In real-world scenarios, datasets collected from randomized experiments are often constrained by size, due to limitations in time and budget. As a result, leveraging large observational datasets becomes a more attractive option for achieving high-quality policy learning. However, most existing offline reinforcement learning (RL) methods depend on two key assumptions--unconfoundedness and positivity--which frequently do not hold in observational data contexts. Recognizing these challenges, we propose a novel policy learning algorithm, PESsimistic CAusal Learning (PESCAL). We utilize the mediator variable based on front-door criterion to remove the confounding bias; additionally, we adopt the pessimistic principle to address the distributional shift between the action distributions induced by candidate policies, and the behavior policy that generates the observational data. Our key observation is that, by incorporating auxiliary variables that mediate the effect of actions on system dynamics, it is sufficient to learn a lower bound of the mediator distribution function, instead of the Q-function, to partially mitigate the issue of distributional shift. This insight significantly simplifies our algorithm, by circumventing the challenging task of sequential uncertainty quantification for the estimated Q-function. Moreover, we provide theoretical guarantees for the algorithms we propose, and demonstrate their efficacy through simulations, as well as real-world experiments utilizing offline datasets from a leading ride-hailing platform.

In this paper, we approach the problem of uncertainty quantification in deep learning through a predictive framework, which captures uncertainty in model parameters by specifying our assumptions about the predictive distribution of unseen future data. Under this view, we show that deep ensembling (Lakshminarayanan et al., 2017) is a fundamentally mis-specified model class, since it assumes that future data are supported on existing observations only -- a situation rarely encountered in practice. To address this limitation, we propose MixupMP, a method that constructs a more realistic predictive distribution using popular data augmentation techniques. MixupMP operates as a drop-in replacement for deep ensembles, where each ensemble member is trained on a random simulation from this predictive distribution. Grounded in the recently-proposed framework of Martingale posteriors (Fong et al., 2023), MixupMP returns samples from an implicitly defined Bayesian posterior. Our empirical analysis showcases that MixupMP achieves superior predictive performance and uncertainty quantification on various image classification datasets, when compared with existing Bayesian and non-Bayesian approaches.

A deterministic temporal process can be determined by its trajectory, an element in the product space of (a) initial condition $z_0 \in \mathcal{Z}$ and (b) transition function $f: (\mathcal{Z}, \mathcal{T}) \to \mathcal{Z}$ often influenced by the control of the underlying dynamical system. Existing methods often model the transition function as a differential equation or as a recurrent neural network. Despite their effectiveness in predicting future measurements, few results have successfully established a method for sampling and statistical inference of trajectories using neural networks, partially due to constraints in the parameterization. In this work, we introduce a mechanism to learn the distribution of trajectories by parameterizing the transition function $f$ explicitly as an element in a function space. Our framework allows efficient synthesis of novel trajectories, while also directly providing a convenient tool for inference, i.e., uncertainty estimation, likelihood evaluations and out of distribution detection for abnormal trajectories. These capabilities can have implications for various downstream tasks, e.g., simulation and evaluation for reinforcement learning.

We focus on the problem of long-range dynamic replanning for off-road autonomous vehicles, where a robot plans paths through a previously unobserved environment while continuously receiving noisy local observations. An effective approach for planning under sensing uncertainty is determinization, where one converts a stochastic world into a deterministic one and plans under this simplification. This makes the planning problem tractable, but the cost of following the planned path in the real world may be different than in the determinized world. This causes collisions if the determinized world optimistically ignores obstacles, or causes unnecessarily long routes if the determinized world pessimistically imagines more obstacles. We aim to be robust to uncertainty over potential worlds while still achieving the efficiency benefits of determinization. We evaluate algorithms for dynamic replanning on a large real-world dataset of challenging long-range planning problems from the DARPA RACER program. Our method, Dynamic Replanning via Evaluating and Aggregating Multiple Samples (DREAMS), outperforms other determinization-based approaches in terms of combined traversal time and collision cost. https://sites.google.com/cs.washington.edu/dreams/

Interest in the use of Denoising Diffusion Models (DDM) as priors for solving inverse Bayesian problems has recently increased significantly. However, sampling from the resulting posterior distribution poses a challenge. To solve this problem, previous works have proposed approximations to bias the drift term of the diffusion. In this work, we take a different approach and utilize the specific structure of the DDM prior to define a set of intermediate and simpler posterior sampling problems, resulting in a lower approximation error compared to previous methods. We empirically demonstrate the reconstruction capability of our method for general linear inverse problems using synthetic examples and various image restoration tasks.

Machine learning-based reliability analysis methods have shown great advancements for their computational efficiency and accuracy. Recently, many efficient learning strategies have been proposed to enhance the computational performance. However, few of them explores the theoretical optimal learning strategy. In this article, we propose several theorems that facilitates such exploration. Specifically, cases that considering and neglecting the correlations among the candidate design samples are well elaborated. Moreover, we prove that the well-known U learning function can be reformulated to the optimal learning function for the case neglecting the Kriging correlation. In addition, the theoretical optimal learning strategy for sequential multiple training samples enrichment is also mathematically explored through the Bayesian estimate with the corresponding lost functions. Simulation results show that the optimal learning strategy considering the Kriging correlation works better than that neglecting the Kriging correlation and other state-of-the art learning functions from the literatures in terms of the reduction of number of evaluations of performance function. However, the implementation needs to investigate very large computational resource.

Energy-Based Models (EBMs) are an important class of probabilistic models, also known as random fields and undirected graphical models. EBMs are un-normalized and thus radically different from other popular self-normalized probabilistic models such as hidden Markov models (HMMs), autoregressive models, generative adversarial nets (GANs) and variational auto-encoders (VAEs). Over the past years, EBMs have attracted increasing interest not only from the core machine learning community, but also from application domains such as speech, vision, natural language processing (NLP) and so on, due to significant theoretical and algorithmic progress. The sequential nature of speech and language also presents special challenges and needs a different treatment from processing fix-dimensional data (e.g., images). Therefore, the purpose of this monograph is to present a systematic introduction to energy-based models, including both algorithmic progress and applications in speech and language processing. First, the basics of EBMs are introduced, including classic models, recent models parameterized by neural networks, sampling methods, and various learning methods from the classic learning algorithms to the most advanced ones. Then, the application of EBMs in three different scenarios is presented, i.e., for modeling marginal, conditional and joint distributions, respectively. 1) EBMs for sequential data with applications in language modeling, where the main focus is on the marginal distribution of a sequence itself; 2) EBMs for modeling conditional distributions of target sequences given observation sequences, with applications in speech recognition, sequence labeling and text generation; 3) EBMs for modeling joint distributions of both sequences of observations and targets, and their applications in semi-supervised learning and calibrated natural language understanding.

Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI methods have made use of neural networks (NN) to provide approximate, yet expressive constructs for the unavailable likelihood function and the posterior distribution. However, they do not generally achieve an optimal trade-off between accuracy and computational demand. In this work, we propose an alternative that provides both approximations to the likelihood and the posterior distribution, using structured mixtures of probability distributions. Our approach produces accurate posterior inference when compared to state-of-the-art NN-based SBI methods, while exhibiting a much smaller computational footprint. We illustrate our results on several benchmark models from the SBI literature.

Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms searching through sets of graphs or for selection of tuning parameters of other methods such as the graphical lasso, which is a likelihood penalization technique. In this paper we establish the consistency of an extended Bayesian information criterion for Gaussian graphical models in a scenario where both the number of variables p and the sample size n grow. Compared to earlier work on the regression case, our treatment allows for growth in the number of non-zero parameters in the true model, which is necessary in order to cover connected graphs. We demonstrate the performance of this criterion on simulated data when used in conjunction with the graphical lasso, and verify that the criterion indeed performs better than either cross-validation or the ordinary Bayesian information criterion when p and the number of non-zero parameters q both scale with n.

Renewal processes are generalizations of the Poisson process on the real line whose intervals are drawn i.i.d.