This paper introduces Elastic Decision Transformer (EDT), a significant advancement over the existing Decision Transformer (DT) and its variants. Although DT purports to generate an optimal trajectory, empirical evidence suggests it struggles with trajectory stitching, a process involving the generation of an optimal or near-optimal trajectory from the best parts of a set of sub-optimal trajectories. The proposed EDT differentiates itself by facilitating trajectory stitching during action inference at test time, achieved by adjusting the history length maintained in DT. Further, the EDT optimizes the trajectory by retaining a longer history when the previous trajectory is optimal and a shorter one when it is sub-optimal, enabling it to "stitch" with a more optimal trajectory. Extensive experimentation demonstrates EDT's ability to bridge the performance gap between DT-based and Q Learning-based approaches. In particular, the EDT outperforms Q Learning-based methods in a multi-task regime on the D4RL locomotion benchmark and Atari games. Videos are available at: https://kristery.github.io/edt/.

Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a simulator posing the need for simulation-based inference (SBI). However, the existing algorithms can yield overconfident posteriors (Hermans *et al.*, 2022) defeating the whole purpose of credibility if the uncertainty quantification is inaccurate. We propose to include a calibration term directly into the training objective of the neural model in selected amortized SBI techniques. By introducing a relaxation of the classical formulation of calibration error we enable end-to-end backpropagation. The proposed method is not tied to any particular neural model and brings moderate computational overhead compared to the profits it introduces. It is directly applicable to existing computational pipelines allowing reliable black-box posterior inference. We empirically show on six benchmark problems that the proposed method achieves competitive or better results in terms of coverage and expected posterior density than the previously existing approaches.

Accurate battery lifetime prediction is important for preventative maintenance, warranties, and improved cell design and manufacturing. However, manufacturing variability and usage-dependent degradation make life prediction challenging. Here, we investigate new features derived from capacity-voltage data in early life to predict the lifetime of cells cycled under widely varying charge rates, discharge rates, and depths of discharge. Features were extracted from regularly scheduled reference performance tests (i.e., low rate full cycles) during cycling. The early-life features capture a cell's state of health and the rate of change of component-level degradation modes, some of which correlate strongly with cell lifetime. Using a newly generated dataset from 225 nickel-manganese-cobalt/graphite Li-ion cells aged under a wide range of conditions, we demonstrate a lifetime prediction of in-distribution cells with 15.1% mean absolute percentage error using no more than the first 15% of data, for most cells. Further testing using a hierarchical Bayesian regression model shows improved performance on extrapolation, achieving 21.8% mean absolute percentage error for out-of-distribution cells. Our approach highlights the importance of using domain knowledge of lithium-ion battery degradation modes to inform feature engineering. Further, we provide the community with a new publicly available battery aging dataset with cells cycled beyond 80% of their rated capacity.

Implementations of Markov chain Monte Carlo (MCMC) methods need to confront two fundamental challenges: accurate representation of prior information and efficient evaluation of likelihoods. Principal component analysis (PCA) and related techniques can in some cases facilitate the definition and sampling of the prior distribution, as well as the training of accurate surrogate models, using for instance, polynomial chaos expansion (PCE). However, complex geological priors with sharp contrasts necessitate more complex dimensionality-reduction techniques, such as, deep generative models (DGMs). By sampling a low-dimensional prior probability distribution defined in the low-dimensional latent space of such a model, it becomes possible to efficiently sample the physical domain at the price of a generator that is typically highly non-linear. Training a surrogate that is capable of capturing intricate non-linear relationships between latent parameters and outputs of forward modeling presents a notable challenge. Indeed, while PCE models provide high accuracy when the input-output relationship can be effectively approximated by relatively low-degree multivariate polynomials, this condition is typically not met when employing latent variables derived from DGMs. In this contribution, we present a strategy combining the excellent reconstruction performances of a variational autoencoder (VAE) with the accuracy of PCA-PCE surrogate modeling in the context of Bayesian ground penetrating radar (GPR) traveltime tomography. Within the MCMC process, the parametrization of the VAE is leveraged for prior exploration and sample proposals. Concurrently, surrogate modeling is conducted using PCE, which operates on either globally or locally defined principal components of the VAE samples under examination.

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.

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.