Bayes' rule describes how to infer posterior beliefs about latent variables given observations, and inference is a critical step in learning algorithms for latent variable models (LVMs). Although there are exact algorithms for inference and learning for certain LVMs such as linear Gaussian models and mixture models, researchers must typically develop approximate inference and learning algorithms when applying novel LVMs. In this paper we study the line that separates LVMs that rely on approximation schemes from those that do not, and develop a general theory of exponential family, latent variable models for which inference and learning may be implemented exactly. Firstly, under mild assumptions about the exponential family form of a given LVM, we derive necessary and sufficient conditions under which the LVM prior is in the same exponential family as its posterior, such that the prior is conjugate to the posterior. We show that all models that satisfy these conditions are constrained forms of a particular class of exponential family graphical model. We then derive general inference and learning algorithms, and demonstrate them on a variety of example models. Finally, we show how to compose our models into graphical models that retain tractable inference and learning. In addition to our theoretical work, we have implemented our algorithms in a collection of libraries with which we provide numerous demonstrations of our theory, and with which researchers may apply our theory in novel statistical settings.

Imbuing machines with the ability to talk has been a longtime pursuit of artificial intelligence (AI) research. From the very beginning, the community has not only aimed to synthesise high-fidelity speech that accurately conveys the semantic meaning of an utterance, but also to colour it with inflections that cover the same range of affective expressions that humans are capable of. After many years of research, it appears that we are on the cusp of achieving this when it comes to single, isolated utterances. This unveils an abundance of potential avenues to explore when it comes to combining these single utterances with the aim of synthesising more complex, longer-term behaviours. In the present chapter, we outline the methodological advances that brought us so far and sketch out the ongoing efforts to reach that coveted next level of artificial expressivity. We also discuss the societal implications coupled with rapidly advancing expressive speech synthesis (ESS) technology and highlight ways to mitigate those risks and ensure the alignment of ESS capabilities with ethical norms.

For nearly three decades, language models derived from the $n$-gram assumption held the state of the art on the task. The key to their success lay in the application of various smoothing techniques that served to combat overfitting. However, when neural language models toppled $n$-gram models as the best performers, $n$-gram smoothing techniques became less relevant. Indeed, it would hardly be an understatement to suggest that the line of inquiry into $n$-gram smoothing techniques became dormant. This paper re-opens the role classical $n$-gram smoothing techniques may play in the age of neural language models. First, we draw a formal equivalence between label smoothing, a popular regularization technique for neural language models, and add-$\lambda$ smoothing. Second, we derive a generalized framework for converting any $n$-gram smoothing technique into a regularizer compatible with neural language models. Our empirical results find that our novel regularizers are comparable to and, indeed, sometimes outperform label smoothing on language modeling and machine translation.

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.

We introduce the concept of imprecise Markov semigroup. It allows us to see Markov chains and processes with imprecise transition probabilities as (a collection of diffusion) operators, and thus to unlock techniques from geometry, functional analysis, and (high dimensional) probability to study their ergodic behavior. We show that, if the initial distribution of an imprecise Markov semigroup is known and invariant, under some conditions that also involve the geometry of the state space, eventually the ambiguity around the transition probability fades. We call this property ergodicity of the imprecise Markov semigroup, and we relate it to the classical (Birkhoff's) notion of ergodicity. We prove ergodicity both when the state space is Euclidean or a Riemannian manifold, and when it is an arbitrary measurable space. The importance of our findings for the fields of machine learning and computer vision is also discussed.

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.

Visual control policies can encounter significant performance degradation when visual conditions like lighting or camera position differ from those seen during training -- often exhibiting sharp declines in capability even for minor differences. In this work, we examine robustness to a suite of these types of visual changes for RGB-D and point cloud based visual control policies. To perform these experiments on both model-free and model-based reinforcement learners, we introduce a novel Point Cloud World Model (PCWM) and point cloud based control policies. Our experiments show that policies that explicitly encode point clouds are significantly more robust than their RGB-D counterparts. Further, we find our proposed PCWM significantly outperforms prior works in terms of sample efficiency during training. Taken together, these results suggest reasoning about the 3D scene through point clouds can improve performance, reduce learning time, and increase robustness for robotic learners. Project Webpage: https://pvskand.github.io/projects/PCWM

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.