Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to model highly stochastic time series data remains a challenge. In this paper, we propose a novel Stochastic Diffusion (StochDiff) model which learns data-driven prior knowledge at each time step by utilizing the representational power of the stochastic latent spaces to model the variability of the multivariate time series data. The learnt prior knowledge helps the model to capture complex temporal dynamics and the inherent uncertainty of the data. This improves its ability to model highly stochastic time series data. Through extensive experiments on real-world datasets, we demonstrate the effectiveness of our proposed model on stochastic time series forecasting. Additionally, we showcase an application of our model for real-world surgical guidance, highlighting its potential to benefit the medical community.

The estimation of directed couplings between the nodes of a network from indirect measurements is a central methodological challenge in scientific fields such as neuroscience, systems biology and economics. Unfortunately, the problem is generally ill-posed due to the possible presence of unknown delays in the measurements. In this paper, we offer a solution of this problem by using a variational Bayes framework, where the uncertainty over the delays is marginalized in order to obtain conservative coupling estimates. To overcome the well-known overconfidence of classical variational methods, we use a hybrid-VI scheme where the (possibly flat or multimodal) posterior over the measurement parameters is estimated using a forward KL loss while the (nearly convex) conditional posterior over the couplings is estimated using the highly scalable gradient-based VI. In our ground-truth experiments, we show that the network provides reliable and conservative estimates of the couplings, greatly outperforming similar methods such as regression DCM.

Reconstructing images from the Event Horizon Telescope (EHT) observations of M87*, the supermassive black hole at the center of the galaxy M87, depends on a prior to impose desired image statistics. However, given the impossibility of directly observing black holes, there is no clear choice for a prior. We present a framework for flexibly designing a range of priors, each bringing different biases to the image reconstruction. These priors can be weak (e.g., impose only basic natural-image statistics) or strong (e.g., impose assumptions of black-hole structure). Our framework uses Bayesian inference with score-based priors, which are data-driven priors arising from a deep generative model that can learn complicated image distributions. Using our Bayesian imaging approach with sophisticated data-driven priors, we can assess how visual features and uncertainty of reconstructed images change depending on the prior. In addition to simulated data, we image the real EHT M87* data and discuss how recovered features are influenced by the choice of prior.

A key challenge in e-learning environments like Intelligent Tutoring Systems (ITSs) is to induce effective pedagogical policies efficiently. While Deep Reinforcement Learning (DRL) often suffers from sample inefficiency and reward function design difficulty, Apprenticeship Learning(AL) algorithms can overcome them. However, most AL algorithms can not handle heterogeneity as they assume all demonstrations are generated with a homogeneous policy driven by a single reward function. Still, some AL algorithms which consider heterogeneity, often can not generalize to large continuous state space and only work with discrete states. In this paper, we propose an expectation-maximization(EM)-EDM, a general AL framework to induce effective pedagogical policies from given optimal or near-optimal demonstrations, which are assumed to be driven by heterogeneous reward functions. We compare the effectiveness of the policies induced by our proposed EM-EDM against four AL-based baselines and two policies induced by DRL on two different but related tasks that involve pedagogical action prediction. Our overall results showed that, for both tasks, EM-EDM outperforms the four AL baselines across all performance metrics and the two DRL baselines. This suggests that EM-EDM can effectively model complex student pedagogical decision-making processes through the ability to manage a large, continuous state space and adapt to handle diverse and heterogeneous reward functions with very few given demonstrations.

We provide a theoretical and computational investigation of the Gamma-Maximin method with soft revision, which was recently proposed as a robust criterion for pseudo-label selection (PLS) in semi-supervised learning. Opposed to traditional methods for PLS we use credal sets of priors ("generalized Bayes") to represent the epistemic modeling uncertainty. These latter are then updated by the Gamma-Maximin method with soft revision. We eventually select pseudo-labeled data that are most likely in light of the least favorable distribution from the so updated credal set. We formalize the task of finding optimal pseudo-labeled data w.r.t. the Gamma-Maximin method with soft revision as an optimization problem. A concrete implementation for the class of logistic models then allows us to compare the predictive power of the method with competing approaches. It is observed that the Gamma-Maximin method with soft revision can achieve very promising results, especially when the proportion of labeled data is low.

We present a novel approach to uncertainty quantification in classification tasks based on label-wise decomposition of uncertainty measures. This label-wise perspective allows uncertainty to be quantified at the individual class level, thereby improving cost-sensitive decision-making and helping understand the sources of uncertainty. Furthermore, it allows to define total, aleatoric, and epistemic uncertainty on the basis of non-categorical measures such as variance, going beyond common entropy-based measures. In particular, variance-based measures address some of the limitations associated with established methods that have recently been discussed in the literature. We show that our proposed measures adhere to a number of desirable properties. Through empirical evaluation on a variety of benchmark data sets -- including applications in the medical domain where accurate uncertainty quantification is crucial -- we establish the effectiveness of label-wise uncertainty quantification.

Learning conditional distributions is challenging because the desired outcome is not a single distribution but multiple distributions that correspond to multiple instances of the covariates. We introduce a novel neural entropic optimal transport method designed to effectively learn generative models of conditional distributions, particularly in scenarios characterized by limited sample sizes. Our method relies on the minimax training of two neural networks: a generative network parametrizing the inverse cumulative distribution functions of the conditional distributions and another network parametrizing the conditional Kantorovich potential. To prevent overfitting, we regularize the objective function by penalizing the Lipschitz constant of the network output. Our experiments on real-world datasets show the effectiveness of our algorithm compared to state-of-the-art conditional distribution learning techniques. Our implementation can be found at https://github.com/nguyenngocbaocmt02/GENTLE.

We theoretically analyze the original version of the denoising diffusion probabilistic models (DDPMs) presented in Ho, J., Jain, A., and Abbeel, P., Advances in Neural Information Processing Systems, 33 (2020), pp. 6840-6851. Our main theorem states that the sequence constructed by the original DDPM sampling algorithm weakly converges to a given data distribution as the number of time steps goes to infinity, under some asymptotic conditions on the parameters for the variance schedule, the $L^2$-based score estimation error, and the noise estimating function with respect to the number of time steps. In proving the theorem, we reveal that the sampling sequence can be seen as an exponential integrator type approximation of a reverse time stochastic differential equation (SDE). Moreover, we give a proper definition of the backward It\^o integral for general continuous processes and prove rigorously the reverse time representation of a given SDE with backward It\^o integral, without using the smoothness and uniqueness of the associated forward Kolmogorov equations.

Expectation propagation (EP) is a family of algorithms for performing approximate inference in probabilistic models. The updates of EP involve the evaluation of moments -- expectations of certain functions -- which can be estimated from Monte Carlo (MC) samples. However, the updates are not robust to MC noise when performed naively, and various prior works have attempted to address this issue in different ways. In this work, we provide a novel perspective on the moment-matching updates of EP; namely, that they perform natural-gradient-based optimisation of a variational objective. We use this insight to motivate two new EP variants, with updates that are particularly well-suited to MC estimation; they remain stable and are most sample-efficient when estimated with just a single sample. These new variants combine the benefits of their predecessors and address key weaknesses. In particular, they are easier to tune, offer an improved speed-accuracy trade-off, and do not rely on the use of debiasing estimators. We demonstrate their efficacy on a variety of probabilistic inference tasks.

Generative modelling paradigms based on denoising diffusion processes have emerged as a leading candidate for conditional sampling in inverse problems. In many real-world applications, we often have access to large, expensively trained unconditional diffusion models, which we aim to exploit for improving conditional sampling. Most recent approaches are motivated heuristically and lack a unifying framework, obscuring connections between them. Further, they often suffer from issues such as being very sensitive to hyperparameters, being expensive to train or needing access to weights hidden behind a closed API. In this work, we unify conditional training and sampling using the mathematically well-understood Doob's h-transform. This new perspective allows us to unify many existing methods under a common umbrella. Under this framework, we propose DEFT (Doob's h-transform Efficient FineTuning), a new approach for conditional generation that simply fine-tunes a very small network to quickly learn the conditional $h$-transform, while keeping the larger unconditional network unchanged. DEFT is much faster than existing baselines while achieving state-of-the-art performance across a variety of linear and non-linear benchmarks. On image reconstruction tasks, we achieve speedups of up to 1.6$\times$, while having the best perceptual quality on natural images and reconstruction performance on medical images.