In Diffusion Probabilistic Models (DPMs), the task of modeling the score evolution via a single time-dependent neural network necessitates extended training periods and may potentially impede modeling flexibility and capacity. To counteract these challenges, we propose leveraging the independence of learning tasks at different time points inherent to DPMs. More specifically, we partition the learning task by utilizing independent networks, each dedicated to learning the evolution of scores within a specific time sub-interval. Further, inspired by residual flows, we extend this strategy to its logical conclusion by employing separate networks to independently model the score at each individual time point. As empirically demonstrated on synthetic and image datasets, our approach not only significantly accelerates the training process by introducing an additional layer of parallelization atop data parallelization, but it also enhances density estimation performance when compared to the conventional training methodology for DPMs.

Healthcare in Africa is a complex issue influenced by many factors including poverty, lack of infrastructure, and inadequate funding. However, Artificial intelligence (AI) applied to healthcare, has the potential to transform healthcare in Africa by improving the accuracy and efficiency of diagnosis, enabling earlier detection of diseases, and supporting the delivery of personalized medicine. This paper reviews the current state of how AI Algorithms can be used to improve diagnostics, treatment, and disease monitoring, as well as how AI can be used to improve access to healthcare in Africa as a low-resource setting and discusses some of the critical challenges and opportunities for its adoption. As such, there is a need for a well-coordinated effort by the governments, private sector, healthcare providers, and international organizations to create sustainable AI solutions that meet the unique needs of the African healthcare system.

Variational auto-encoders are powerful probabilistic models in generative tasks but suffer from generating low-quality samples which are caused by the holes in the prior. We propose the Coupled Variational Auto-Encoder (C-VAE), which formulates the VAE problem as one of Optimal Transport (OT) between the prior and data distributions. The C-VAE allows greater flexibility in priors and natural resolution of the prior hole problem by enforcing coupling between the prior and the data distribution and enables flexible optimization through the primal, dual, and semi-dual formulations of entropic OT. Simulations on synthetic and real data show that the C-VAE outperforms alternatives including VAE, WAE, and InfoVAE in fidelity to the data, quality of the latent representation, and in quality of generated samples.

We address the tasks of Bayesian state estimation and forecasting for a model-free process in an unsupervised learning setup. In the article, we propose DANSE -- a Data-driven Nonlinear State Estimation method. DANSE provides a closed-form posterior of the state of the model-free process, given linear measurements of the state. In addition, it provides a closed-form posterior for forecasting. A data-driven recurrent neural network (RNN) is used in DANSE to provide the parameters of a prior of the state. The prior depends on the past measurements as input, and then we find the closed-form posterior of the state using the current measurement as input. The data-driven RNN captures the underlying non-linear dynamics of the model-free process. The training of DANSE, mainly learning the parameters of the RNN, is executed using an unsupervised learning approach. In unsupervised learning, we have access to a training dataset comprising only a set of measurement data trajectories, but we do not have any access to the state trajectories. Therefore, DANSE does not have access to state information in the training data and can not use supervised learning. Using simulated linear and non-linear process models (Lorenz attractor and Chen attractor), we evaluate the unsupervised learning-based DANSE. We show that the proposed DANSE, without knowledge of the process model and without supervised learning, provides a competitive performance against model-driven methods, such as the Kalman filter (KF), extended KF (EKF), unscented KF (UKF), and a recently proposed hybrid method called KalmanNet.

Probabilistic time series forecasting predicts the conditional probability distributions of the time series at a future time given past realizations. Such techniques are critical in risk-based decision-making and planning under uncertainties. Existing approaches are primarily based on parametric or semi-parametric time-series models that are restrictive, difficult to validate, and challenging to adapt to varying conditions. This paper proposes a nonparametric method based on the classic notion of {\em innovations} pioneered by Norbert Wiener and Gopinath Kallianpur that causally transforms a nonparametric random process to an independent and identical uniformly distributed {\em innovations process}. We present a machine-learning architecture and a learning algorithm that circumvent two limitations of the original Wiener-Kallianpur innovations representation: (i) the need for known probability distributions of the time series and (ii) the existence of a causal decoder that reproduces the original time series from the innovations representation. We develop a deep-learning approach and a Monte Carlo sampling technique to obtain a generative model for the predicted conditional probability distribution of the time series based on a weak notion of Wiener-Kallianpur innovations representation. The efficacy of the proposed probabilistic forecasting technique is demonstrated on a variety of electricity price datasets, showing marked improvement over leading benchmarks of probabilistic forecasting techniques.

Models of many real-life applications, such as queuing models of communication networks or computing systems, have a countably infinite state-space. Algorithmic and learning procedures that have been developed to produce optimal policies mainly focus on finite state settings, and do not directly apply to these models. To overcome this lacuna, in this work we study the problem of optimal control of a family of discrete-time countable state-space Markov Decision Processes (MDPs) governed by an unknown parameter $\theta\in\Theta$, and defined on a countably-infinite state space $\mathcal X=\mathbb{Z}_+^d$, with finite action space $\mathcal A$, and an unbounded cost function. We take a Bayesian perspective with the random unknown parameter $\boldsymbol{\theta}^*$ generated via a given fixed prior distribution on $\Theta$. To optimally control the unknown MDP, we propose an algorithm based on Thompson sampling with dynamically-sized episodes: at the beginning of each episode, the posterior distribution formed via Bayes' rule is used to produce a parameter estimate, which then decides the policy applied during the episode. To ensure the stability of the Markov chain obtained by following the policy chosen for each parameter, we impose ergodicity assumptions. From this condition and using the solution of the average cost Bellman equation, we establish an $\tilde O(\sqrt{|\mathcal A|T})$ upper bound on the Bayesian regret of our algorithm, where $T$ is the time-horizon. Finally, to elucidate the applicability of our algorithm, we consider two different queuing models with unknown dynamics, and show that our algorithm can be applied to develop approximately optimal control algorithms.

We propose a unified approach to obtain structured sparse optimal paths in the latent space of a variational autoencoder (VAE) using dynamic programming and Gumbel propagation. We solve the classical optimal path problem by a probability softening solution, called the stochastic optimal path, and transform a wide range of DP problems into directed acyclic graphs in which all possible paths follow a Gibbs distribution. We show the equivalence of the Gibbs distribution to a message-passing algorithm by the properties of the Gumbel distribution and give all the ingredients required for variational Bayesian inference. Our approach obtaining latent optimal paths enables end-to-end training for generative tasks in which models rely on the information of unobserved structural features. We validate the behavior of our approach and showcase its applicability in two real-world applications: text-to-speech and singing voice synthesis.

Commonly used objective functions (losses) for a supervised optimization of discriminative neural network classifiers were either distribution-based or metric-based. The distribution-based losses could compromise the generalization or cause classification biases towards the dominant classes of an imbalanced class-sample distribution. The metric-based losses could make the network model independent of any distribution and thus improve its generalization. However, they could still be biased towards the dominant classes and could suffer from discrepancies when a class was absent in both the reference (ground truth) and the predicted labels. In this paper, we proposed a novel optimization process which not only tackled the unbalancedness of the class-sample distribution of the training samples but also provided a mechanism to tackle errors in the reference labels of the training samples. This was achieved by proposing a novel algorithm to find candidate classification labels of the training samples from their prior probabilities and the currently estimated posteriors on the network and a novel objective function for the optimizations. The algorithm was the result of casting the generalized Kelly criterion for optimal betting into a multiclass classification problem. The proposed objective function was the expected free energy of a prospective active inference and could incorporate the candidate labels, the original reference labels, and the priors of the training samples while still being distribution-based. The incorporation of the priors into the optimization not only helped to tackle errors in the reference labels but also allowed to reduce classification biases towards the dominant classes by focusing the attention of the neural network on important but minority foreground classes.

Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically and empirically that the KSD test can suffer from low power when the target and the alternative distributions have the same well-separated modes but differ in mixing proportions. We propose to perturb the observed sample via Markov transition kernels, with respect to which the target distribution is invariant. This allows us to then employ the KSD test on the perturbed sample. We provide numerical evidence that with suitably chosen transition kernels the proposed approach can lead to substantially higher power than the KSD test.

Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty in the parameter values, functional forms with diverse parameterizations, level of complexity needed, and thus in the state fields. We develop a Bayesian model learning methodology that allows interpolation in the space of candidate models and discovery of new models from noisy, sparse, and indirect observations, all while estimating state fields and parameter values, as well as the joint PDFs of all learned quantities. We address the challenges of high-dimensional and multidisciplinary dynamics governed by PDEs by using state augmentation and the computationally efficient GMM-DO filter. Our innovations include stochastic formulation and complexity parameters to unify candidate models into a single general model as well as stochastic expansion parameters within piecewise function approximations to generate dense candidate model spaces. These innovations allow handling many compatible and embedded candidate models, possibly none of which are accurate, and learning elusive unknown functional forms. Our new methodology is generalizable, interpretable, and extrapolates out of the space of models to discover new ones. We perform a series of twin experiments based on flows past a ridge coupled with three-to-five component ecosystem models, including flows with chaotic advection. The probabilities of known, uncertain, and unknown model formulations, and of state fields and parameters, are updated jointly using Bayes' law. Non-Gaussian statistics, ambiguity, and biases are captured. The parameter values and model formulations that best explain the data are identified. When observations are sufficiently informative, model complexity and functions are discovered.