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.

Labeling mistakes are frequently encountered in real-world applications. If not treated well, the labeling mistakes can deteriorate the classification performances of a model seriously. To address this issue, we propose an improved Naive Bayes method for text classification. It is analytically simple and free of subjective judgements on the correct and incorrect labels. By specifying the generating mechanism of incorrect labels, we optimize the corresponding log-likelihood function iteratively by using an EM algorithm. Our simulation and experiment results show that the improved Naive Bayes method greatly improves the performances of the Naive Bayes method with mislabeled data.

Sepsis is a life-threatening organ malfunction caused by the host's inability to fight infection, which can lead to death without proper and immediate treatment. Therefore, early diagnosis and medical treatment of sepsis in critically ill populations at high risk for sepsis and sepsis-associated mortality are vital to providing the patient with rapid therapy. Studies show that advancing sepsis detection by 6 hours leads to earlier administration of antibiotics, which is associated with improved mortality. However, clinical scores like Sequential Organ Failure Assessment (SOFA) are not applicable for early prediction, while machine learning algorithms can help capture the progressing pattern for early prediction. Therefore, we aim to develop a machine learning algorithm that predicts sepsis onset 6 hours before it is suspected clinically. Although some machine learning algorithms have been applied to sepsis prediction, many of them did not consider the fact that six hours is not a small gap. To overcome this big gap challenge, we explore a multi-subset approach in which the likelihood of sepsis occurring earlier than 6 hours is output from a previous subset and feed to the target subset as additional features. Moreover, we use the hourly sampled data like vital signs in an observation window to derive a temporal change trend to further assist, which however is often ignored by previous studies. Our empirical study shows that both the multi-subset approach to alleviating the 6-hour gap and the added temporal trend features can help improve the performance of sepsis-related early prediction.

Google AlphaGos win has significantly motivated and sped up machine learning (ML) research and development, which led to tremendous ML technical advances and wider adoptions in various domains (e.g., Finance, Health, Defense, and Education). These advances have resulted in numerous new concepts and technologies, which are too many for people to catch up to and even make them confused, especially for newcomers to the ML area. This paper is aimed to present a clear picture of the state-of-the-art of the existing ML technologies with a comprehensive survey. We lay out this survey by viewing ML as a MLOps (ML Operations) process, where the key concepts and activities are collected and elaborated with representative works and surveys. We hope that this paper can serve as a quick reference manual (a survey of surveys) for newcomers (e.g., researchers, practitioners) of ML to get an overview of the MLOps process, as well as a good understanding of the key technologies used in each step of the ML process, and know where to find more details.

Bayesian neural networks (BNNs) have received an increased interest in the last years. In BNNs, a complete posterior distribution of the unknown weight and bias parameters of the network is produced during the training stage. This probabilistic estimation offers several advantages with respect to point-wise estimates, in particular, the ability to provide uncertainty quantification when predicting new data. This feature inherent to the Bayesian paradigm, is useful in countless machine learning applications. It is particularly appealing in areas where decision-making has a crucial impact, such as medical healthcare or autonomous driving. The main challenge of BNNs is the computational cost of the training procedure since Bayesian techniques often face a severe curse of dimensionality. Adaptive importance sampling (AIS) is one of the most prominent Monte Carlo methodologies benefiting from sounded convergence guarantees and ease for adaptation. This work aims to show that AIS constitutes a successful approach for designing BNNs. More precisely, we propose a novel algorithm PMCnet that includes an efficient adaptation mechanism, exploiting geometric information on the complex (often multimodal) posterior distribution. Numerical results illustrate the excellent performance and the improved exploration capabilities of the proposed method for both shallow and deep neural networks.

Training a classifier with noisy labels typically requires the learner to specify the distribution of label noise, which is often unknown in practice. Although there have been some recent attempts to relax that requirement, we show that the Bayes decision rule is unidentified in most classification problems with noisy labels. This suggests it is generally not possible to bypass/relax the requirement. In the special cases in which the Bayes decision rule is identified, we develop a simple algorithm to learn the Bayes decision rule, that does not require knowledge of the noise distribution. In this paper, we consider classification with noisy labels.

The remarkable performance of overparameterized deep neural networks (DNNs) must arise from an interplay between network architecture, training algorithms, and structure in the data. To disentangle these three components, we apply a Bayesian picture, based on the functions expressed by a DNN, to supervised learning. The prior over functions is determined by the network, and is varied by exploiting a transition between ordered and chaotic regimes. For Boolean function classification, we approximate the likelihood using the error spectrum of functions on data. When combined with the prior, this accurately predicts the posterior, measured for DNNs trained with stochastic gradient descent. This analysis reveals that structured data, combined with an intrinsic Occam's razor-like inductive bias towards (Kolmogorov) simple functions that is strong enough to counteract the exponential growth of the number of functions with complexity, is a key to the success of DNNs.

Autonomous driving services rely heavily on sensors such as cameras, LiDAR, radar, and communication modules. A common practice of processing the sensed data is using a high-performance computing unit placed inside the vehicle, which deploys AI models and algorithms to act as the brain or administrator of the vehicle. The vehicular data generated from average hours of driving can be up to 20 Terabytes depending on the data rate and specification of the sensors. Given the scale and fast growth of services for autonomous driving, it is essential to improve the overall energy and environmental efficiency, especially in the trend towards vehicular electrification (e.g., battery-powered). Although the areas have seen significant advancements in sensor technologies, wireless communications, computing and AI/ML algorithms, the challenge still exists in how to apply and integrate those technology innovations to achieve energy efficiency. This survey reviews and compares the connected vehicular applications, vehicular communications, approximation and Edge AI techniques. The focus is on energy efficiency by covering newly proposed approximation and enabling frameworks. To the best of our knowledge, this survey is the first to review the latest approximate Edge AI frameworks and publicly available datasets in energy-efficient autonomous driving. The insights and vision from this survey can be beneficial for the collaborative driving service development on low-power and memory-constrained systems and also for the energy optimization of autonomous vehicles.

This technical report studies the problem of ranking from pairwise comparisons in the classical Bradley-Terry-Luce (BTL) model, with a focus on score estimation. For general graphs, we show that, with sufficiently many samples, maximum likelihood estimation (MLE) achieves an entrywise estimation error matching the Cram\'er-Rao lower bound, which can be stated in terms of effective resistances; the key to our analysis is a connection between statistical estimation and iterative optimization by preconditioned gradient descent. We are also particularly interested in graphs with locality, where only nearby items can be connected by edges; our analysis identifies conditions under which locality does not hurt, i.e. comparing the scores between a pair of items that are far apart in the graph is nearly as easy as comparing a pair of nearby items. We further explore divide-and-conquer algorithms that can provably achieve similar guarantees even in the regime with the sparsest samples, while enjoying certain computational advantages. Numerical results validate our theory and confirm the efficacy of the proposed algorithms.