Parkinson's disease is a widespread neurodegenerative condition necessitating early diagnosis for effective intervention. This paper introduces an innovative method for diagnosing Parkinson's disease through the analysis of human EEG signals, employing a Support Vector Machine (SVM) classification model. this research presents novel contributions to enhance diagnostic accuracy and reliability. Our approach incorporates a comprehensive review of EEG signal analysis techniques and machine learning methods. Drawing from recent studies, we have engineered an advanced SVM-based model optimized for Parkinson's disease diagnosis. Utilizing cutting-edge feature engineering, extensive hyperparameter tuning, and kernel selection, our method achieves not only heightened diagnostic accuracy but also emphasizes model interpretability, catering to both clinicians and researchers. Moreover, ethical concerns in healthcare machine learning, such as data privacy and biases, are conscientiously addressed. We assess our method's performance through experiments on a diverse dataset comprising EEG recordings from Parkinson's disease patients and healthy controls, demonstrating significantly improved diagnostic accuracy compared to conventional techniques. In conclusion, this paper introduces an innovative SVM-based approach for diagnosing Parkinson's disease from human EEG signals. Building upon the IEEE framework and previous research, its novelty lies in the capacity to enhance diagnostic accuracy while upholding interpretability and ethical considerations for practical healthcare applications. These advances promise to revolutionize early Parkinson's disease detection and management, ultimately contributing to enhanced patient outcomes and quality of life.

Brain responses related to working memory originate from distinct brain areas and oscillate at different frequencies. EEG signals with high temporal correlation can effectively capture these responses. Therefore, estimating the functional connectivity of EEG for working memory protocols in different frequency bands plays a significant role in analyzing the brain dynamics with increasing memory and cognitive loads, which remains largely unexplored. The present study introduces a Bayesian structure learning algorithm to learn the functional connectivity of EEG in sensor space. Next, the functional connectivity graphs are taken as input to the graph convolutional network to classify the working memory loads. The intrasubject (subject-specific) classification performed on 154 subjects for six different verbal working memory loads produced the highest classification accuracy of 96% and average classification accuracy of 89%, outperforming state-of-the-art classification models proposed in the literature. Furthermore, the proposed Bayesian structure learning algorithm is compared with state-of-the-art functional connectivity estimation methods through intersubject and intrasubject statistical analysis of variance. The results also show that the alpha and theta bands have better classification accuracy than the beta band.

Averaging predictions from multiple competing inferential models frequently outperforms predictions from any single model, providing that models are optimally weighted to maximize predictive performance. This is particularly the case in so-called $\mathcal{M}$-open settings where the true model is not in the set of candidate models, and may be neither mathematically reifiable nor known precisely. This practice of model averaging has a rich history in statistics and machine learning, and there are currently a number of methods to estimate the weights for constructing model-averaged predictive distributions. Nonetheless, there are few existing software packages that can estimate model weights from the full variety of methods available, and none that blend model predictions into a coherent predictive distribution according to the estimated weights. In this paper, we introduce the BayesBlend Python package, which provides a user-friendly programming interface to estimate weights and blend multiple (Bayesian) models' predictive distributions. BayesBlend implements pseudo-Bayesian model averaging, stacking and, uniquely, hierarchical Bayesian stacking to estimate model weights. We demonstrate the usage of BayesBlend with examples of insurance loss modeling.

Deep generative models have been accelerating the inverse design process in material and drug design. Unlike their counterpart property predictors in typical molecular design frameworks, generative molecular design models have seen fewer efforts on uncertainty quantification (UQ) due to computational challenges in Bayesian inference posed by their large number of parameters. In this work, we focus on the junction-tree variational autoencoder (JT-VAE), a popular model for generative molecular design, and address this issue by leveraging the low dimensional active subspace to capture the uncertainty in the model parameters. Specifically, we approximate the posterior distribution over the active subspace parameters to estimate the epistemic model uncertainty in an extremely high dimensional parameter space. The proposed UQ scheme does not require alteration of the model architecture, making it readily applicable to any pre-trained model. Our experiments demonstrate the efficacy of the AS-based UQ and its potential impact on molecular optimization by exploring the model diversity under epistemic uncertainty.

MTL is a learning paradigm that effectively leverages both task-specific and shared information to address multiple related tasks simultaneously. In contrast to STL, MTL offers a suite of benefits that enhance both the training process and the inference efficiency. MTL's key advantages encompass streamlined model architecture, performance enhancement, and cross-domain generalizability. Over the past twenty years, MTL has become widely recognized as a flexible and effective approach in various fields, including CV, NLP, recommendation systems, disease prognosis and diagnosis, and robotics. This survey provides a comprehensive overview of the evolution of MTL, encompassing the technical aspects of cutting-edge methods from traditional approaches to deep learning and the latest trend of pretrained foundation models. Our survey methodically categorizes MTL techniques into five key areas: regularization, relationship learning, feature propagation, optimization, and pre-training. This categorization not only chronologically outlines the development of MTL but also dives into various specialized strategies within each category. Furthermore, the survey reveals how the MTL evolves from handling a fixed set of tasks to embracing a more flexible approach free from task or modality constraints. It explores the concepts of task-promptable and -agnostic training, along with the capacity for ZSL, which unleashes the untapped potential of this historically coveted learning paradigm. Overall, we hope this survey provides the research community with a comprehensive overview of the advancements in MTL from its inception in 1997 to the present in 2023. We address present challenges and look ahead to future possibilities, shedding light on the opportunities and potential avenues for MTL research in a broad manner. This project is publicly available at https://github.com/junfish/Awesome-Multitask-Learning.

Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process tomography, in which the goal is to retrieve the underlying quantum process based on a given set of measurement data. In this paper, we introduce a modified version of stochastic gradient descent on a Riemannian manifold that integrates recent advancements in numerical methods for Riemannian optimization. This approach inherently supports the physically driven constraints of a quantum process, takes advantage of state-of-the-art large-scale stochastic objective optimization, and has superior performance to traditional approaches such as maximum likelihood estimation and projected least squares. The data-driven approach enables accurate, order-of-magnitude faster results, and works with incomplete data. We demonstrate our approach on simulations of quantum processes and in hardware by characterizing an engineered process on quantum computers.

Synthetic microbiomes offer new possibilities for modulating microbiota, to address the barriers in multidtug resistance (MDR) research. We present a Bayesian optimization approach to enable efficient searching over the space of synthetic microbiome variants to identify candidates predictive of reduced MDR. Microbiome datasets were encoded into a low-dimensional latent space using autoencoders. Sampling from this space allowed generation of synthetic microbiome signatures. Bayesian optimization was then implemented to select variants for biological screening to maximize identification of designs with restricted MDR pathogens based on minimal samples. Four acquisition functions were evaluated: expected improvement, upper confidence bound, Thompson sampling, and probability of improvement. Based on each strategy, synthetic samples were prioritized according to their MDR detection. Expected improvement, upper confidence bound, and probability of improvement consistently produced synthetic microbiome candidates with significantly fewer searches than Thompson sampling. By combining deep latent space mapping and Bayesian learning for efficient guided screening, this study demonstrated the feasibility of creating bespoke synthetic microbiomes with customized MDR profiles.

Explanatory inference is the creation and evaluation of hypotheses that provide explanations, and is sometimes known as abduction or abductive inference. Generative AI is a new set of artificial intelligence models based on novel algorithms for generating text, images, and sounds. This paper proposes a set of benchmarks for assessing the ability of AI programs to perform explanatory inference, and uses them to determine the extent to which ChatGPT, a leading generative AI model, is capable of making explanatory inferences. Tests on the benchmarks reveal that ChatGPT performs creative and evaluative inferences in many domains, although it is limited to verbal and visual modalities. Claims that ChatGPT and similar models are incapable of explanation, understanding, causal reasoning, meaning, and creativity are rebutted.

Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may result in overconfident predictions and it prevents the use of deep learning models for sequential decision making. This thesis develops scalable methods to equip neural networks with model uncertainty. In particular, we leverage the linearised Laplace approximation to equip pre-trained neural networks with the uncertainty estimates provided by their tangent linear models. This turns the problem of Bayesian inference in neural networks into one of Bayesian inference in conjugate Gaussian-linear models. Alas, the cost of this remains cubic in either the number of network parameters or in the number of observations times output dimensions. By assumption, neither are tractable. We address this intractability by using stochastic gradient descent (SGD) -- the workhorse algorithm of deep learning -- to perform posterior sampling in linear models and their convex duals: Gaussian processes. With this, we turn back to linearised neural networks, finding the linearised Laplace approximation to present a number of incompatibilities with modern deep learning practices -- namely, stochastic optimisation, early stopping and normalisation layers -- when used for hyperparameter learning. We resolve these and construct a sample-based EM algorithm for scalable hyperparameter learning with linearised neural networks. We apply the above methods to perform linearised neural network inference with ResNet-50 (25M parameters) trained on Imagenet (1.2M observations and 1000 output dimensions). Additionally, we apply our methods to estimate uncertainty for 3d tomographic reconstructions obtained with the deep image prior network.

We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional, stationary matrix-variate Gaussian time series. All past work on high-dimensional matrix graphical models assumes that independent and identically distributed (i.i.d.) observations of the matrix-variate are available. Here we allow dependent observations. We consider a sparse-group lasso-based frequency-domain formulation of the problem with a Kronecker-decomposable power spectral density (PSD), and solve it via an alternating direction method of multipliers (ADMM) approach. The problem is bi-convex which is solved via flip-flop optimization. We provide sufficient conditions for local convergence in the Frobenius norm of the inverse PSD estimators to the true value. This result also yields a rate of convergence. We illustrate our approach using numerical examples utilizing both synthetic and real data.