Continuous normalizing flows (CNFs) are a generative method for learning probability distributions, which is based on ordinary differential equations. This method has shown remarkable empirical success across various applications, including large-scale image synthesis, protein structure prediction, and molecule generation. In this work, we study the theoretical properties of CNFs with linear interpolation in learning probability distributions from a finite random sample, using a flow matching objective function. We establish non-asymptotic error bounds for the distribution estimator based on CNFs, in terms of the Wasserstein-2 distance. The key assumption in our analysis is that the target distribution satisfies one of the following three conditions: it either has a bounded support, is strongly log-concave, or is a finite or infinite mixture of Gaussian distributions. We present a convergence analysis framework that encompasses the error due to velocity estimation, the discretization error, and the early stopping error. A key step in our analysis involves establishing the regularity properties of the velocity field and its estimator for CNFs constructed with linear interpolation. This necessitates the development of uniform error bounds with Lipschitz regularity control of deep ReLU networks that approximate the Lipschitz function class, which could be of independent interest. Our nonparametric convergence analysis offers theoretical guarantees for using CNFs to learn probability distributions from a finite random sample.

Bayesian filtering serves as the mainstream framework of state estimation in dynamic systems. Its standard version utilizes total probability rule and Bayes' law alternatively, where how to define and compute conditional probability is critical to state distribution inference. Previously, the conditional probability is assumed to be exactly known, which represents a measure of the occurrence probability of one event, given the second event. In this paper, we find that by adding an additional event that stipulates an inequality condition, we can transform the conditional probability into a special integration that is analogous to convolution. Based on this transformation, we show that both transition probability and output probability can be generalized to convolutional forms, resulting in a more general filtering framework that we call convolutional Bayesian filtering. This new framework encompasses standard Bayesian filtering as a special case when the distance metric of the inequality condition is selected as Dirac delta function. It also allows for a more nuanced consideration of model mismatch by choosing different types of inequality conditions. For instance, when the distance metric is defined in a distributional sense, the transition probability and output probability can be approximated by simply rescaling them into fractional powers. Under this framework, a robust version of Kalman filter can be constructed by only altering the noise covariance matrix, while maintaining the conjugate nature of Gaussian distributions. Finally, we exemplify the effectiveness of our approach by reshaping classic filtering algorithms into convolutional versions, including Kalman filter, extended Kalman filter, unscented Kalman filter and particle filter.

Price prediction algorithms propose prices for every product or service according to market trends, projected demand, and other characteristics, including government rules, international transactions, and speculation and expectation. As the dependent variable in price prediction, it is affected by several independent and correlated variables which may challenge the price prediction. To overcome this challenge, machine learning algorithms allow more accurate price prediction without explicitly modeling the relatedness between variables. However, as inputs increase, it challenges the existing machine learning approaches regarding computing efficiency and prediction effectiveness. Hence, this study introduces a novel decision level fusion approach to select informative variables in price prediction. The suggested metaheuristic algorithm balances two competitive objective functions, which are defined to improve the prediction utilized variables and reduce the error rate simultaneously. To generate Pareto optimal solutions, an Elastic net approach is employed to eliminate unrelated and redundant variables to increase the accuracy. Afterward, we propose a novel method for combining solutions and ensuring that a subset of features is optimal. Two various real datasets evaluate the proposed price prediction method. The results support the suggested superiority of the model concerning its relative root mean square error and adjusted correlation coefficient.

Global Navigation Satellite Systems (GNSS)-based positioning plays a crucial role in various applications, including navigation, transportation, logistics, mapping, and emergency services. Traditional GNSS positioning methods are model-based and they utilize satellite geometry and the known properties of satellite signals. However, model-based methods have limitations in challenging environments and often lack adaptability to uncertain noise models. This paper highlights recent advances in Machine Learning (ML) and its potential to address these limitations. It covers a broad range of ML methods, including supervised learning, unsupervised learning, deep learning, and hybrid approaches. The survey provides insights into positioning applications related to GNSS such as signal analysis, anomaly detection, multi-sensor integration, prediction, and accuracy enhancement using ML. It discusses the strengths, limitations, and challenges of current ML-based approaches for GNSS positioning, providing a comprehensive overview of the field.

Objectives: Metabolic Bariatric Surgery (MBS) is a critical intervention for patients living with obesity and related health issues. Accurate classification and prediction of patient outcomes are vital for optimizing treatment strategies. This study presents a novel machine learning approach to classify patients in the context of metabolic bariatric surgery, providing insights into the efficacy of different models and variable types. Methods: Various machine learning models, including GaussianNB, ComplementNB, KNN, Decision Tree, KNN with RandomOverSampler, and KNN with SMOTE, were applied to a dataset of 73 patients. The dataset, comprising psychometric, socioeconomic, and analytical variables, was analyzed to determine the most efficient predictive model. The study also explored the impact of different variable groupings and oversampling techniques. Results: Experimental results indicate average accuracy values as high as 66.7% for the best model. Enhanced versions of KNN and Decision Tree, along with variations of KNN such as RandomOverSampler and SMOTE, yielded the best results. Conclusions: The study unveils a promising avenue for classifying patients in the realm of metabolic bariatric surgery. The results underscore the importance of selecting appropriate variables and employing diverse approaches to achieve optimal performance. The developed system holds potential as a tool to assist healthcare professionals in decision-making, thereby enhancing metabolic bariatric surgery outcomes. These findings lay the groundwork for future collaboration between hospitals and healthcare entities to improve patient care through the utilization of machine learning algorithms. Moreover, the findings suggest room for improvement, potentially achievable with a larger dataset and careful parameter tuning.

Learning using statistical invariants (LUSI) is a new learning paradigm, which adopts weak convergence mechanism, and can be applied to a wider range of classification problems. However, the computation cost of invariant matrices in LUSI is high for large-scale datasets during training. To settle this issue, this paper introduces a granularity statistical invariant for LUSI, and develops a new learning paradigm called learning using granularity statistical invariants (LUGSI). LUGSI employs both strong and weak convergence mechanisms, taking a perspective of minimizing expected risk. As far as we know, it is the first time to construct granularity statistical invariants. Compared to LUSI, the introduction of this new statistical invariant brings two advantages. Firstly, it enhances the structural information of the data. Secondly, LUGSI transforms a large invariant matrix into a smaller one by maximizing the distance between classes, achieving feasibility for large-scale datasets classification problems and significantly enhancing the training speed of model operations. Experimental results indicate that LUGSI not only exhibits improved generalization capabilities but also demonstrates faster training speed, particularly for large-scale datasets.

The goal of positive-unlabeled (PU) learning is to train a binary classifier on the basis of training data containing positive and unlabeled instances, where unlabeled observations can belong either to the positive class or to the negative class. Modeling PU data requires certain assumptions on the labeling mechanism that describes which positive observations are assigned a label. The simplest assumption, considered in early works, is SCAR (Selected Completely at Random Assumption), according to which the propensity score function, defined as the probability of assigning a label to a positive observation, is constant. On the other hand, a much more realistic assumption is SAR (Selected at Random), which states that the propensity function solely depends on the observed feature vector. SCAR-based algorithms are much simpler and computationally much faster compared to SAR-based algorithms, which usually require challenging estimation of the propensity score. In this work, we propose a relatively simple and computationally fast test that can be used to determine whether the observed data meet the SCAR assumption. Our test is based on generating artificial labels conforming to the SCAR case, which in turn allows to mimic the distribution of the test statistic under the null hypothesis of SCAR. We justify our method theoretically. In experiments, we demonstrate that the test successfully detects various deviations from SCAR scenario and at the same time it is possible to effectively control the type I error. The proposed test can be recommended as a pre-processing step to decide which final PU algorithm to choose in cases when nature of labeling mechanism is not known.

Bayesian nonparametric models offer a flexible and powerful framework for statistical model selection, enabling the adaptation of model complexity to the intricacies of diverse datasets. This survey intends to delve into the significance of Bayesian nonparametrics, particularly in addressing complex challenges across various domains such as statistics, computer science, and electrical engineering. By elucidating the basic properties and theoretical foundations of these nonparametric models, this survey aims to provide a comprehensive understanding of Bayesian nonparametrics and their relevance in addressing complex problems, particularly in the domain of multi-object tracking. Through this exploration, we uncover the versatility and efficacy of Bayesian nonparametric methodologies, paving the way for innovative solutions to intricate challenges across diverse disciplines.

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods developed in the parametric setting, where the inner objective is strongly convex with respect to the parameters of the prediction function. The functional point of view does not rely on this assumption and notably allows using over-parameterized neural networks as the inner prediction function. We propose scalable and efficient algorithms for the functional bilevel optimization problem and illustrate the benefits of our approach on instrumental regression and reinforcement learning tasks, which admit natural functional bilevel structures.

Lithium-ion batteries (Li-ion) have revolutionized energy storage technology, becoming integral to our daily lives by powering a diverse range of devices and applications. Their high energy density, fast power response, recyclability, and mobility advantages have made them the preferred choice for numerous sectors. This paper explores the seamless integration of Prognostics and Health Management within batteries, presenting a multidisciplinary approach that enhances the reliability, safety, and performance of these powerhouses. Remaining useful life (RUL), a critical concept in prognostics, is examined in depth, emphasizing its role in predicting component failure before it occurs. The paper reviews various RUL prediction methods, from traditional models to cutting-edge data-driven techniques. Furthermore, it highlights the paradigm shift toward deep learning architectures within the field of Li-ion battery health prognostics, elucidating the pivotal role of deep learning in addressing battery system complexities. Practical applications of PHM across industries are also explored, offering readers insights into real-world implementations.This paper serves as a comprehensive guide, catering to both researchers and practitioners in the field of Li-ion battery PHM.