This dissertation attempts to drive innovation in the field of generative modeling for computer vision, by exploring novel formulations of conditional generative models, and innovative applications in images, 3D animations, and video. Our research focuses on architectures that offer reversible transformations of noise and visual data, and the application of encoder-decoder architectures for generative tasks and 3D content manipulation. In all instances, we incorporate conditional information to enhance the synthesis of visual data, improving the efficiency of the generation process as well as the generated content. We introduce the use of Neural ODEs to model video dynamics using an encoder-decoder architecture, demonstrating their ability to predict future video frames despite being trained solely to reconstruct current frames. Next, we propose a conditional variant of continuous normalizing flows that enables higher-resolution image generation based on lower-resolution input, achieving comparable image quality while reducing parameters and training time. Our next contribution presents a pipeline that takes human images as input, automatically aligns a user-specified 3D character with the pose of the human, and facilitates pose editing based on partial inputs. Next, we derive the relevant mathematical details for denoising diffusion models that use non-isotropic Gaussian processes, and show comparable generation quality. Finally, we devise a novel denoising diffusion framework capable of solving all three video tasks of prediction, generation, and interpolation. We perform ablation studies, and show SOTA results on multiple datasets. Our contributions are published articles at peer-reviewed venues. Overall, our research aims to make a meaningful contribution to the pursuit of more efficient and flexible generative models, with the potential to shape the future of computer vision.

Bayesian Neural Networks (BNNs) have become one of the promising approaches for uncertainty estimation due to the solid theorical foundations. However, the performance of BNNs is affected by the ability of catching uncertainty. Instead of only seeking the distribution of neural network weights by in-distribution (ID) data, in this paper, we propose a new Bayesian Neural Network with an Attached structure (ABNN) to catch more uncertainty from out-of-distribution (OOD) data. We first construct a mathematical description for the uncertainty of OOD data according to the prior distribution, and then develop an attached Bayesian structure to integrate the uncertainty of OOD data into the backbone network. ABNN is composed of an expectation module and several distribution modules. The expectation module is a backbone deep network which focuses on the original task, and the distribution modules are mini Bayesian structures which serve as attachments of the backbone. In particular, the distribution modules aim at extracting the uncertainty from both ID and OOD data. We further provide theoretical analysis for the convergence of ABNN, and experimentally validate its superiority by comparing with some state-of-the-art uncertainty estimation methods Code will be made available.

We develop a probabilistic graphical model (PGM) for artificially intelligent (AI) agents to infer human beliefs during a simulated urban search and rescue (USAR) scenario executed in a Minecraft environment with a team of three players. The PGM approach makes observable states and actions explicit, as well as beliefs and intentions grounded by evidence about what players see and do over time. This approach also supports inferring the effect of interventions, which are vital if AI agents are to assist human teams. The experiment incorporates manipulations of players' knowledge, and the virtual Minecraft-based testbed provides access to several streams of information, including the objects in the players' field of view. The participants are equipped with a set of marker blocks that can be placed near room entrances to signal the presence or absence of victims in the rooms to their teammates. In each team, one of the members is given a different legend for the markers than the other two, which may mislead them about the state of the rooms; that is, they will hold a false belief. We extend previous works in this field by introducing ToMCAT, an AI agent that can reason about individual and shared mental states. We find that the players' behaviors are affected by what they see in their in-game field of view, their beliefs about the meaning of the markers, and their beliefs about which meaning the team decided to adopt. In addition, we show that ToMCAT's beliefs are consistent with the players' actions and that it can infer false beliefs with accuracy significantly better than chance and comparable to inferences made by human observers.

Robots can learn to imitate humans by inferring what the human is optimizing for. One common framework for this is Bayesian reward learning, where the robot treats the human's demonstrations and corrections as observations of their underlying reward function. Unfortunately, this inference is doubly-intractable: the robot must reason over all the trajectories the person could have provided and all the rewards the person could have in mind. Prior work uses existing robotic tools to approximate this normalizer. In this paper, we group previous approaches into three fundamental classes and analyze the theoretical pros and cons of their approach. We then leverage recent research from the statistics community to introduce Double MH reward learning, a Monte Carlo method for asymptotically learning the human's reward in continuous spaces. We extend Double MH to conditionally independent settings (where each human correction is viewed as completely separate) and conditionally dependent environments (where the human's current correction may build on previous inputs). Across simulations and user studies, our proposed approach infers the human's reward parameters more accurately than the alternate approximations when learning from either demonstrations or corrections. See videos here: https://youtu.be/EkmT3o5K5ko

As two cornerstones of modern day technologies, speech processing and natural language processing (NLP) are innately sequence learning problems to extract information from these linguistic or speech signals and provide insights into interactive systems to communicate in human understandable languages. The sequential and interactive nature of these problems can make them well-suited into the algorithmic framework of reinforcement learning (RL). In a reinforcement learning setting, an agent interacts with an environment through observations and actions, and based on the reward feedback attributed by the underlying reward function of this environment, the agent learns how to perform the task of interest through trials and errors. While the successful applications of reinforcement learning have been highlighted by a wide range of surveys in many real-world engineering domains such as robotics [1], vision [2], finance [3], healthcare [4], linguistics [5], and energy management [6], there have not been one for the rich community of both the speech and language domains. This is the first survey that emphasizes the synergy among the growing fields of the speech processing, natural language processing and the reinforcement learning. We aim to fill this gap by adopting a complete, timely and classical view of the reinforcement learning problems and their connections to speech and language processing.

Although the Bayesian paradigm offers a formal framework for estimating the entire probability distribution over uncertain parameters, its online implementation can be challenging due to high computational costs. We suggest the Adaptive Recursive Markov Chain Monte Carlo (ARMCMC) method, which eliminates the shortcomings of conventional online techniques while computing the entire probability density function of model parameters. The limitations to Gaussian noise, the application to only linear in the parameters (LIP) systems, and the persistent excitation (PE) needs are some of these drawbacks. In ARMCMC, a temporal forgetting factor (TFF)-based variable jump distribution is proposed. The forgetting factor can be presented adaptively using the TFF in many dynamical systems as an alternative to a constant hyperparameter. By offering a trade-off between exploitation and exploration, the specific jump distribution has been optimised towards hybrid/multi-modal systems that permit inferences among modes. These trade-off are adjusted based on parameter evolution rate. We demonstrate that ARMCMC requires fewer samples than conventional MCMC methods to achieve the same precision and reliability. We demonstrate our approach using parameter estimation in a soft bending actuator and the Hunt-Crossley dynamic model, two challenging hybrid/multi-modal benchmarks. Additionally, we compare our method with recursive least squares and the particle filter, and show that our technique has significantly more accurate point estimates as well as a decrease in tracking error of the value of interest.

Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting, where the goal is to model and forecast multivariate time-series that have underlying hierarchical relations. Most methods focus on point predictions and do not provide well-calibrated probabilistic forecasts distributions. Recent state-of-art probabilistic forecasting methods also impose hierarchical relations on point predictions and samples of distribution which does not account for coherency of forecast distributions. Previous works also silently assume that datasets are always consistent with given hierarchical relations and do not adapt to real-world datasets that show deviation from this assumption. We close both these gap and propose PROFHiT, which is a fully probabilistic hierarchical forecasting model that jointly models forecast distribution of entire hierarchy. PROFHiT uses a flexible probabilistic Bayesian approach and introduces a novel Distributional Coherency regularization to learn from hierarchical relations for entire forecast distribution that enables robust and calibrated forecasts as well as adapt to datasets of varying hierarchical consistency. On evaluating PROFHiT over wide range of datasets, we observed 41-88% better performance in accuracy and significantly better calibration. Due to modeling the coherency over full distribution, we observed that PROFHiT can robustly provide reliable forecasts even if up to 10% of input time-series data is missing where other methods' performance severely degrade by over 70%.

Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter weighting information in the loss relative to the prior and providing a control of posterior uncertainty. Gibbs posteriors provide a principled framework for likelihood-free Bayesian inference, but in many situations, including a single tuning parameter inevitably leads to poor uncertainty quantification. In particular, regardless of the value of the parameter, credible regions have far from the nominal frequentist coverage even in large samples. We propose a sequential extension to Gibbs posteriors to address this problem. We prove the proposed sequential posterior exhibits concentration and a Bernstein-von Mises theorem, which holds under easy to verify conditions in Euclidean space and on manifolds. As a byproduct, we obtain the first Bernstein-von Mises theorem for traditional likelihood-based Bayesian posteriors on manifolds. All methods are illustrated with an application to principal component analysis.

In order to trust the predictions of a machine learning algorithm, it is necessary to understand the factors that contribute to those predictions. In the case of probabilistic and uncertainty-aware models, it is necessary to understand not only the reasons for the predictions themselves, but also the model's level of confidence in those predictions. In this paper, we show how existing methods in explainability can be extended to uncertainty-aware models and how such extensions can be used to understand the sources of uncertainty in a model's predictive distribution. In particular, by adapting permutation feature importance, partial dependence plots, and individual conditional expectation plots, we demonstrate that novel insights into model behaviour may be obtained and that these methods can be used to measure the impact of features on both the entropy of the predictive distribution and the log-likelihood of the ground truth labels under that distribution. With experiments using both synthetic and real-world data, we demonstrate the utility of these approaches in understanding both the sources of uncertainty and their impact on model performance.

We propose in this paper, STANLEY, a STochastic gradient ANisotropic LangEvin dYnamics, for sampling high dimensional data. With the growing efficacy and potential of Energy-Based modeling, also known as non-normalized probabilistic modeling, for modeling a generative process of different natures of high dimensional data observations, we present an end-to-end learning algorithm for Energy-Based models (EBM) with the purpose of improving the quality of the resulting sampled data points. While the unknown normalizing constant of EBMs makes the training procedure intractable, resorting to Markov Chain Monte Carlo (MCMC) is in general a viable option. Realizing what MCMC entails for the EBM training, we propose in this paper, a novel high dimensional sampling method, based on an anisotropic stepsize and a gradient-informed covariance matrix, embedded into a discretized Langevin diffusion. We motivate the necessity for an anisotropic update of the negative samples in the Markov Chain by the nonlinearity of the backbone of the EBM, here a Convolutional Neural Network. Our resulting method, namely STANLEY, is an optimization algorithm for training Energy-Based models via our newly introduced MCMC method. We provide a theoretical understanding of our sampling scheme by proving that the sampler leads to a geometrically uniformly ergodic Markov Chain. Several image generation experiments are provided in our paper to show the effectiveness of our method.