Since their inception, Variational Autoencoders (VAEs) have become central in machine learning. Despite their widespread use, numerous questions regarding their theoretical properties remain open. Using PAC-Bayesian theory, this work develops statistical guarantees for VAEs. First, we derive the first PAC-Bayesian bound for posterior distributions conditioned on individual samples from the data-generating distribution. Then, we utilize this result to develop generalization guarantees for the VAE's reconstruction loss, as well as upper bounds on the distance between the input and the regenerated distributions. More importantly, we provide upper bounds on the Wasserstein distance between the input distribution and the distribution defined by the VAE's generative model.

Fall detection, particularly critical for high-risk demographics like the elderly, is a key public health concern where timely detection can greatly minimize harm. With the advancements in radio frequency technology, radar has emerged as a powerful tool for human detection and tracking. Traditional machine learning algorithms, such as Support Vector Machines (SVM) and k-Nearest Neighbors (kNN), have shown promising outcomes. However, deep learning approaches, notably Convolutional Neural Networks (CNN) and Recurrent Neural Networks (RNN), have outperformed in learning intricate features and managing large, unstructured datasets. This survey offers an in-depth analysis of radar-based fall detection, with emphasis on Micro-Doppler, Range-Doppler, and Range-Doppler-Angles techniques. We discuss the intricacies and challenges in fall detection and emphasize the necessity for a clear definition of falls and appropriate detection criteria, informed by diverse influencing factors. We present an overview of radar signal processing principles and the underlying technology of radar-based fall detection, providing an accessible insight into machine learning and deep learning algorithms. After examining 74 research articles on radar-based fall detection published since 2000, we aim to bridge current research gaps and underscore the potential future research strategies, emphasizing the real-world applications possibility and the unexplored potential of deep learning in improving radar-based fall detection.

The healthcare industry generates enormous amounts of complex clinical data that make the prediction of disease detection a complicated process. In medical informatics, making effective and efficient decisions is very important. Data Mining (DM) techniques are mainly used to identify and extract hidden patterns and interesting knowledge to diagnose and predict diseases in medical datasets. Nowadays, heart disease is considered one of the most important problems in the healthcare field. Therefore, early diagnosis leads to a reduction in deaths. DM techniques have proven highly effective for predicting and diagnosing heart diseases. This work utilizes the classification algorithms with a medical dataset of heart disease; namely, J48, Random Forest, and Na\"ive Bayes to discover the accuracy of their performance. We also examine the impact of the feature selection method. A comparative and analysis study was performed to determine the best technique using Waikato Environment for Knowledge Analysis (Weka) software, version 3.8.6. The performance of the utilized algorithms was evaluated using standard metrics such as accuracy, sensitivity and specificity. The importance of using classification techniques for heart disease diagnosis has been highlighted. We also reduced the number of attributes in the dataset, which showed a significant improvement in prediction accuracy. The results indicate that the best algorithm for predicting heart disease was Random Forest with an accuracy of 99.24%.

Graph Neural Networks (GNN) have recently gained popularity in the forecasting domain due to their ability to model complex spatial and temporal patterns in tasks such as traffic forecasting and region-based demand forecasting. Most of these methods require a predefined graph as input, whereas in real-life multivariate time series problems, a well-predefined dependency graph rarely exists. This requirement makes it harder for GNNs to be utilised widely for multivariate forecasting problems in other domains such as retail or energy. In this paper, we propose a hybrid approach combining neural networks and statistical structure learning models to self-learn the dependencies and construct a dynamically changing dependency graph from multivariate data aiming to enable the use of GNNs for multivariate forecasting even when a well-defined graph does not exist. The statistical structure modeling in conjunction with neural networks provides a well-principled and efficient approach by bringing in causal semantics to determine dependencies among the series. Finally, we demonstrate significantly improved performance using our proposed approach on real-world benchmark datasets without a pre-defined dependency graph.

Machine learning models are often trained to predict the outcome resulting from a human decision. For example, if a doctor decides to test a patient for disease, will the patient test positive? A challenge is that the human decision censors the outcome data: we only observe test outcomes for patients doctors historically tested. Untested patients, for whom outcomes are unobserved, may differ from tested patients along observed and unobserved dimensions. We propose a Bayesian model class which captures this setting. The purpose of the model is to accurately estimate risk for both tested and untested patients. Estimating this model is challenging due to the wide range of possibilities for untested patients. To address this, we propose two domain constraints which are plausible in health settings: a prevalence constraint, where the overall disease prevalence is known, and an expertise constraint, where the human decision-maker deviates from purely risk-based decision-making only along a constrained feature set. We show theoretically and on synthetic data that domain constraints improve parameter inference. We apply our model to a case study of cancer risk prediction, showing that the model's inferred risk predicts cancer diagnoses, its inferred testing policy captures known public health policies, and it can identify suboptimalities in test allocation. Though our case study is in healthcare, our analysis reveals a general class of domain constraints which can improve model estimation in many settings.

We observe the emergence of binary encoding within the latent space of deep-neural-network classifiers. Such binary encoding is induced by introducing a linear penultimate layer, which is equipped during training with a loss function that grows as $\exp(\vec{x}^2)$, where $\vec{x}$ are the coordinates in the latent space. The phenomenon we describe represents a specific instance of a well-documented occurrence known as \textit{neural collapse}, which arises in the terminal phase of training and entails the collapse of latent class means to the vertices of a simplex equiangular tight frame (ETF). We show that binary encoding accelerates convergence toward the simplex ETF and enhances classification accuracy.

Imitation learning methods seek to learn from an expert either through behavioral cloning (BC) of the policy or inverse reinforcement learning (IRL) of the reward. Such methods enable agents to learn complex tasks from humans that are difficult to capture with hand-designed reward functions. Choosing BC or IRL for imitation depends on the quality and state-action coverage of the demonstrations, as well as additional access to the Markov decision process. Hybrid strategies that combine BC and IRL are not common, as initial policy optimization against inaccurate rewards diminishes the benefit of pretraining the policy with BC. This work derives an imitation method that captures the strengths of both BC and IRL. In the entropy-regularized ('soft') reinforcement learning setting, we show that the behaviour-cloned policy can be used as both a shaped reward and a critic hypothesis space by inverting the regularized policy update. This coherency facilitates fine-tuning cloned policies using the reward estimate and additional interactions with the environment. This approach conveniently achieves imitation learning through initial behaviour cloning, followed by refinement via RL with online or offline data sources. The simplicity of the approach enables graceful scaling to high-dimensional and vision-based tasks, with stable learning and minimal hyperparameter tuning, in contrast to adversarial approaches. For the open-source implementation and simulation results, see https://joemwatson.github.io/csil/.

Social media networks have become a significant aspect of people's lives, serving as a platform for their ideas, opinions and emotions. Consequently, automated sentiment analysis (SA) is critical for recognising people's feelings in ways that other information sources cannot. The analysis of these feelings revealed various applications, including brand evaluations, YouTube film reviews and healthcare applications. As social media continues to develop, people post a massive amount of information in different forms, including text, photos, audio and video. Thus, traditional SA algorithms have become limited, as they do not consider the expressiveness of other modalities. By including such characteristics from various material sources, these multimodal data streams provide new opportunities for optimising the expected results beyond text-based SA. Our study focuses on the forefront field of multimodal SA, which examines visual and textual data posted on social media networks. Many people are more likely to utilise this information to express themselves on these platforms. To serve as a resource for academics in this rapidly growing field, we introduce a comprehensive overview of textual and visual SA, including data pre-processing, feature extraction techniques, sentiment benchmark datasets, and the efficacy of multiple classification methodologies suited to each field. We also provide a brief introduction of the most frequently utilised data fusion strategies and a summary of existing research on visual-textual SA. Finally, we highlight the most significant challenges and investigate several important sentiment applications.

Estimating the parameters of ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODEs are typically approximated with deterministic algorithms, new research on probabilistic solvers indicates that they produce more reliable parameter estimates by better accounting for numerical errors. However, many ODE systems are highly sensitive to their parameter values. This produces deep local maxima in the likelihood function -- a problem which existing probabilistic solvers have yet to resolve. Here we present a novel probabilistic ODE likelihood approximation, DALTON, which can dramatically reduce parameter sensitivity by learning from noisy ODE measurements in a data-adaptive manner. Our approximation scales linearly in both ODE variables and time discretization points, and is applicable to ODEs with both partially-unobserved components and non-Gaussian measurement models. Several examples demonstrate that DALTON produces more accurate parameter estimates via numerical optimization than existing probabilistic ODE solvers, and even in some cases than the exact ODE likelihood itself.

We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of our unknown variables of interest while being computationally more efficient than their first-order counterpart and the non-conditioned versions of both dynamics. Moreover, we prove that both pre-conditioned dynamics are well-defined and have the same unique invariant distributions as the non-conditioned cases. We also incorporate an annealing procedure that has the double benefit of further accelerating the convergence of the algorithm and allowing us to accommodate the case where the unknown variables are discrete. Numerical experiments in two different tasks in communications (MIMO symbol detection and channel estimation) and in three tasks for images showcase the generality of our method and illustrate the high performance achieved relative to competing approaches (including learning-based ones) while having comparable or lower computational complexity.