This paper presents two computationally efficient algorithms for the orientation estimation of inertial measurement units (IMUs): the correntropy-based gradient descent (CGD) and the correntropy-based decoupled orientation estimation (CDOE). Traditional methods, such as gradient descent (GD) and decoupled orientation estimation (DOE), rely on the mean squared error (MSE) criterion, making them vulnerable to external acceleration and magnetic interference. To address this issue, we demonstrate that the multi-kernel correntropy loss (MKCL) is an optimal objective function for maximum likelihood estimation (MLE) when the noise follows a type of heavy-tailed distribution. In certain situations, the estimation error of the MKCL is bounded even in the presence of arbitrarily large outliers. By replacing the standard MSE cost function with MKCL, we develop the CGD and CDOE algorithms. We evaluate the effectiveness of our proposed methods by comparing them with existing algorithms in various situations. Experimental results indicate that our proposed methods (CGD and CDOE) outperform their conventional counterparts (GD and DOE), especially when faced with external acceleration and magnetic disturbances. Furthermore, the new algorithms demonstrate significantly lower computational complexity than Kalman filter-based approaches, making them suitable for applications with low-cost microprocessors.

This paper provides a comprehensive survey of bias mitigation methods for achieving fairness in Machine Learning (ML) models. We collect a total of 341 publications concerning bias mitigation for ML classifiers. These methods can be distinguished based on their intervention procedure (i.e., pre-processing, in-processing, post-processing) and the technique they apply. We investigate how existing bias mitigation methods are evaluated in the literature. In particular, we consider datasets, metrics and benchmarking. Based on the gathered insights (e.g., What is the most popular fairness metric? How many datasets are used for evaluating bias mitigation methods?), we hope to support practitioners in making informed choices when developing and evaluating new bias mitigation methods.

Fatigue crack growth is one of the most common types of deterioration in metal structures with significant implications on their reliability. Recent advances in Structural Health Monitoring (SHM) have motivated the use of structural response data to predict future crack growth under uncertainty, in order to enable a transition towards predictive maintenance. Accurately representing different sources of uncertainty in stochastic crack growth (SCG) processes is a non-trivial task. The present work builds on previous research on physics-based SCG modeling under both material and load-related uncertainty. The aim here is to construct computationally efficient, probabilistic surrogate models for SCG processes that successfully encode these different sources of uncertainty. An approach inspired by latent variable modeling is employed that utilizes Gaussian Process (GP) regression models to enable the surrogates to be used to generate prior distributions for different Bayesian SHM tasks as the application of interest. Implementation is carried out in a numerical setting and model performance is assessed for two fundamental crack SHM problems; namely crack length monitoring (damage quantification) and crack growth monitoring (damage prognosis).

In this paper, we conduct a comprehensive study of In-Context Learning (ICL) by addressing several open questions: (a) What type of ICL estimator is learned by large language models? (b) What is a proper performance metric for ICL and what is the error rate? (c) How does the transformer architecture enable ICL? To answer these questions, we adopt a Bayesian view and formulate ICL as a problem of predicting the response corresponding to the current covariate, given a number of examples drawn from a latent variable model. To answer (a), we show that, without updating the neural network parameters, ICL implicitly implements the Bayesian model averaging algorithm, which is proven to be approximately parameterized by the attention mechanism. For (b), we analyze the ICL performance from an online learning perspective and establish a $\mathcal{O}(1/T)$ regret bound for perfectly pretrained ICL, where $T$ is the number of examples in the prompt. To answer (c), we show that, in addition to encoding Bayesian model averaging via attention, the transformer architecture also enables a fine-grained statistical analysis of pretraining under realistic assumptions. In particular, we prove that the error of pretrained model is bounded by a sum of an approximation error and a generalization error, where the former decays to zero exponentially as the depth grows, and the latter decays to zero sublinearly with the number of tokens in the pretraining dataset. Our results provide a unified understanding of the transformer and its ICL ability with bounds on ICL regret, approximation, and generalization, which deepens our knowledge of these essential aspects of modern language models.

While code generation has been widely used in various software development scenarios, the quality of the generated code is not guaranteed. This has been a particular concern in the era of large language models (LLMs)- based code generation, where LLMs, deemed a complex and powerful black-box model, is instructed by a high-level natural language specification, namely a prompt, to generate code. Nevertheless, effectively evaluating and explaining the code generation capability of LLMs is inherently challenging, given the complexity of LLMs and the lack of transparency. Inspired by the recent progress in causality analysis and its application in software engineering, this paper launches a causality analysis-based approach to systematically analyze the causal relations between the LLM input prompts and the generated code. To handle various technical challenges in this study, we first propose a novel causal graph-based representation of the prompt and the generated code, which is established over the fine-grained, human-understandable concepts in the input prompts. The formed causal graph is then used to identify the causal relations between the prompt and the derived code. We illustrate the insights that our framework can provide by studying over 3 popular LLMs with over 12 prompt adjustment strategies. The results of these studies illustrate the potential of our technique to provide insights into LLM effectiveness, and aid end-users in understanding predictions. Additionally, we demonstrate that our approach provides actionable insights to improve the quality of the LLM-generated code by properly calibrating the prompt.

Although existing machine learning-based methods for traffic accident analysis can provide good quality results to downstream tasks, they lack interpretability which is crucial for this critical problem. This paper proposes an interpretable framework based on Bayesian Networks for traffic accident prediction. To enable the ease of interpretability, we design a dataset construction pipeline to feed the traffic data into the framework while retaining the essential traffic data information. With a concrete case study, our framework can derive a Bayesian Network from a dataset based on the causal relationships between weather and traffic events across the United States. Consequently, our framework enables the prediction of traffic accidents with competitive accuracy while examining how the probability of these events changes under different conditions, thus illustrating transparent relationships between traffic and weather events. Additionally, the visualization of the network simplifies the analysis of relationships between different variables, revealing the primary causes of traffic accidents and ultimately providing a valuable reference for reducing traffic accidents.

We propose FedGT, a novel framework for identifying malicious clients in federated learning with secure aggregation. Inspired by group testing, the framework leverages overlapping groups of clients to identify the presence of malicious clients in the groups via a decoding operation. The clients identified as malicious are then removed from the training of the model, which is performed over the remaining clients. By choosing the size, number, and overlap between groups, FedGT strikes a balance between privacy and security. Specifically, the server learns the aggregated model of the clients in each group - vanilla federated learning and secure aggregation correspond to the extreme cases of FedGT with group size equal to one and the total number of clients, respectively. The effectiveness of FedGT is demonstrated through extensive experiments on the MNIST, CIFAR-10, and ISIC2019 datasets in a cross-silo setting under different data-poisoning attacks. These experiments showcase FedGT's ability to identify malicious clients, resulting in high model utility. We further show that FedGT significantly outperforms the private robust aggregation approach based on the geometric median recently proposed by Pillutla et al. on heterogeneous client data (ISIC2019) and in the presence of targeted attacks (CIFAR-10 and ISIC2019).

In fields such as finance, climate science, and neuroscience, inferring causal relationships from time series data poses a formidable challenge. While contemporary techniques can handle nonlinear relationships between variables and flexible noise distributions, they rely on the simplifying assumption that data originates from the same underlying causal model. In this work, we relax this assumption and perform causal discovery from time series data originating from mixtures of different causal models. We infer both the underlying structural causal models and the posterior probability for each sample belonging to a specific mixture component. Our approach employs an end-to-end training process that maximizes an evidence-lower bound for data likelihood. Through extensive experimentation on both synthetic and real-world datasets, we demonstrate that our method surpasses state-of-the-art benchmarks in causal discovery tasks, particularly when the data emanates from diverse underlying causal graphs. Theoretically, we prove the identifiability of such a model under some mild assumptions.

A hierarchical Bayesian framework is introduced for developing rich mixture models for real-valued time series, partly motivated by important applications in financial time series analysis. At the top level, meaningful discrete states are identified as appropriately quantised values of some of the most recent samples. These observable states are described as a discrete context-tree model. At the bottom level, a different, arbitrary model for real-valued time series -- a base model -- is associated with each state. This defines a very general framework that can be used in conjunction with any existing model class to build flexible and interpretable mixture models. We call this the Bayesian Context Trees State Space Model, or the BCT-X framework. Efficient algorithms are introduced that allow for effective, exact Bayesian inference and learning in this setting; in particular, the maximum a posteriori probability (MAP) context-tree model can be identified. These algorithms can be updated sequentially, facilitating efficient online forecasting. The utility of the general framework is illustrated in two particular instances: When autoregressive (AR) models are used as base models, resulting in a nonlinear AR mixture model, and when conditional heteroscedastic (ARCH) models are used, resulting in a mixture model that offers a powerful and systematic way of modelling the well-known volatility asymmetries in financial data. In forecasting, the BCT-X methods are found to outperform state-of-the-art techniques on simulated and real-world data, both in terms of accuracy and computational requirements. In modelling, the BCT-X structure finds natural structure present in the data. In particular, the BCT-ARCH model reveals a novel, important feature of stock market index data, in the form of an enhanced leverage effect.

Gaussian processes are the model of choice in Bayesian optimization and active learning. Yet, they are highly dependent on cleverly chosen hyperparameters to reach their full potential, and little effort is devoted to finding good hyperparameters in the literature. We demonstrate the impact of selecting good hyperparameters for GPs and present two acquisition functions that explicitly prioritize hyperparameter learning. Statistical distance-based Active Learning (SAL) considers the average disagreement between samples from the posterior, as measured by a statistical distance. SAL outperforms the state-of-the-art in Bayesian active learning on several test functions. We then introduce Self-Correcting Bayesian Optimization (SCoreBO), which extends SAL to perform Bayesian optimization and active learning simultaneously. SCoreBO learns the model hyperparameters at improved rates compared to vanilla BO, while outperforming the latest Bayesian optimization methods on traditional benchmarks. Moreover, we demonstrate the importance of self-correction on atypical Bayesian optimization tasks.