoor Positioning System (IPS). The FT-WNB classifier assigns each signal feature a specific weight and fine-tunes its probabilities to address the mismatch between the predicted and actual class. The performance of the FT-WNB classifier is compared with the state-of-the-art Machine Learning (ML) classifiers such as minimum Redundancy Maximum Relevance (mRMR)- $k$-Nearest Neighbour (KNN), Support Vector Machine (SVM), Decision Tree (DT), Na\"ive Bayes (NB), and Neural Network (NN). It is demonstrated that the proposed classifier outperforms other algorithms by achieving a high NLoS classification accuracy of $99.7\%$ with imbalanced data and $99.8\%$ with balanced data. The experimental results indicate that our proposed FT-WNB classifier significantly outperforms the existing state-of-the-art ML methods for LoS and NLoS signals in IPS in the considered scenario.

Performance monitoring of machine learning (ML)-based risk prediction models in healthcare is complicated by the issue of confounding medical interventions (CMI): when an algorithm predicts a patient to be at high risk for an adverse event, clinicians are more likely to administer prophylactic treatment and alter the very target that the algorithm aims to predict. A simple approach is to ignore CMI and monitor only the untreated patients, whose outcomes remain unaltered. In general, ignoring CMI may inflate Type I error because (i) untreated patients disproportionally represent those with low predicted risk and (ii) evolution in both the model and clinician trust in the model can induce complex dependencies that violate standard assumptions. Nevertheless, we show that valid inference is still possible if one monitors conditional performance and if either conditional exchangeability or time-constant selection bias hold. Specifically, we develop a new score-based cumulative sum (CUSUM) monitoring procedure with dynamic control limits. Through simulations, we demonstrate the benefits of combining model updating with monitoring and investigate how over-trust in a prediction model may delay detection of performance deterioration. Finally, we illustrate how these monitoring methods can be used to detect calibration decay of an ML-based risk calculator for postoperative nausea and vomiting during the COVID-19 pandemic.

Non-Line-of-Sight (NLoS) propagation condition is a crucial factor affecting the precision of the localization in the Ultra-Wideband (UWB) Indoor Positioning System (IPS). Numerous supervised Machine Learning (ML) approaches have been applied for NLoS identification to improve the accuracy of the IPS. However, it is difficult for existing ML approaches to maintain a high classification accuracy when the database contains a small number of NLoS signals and a large number of Line-of-Sight (LoS) signals. The inaccurate localization of the target node caused by this small number of NLoS signals can still be problematic. To solve this issue, we propose feature-based Gaussian Distribution (GD) and Generalized Gaussian Distribution (GGD) NLoS detection algorithms. By employing our detection algorithm for the imbalanced dataset, a classification accuracy of $96.7\%$ and $98.0\%$ can be achieved. We also compared the proposed algorithm with the existing cutting-edge such as Support-Vector-Machine (SVM), Decision Tree (DT), Naive Bayes (NB), and Neural Network (NN), which can achieve an accuracy of $92.6\%$, $92.8\%$, $93.2\%$, and $95.5\%$, respectively. The results demonstrate that the GGD algorithm can achieve high classification accuracy with the imbalanced dataset. Finally, the proposed algorithm can also achieve a higher classification accuracy for different ratios of LoS and NLoS signals which proves the robustness and effectiveness of the proposed method.

Considering a probability distribution over parameters is known as an efficient strategy to learn a neural network with non-differentiable activation functions. We study the expectation of a probabilistic neural network as a predictor by itself, focusing on the aggregation of binary activated neural networks with normal distributions over real-valued weights. Our work leverages a recent analysis derived from the PAC-Bayesian framework that derives tight generalization bounds and learning procedures for the expected output value of such an aggregation, which is given by an analytical expression. While the combinatorial nature of the latter has been circumvented by approximations in previous works, we show that the exact computation remains tractable for deep but narrow neural networks, thanks to a dynamic programming approach. This leads us to a peculiar bound minimization learning algorithm for binary activated neural networks, where the forward pass propagates probabilities over representations instead of activation values. A stochastic counterpart that scales to wide architectures is proposed.

Most signal processing and statistical applications heavily rely on specific data distribution models. The Gaussian distributions, although being the most common choice, are inadequate in most real world scenarios as they fail to account for data coming from heavy-tailed populations or contaminated by outliers. Such problems call for the use of Robust Statistics. The robust models and estimators are usually based on elliptical populations, making the latter ubiquitous in all methods of robust statistics. To determine whether such tools are applicable in any specific case, goodness-of-fit (GoF) tests are used to verify the ellipticity hypothesis. Ellipticity GoF tests are usually hard to analyze and often their statistical power is not particularly strong. In this work, assuming the true covariance matrix is unknown we design and rigorously analyze a robust GoF test consistent against all alternatives to ellipticity on the unit sphere. The proposed test is based on Tyler's estimator and is formulated in terms of easily computable statistics of the data. For its rigorous analysis, we develop a novel framework based on the exchangeable random variables calculus introduced by de Finetti. Our findings are supported by numerical simulations comparing them to other popular GoF tests and demonstrating the significantly higher statistical power of the suggested technique.

The brain-computer interface (BCI) enables individuals with severe physical impairments to communicate with the world. BCIs offer computational neuroscience opportunities and challenges in converting real-time brain activities to computer commands and are typically framed as a classification problem. This article focuses on the P300 BCI that uses the event-related potential (ERP) BCI design, where the primary challenge is classifying target/non-target stimuli. We develop a novel Gaussian latent group model with sparse time-varying effects (GLASS) for making Bayesian inferences on the P300 BCI. GLASS adopts a multinomial regression framework that directly addresses the dataset imbalance in BCI applications. The prior specifications facilitate i) feature selection and noise reduction using soft-thresholding, ii) smoothing of the time-varying effects using global shrinkage, and iii) clustering of latent groups to alleviate high spatial correlations of EEG data. We develop an efficient gradient-based variational inference (GBVI) algorithm for posterior computation and provide a user-friendly Python module available at https://github.com/BangyaoZhao/GLASS. The application of GLASS identifies important EEG channels (PO8, Oz, PO7, Pz, C3) that align with existing literature. GLASS further reveals a group effect from channels in the parieto-occipital region (PO8, Oz, PO7), which is validated in cross-participant analysis.