Bayesian deep learning seeks to equip deep neural networks with the ability to precisely quantify their predictive uncertainty, and has promised to make deep learning more reliable for safety-critical real-world applications. Yet, existing Bayesian deep learning methods fall short of this promise; new methods continue to be evaluated on unrealistic test beds that do not reflect the complexities of downstream real-world tasks that would benefit most from reliable uncertainty quantification. We propose the RETINA Benchmark, a set of real-world tasks that accurately reflect such complexities and are designed to assess the reliability of predictive models in safety-critical scenarios. Specifically, we curate two publicly available datasets of high-resolution human retina images exhibiting varying degrees of diabetic retinopathy, a medical condition that can lead to blindness, and use them to design a suite of automated diagnosis tasks that require reliable predictive uncertainty quantification. We use these tasks to benchmark well-established and state-of-the-art Bayesian deep learning methods on task-specific evaluation metrics. We provide an easy-to-use codebase for fast and easy benchmarking following reproducibility and software design principles. We provide implementations of all methods included in the benchmark as well as results computed over 100 TPU days, 20 GPU days, 400 hyperparameter configurations, and evaluation on at least 6 random seeds each.

We mimic the cognitive ability of Human perception, based on Bayesian hypothesis, to recognize view-based 3D objects. We consider approximate Bayesian (Empirical Bayesian) for perceptual inference for recognition. We essentially handle computation with perception.

We study the optimization landscape of the log-likelihood function and the convergence of the Expectation-Maximization (EM) algorithm in latent Gaussian tree models, i.e. tree-structured Gaussian graphical models whose leaf nodes are observable and non-leaf nodes are unobservable. We show that the unique non-trivial stationary point of the population log-likelihood is its global maximum, and establish that the expectation-maximization algorithm is guaranteed to converge to it in the single latent variable case. Our results for the landscape of the log-likelihood function in general latent tree models provide support for the extensive practical use of maximum likelihood based-methods in this setting. Our results for the EM algorithm extend an emerging line of work on obtaining global convergence guarantees for this celebrated algorithm. We show our results for the non-trivial stationary points of the log-likelihood by arguing that a certain system of polynomial equations obtained from the EM updates has a unique non-trivial solution. The global convergence of the EM algorithm follows by arguing that all trivial fixed points are higher-order saddle points.

In maximum-likelihood quantum state tomography, both the sample size and dimension grow exponentially with the number of qubits. It is therefore desirable to develop a stochastic first-order method, just like stochastic gradient descent for modern machine learning, to compute the maximum-likelihood estimate. To this end, we propose an algorithm called stochastic mirror descent with the Burg entropy. Its expected optimization error vanishes at a $O ( \sqrt{ ( 1 / t ) d \log t } )$ rate, where $d$ and $t$ denote the dimension and number of iterations, respectively. Its per-iteration time complexity is $O ( d^3 )$, independent of the sample size. To the best of our knowledge, this is currently the computationally fastest stochastic first-order method for maximum-likelihood quantum state tomography.

This paper introduces a simple efficient learning algorithms for general sequential decision making. The algorithm combines Optimism for exploration with Maximum Likelihood Estimation for model estimation, which is thus named OMLE. We prove that OMLE learns the near-optimal policies of an enormously rich class of sequential decision making problems in a polynomial number of samples. This rich class includes not only a majority of known tractable model-based Reinforcement Learning (RL) problems (such as tabular MDPs, factored MDPs, low witness rank problems, tabular weakly-revealing/observable POMDPs and multi-step decodable POMDPs), but also many new challenging RL problems especially in the partially observable setting that were not previously known to be tractable. Notably, the new problems addressed by this paper include (1) observable POMDPs with continuous observation and function approximation, where we achieve the first sample complexity that is completely independent of the size of observation space; (2) well-conditioned low-rank sequential decision making problems (also known as Predictive State Representations (PSRs)), which include and generalize all known tractable POMDP examples under a more intrinsic representation; (3) general sequential decision making problems under SAIL condition, which unifies our existing understandings of model-based RL in both fully observable and partially observable settings. SAIL condition is identified by this paper, which can be viewed as a natural generalization of Bellman/witness rank to address partial observability. This paper also presents a reward-free variant of OMLE algorithm, which learns approximate dynamic models that enable the computation of near-optimal policies for all reward functions simultaneously.

Natural and formal languages provide an effective mechanism for humans to specify instructions and reward functions. We investigate how to generate policies via RL when reward functions are specified in a symbolic language captured by Reward Machines, an increasingly popular automaton-inspired structure. We are interested in the case where the mapping of environment state to a symbolic (here, Reward Machine) vocabulary -- commonly known as the labelling function -- is uncertain from the perspective of the agent. We formulate the problem of policy learning in Reward Machines with noisy symbolic abstractions as a special class of POMDP optimization problem, and investigate several methods to address the problem, building on existing and new techniques, the latter focused on predicting Reward Machine state, rather than on grounding of individual symbols. We analyze these methods and evaluate them experimentally under varying degrees of uncertainty in the correct interpretation of the symbolic vocabulary. We verify the strength of our approach and the limitation of existing methods via an empirical investigation on both illustrative, toy domains and partially observable, deep RL domains.

The latent world model provides a promising way to learn policies in a compact latent space for tasks with high-dimensional observations, however, its generalization across diverse environments with unseen dynamics remains challenging. Although the recurrent structure utilized in current advances helps to capture local dynamics, modeling only state transitions without an explicit understanding of environmental context limits the generalization ability of the dynamics model. To address this issue, we propose a Prototypical Context-Aware Dynamics (ProtoCAD) model, which captures the local dynamics by time consistent latent context and enables dynamics generalization in high-dimensional control tasks. ProtoCAD extracts useful contextual information with the help of the prototypes clustered over batch and benefits model-based RL in two folds: 1) It utilizes a temporally consistent prototypical regularizer that encourages the prototype assignments produced for different time parts of the same latent trajectory to be temporally consistent instead of comparing the features; 2) A context representation is designed which combines both the projection embedding of latent states and aggregated prototypes and can significantly improve the dynamics generalization ability. Extensive experiments show that ProtoCAD surpasses existing methods in terms of dynamics generalization. Compared with the recurrent-based model RSSM, ProtoCAD delivers 13.2% and 26.7% better mean and median performance across all dynamics generalization tasks. Latent world models (Ha & Schmidhuber, 2018) summarize an agent's experience from highdimensional observations to facilitate learning complex behaviors in a compact latent space. Current advances (Hafner et al., 2019; 2020; Deng et al., 2022) leverage Recurrent Neural Networks (RNNs) to extract historical information from high-dimensional observations as compact latent representations and enable imagination in the latent space. However, modeling only latent state transitions without an explicit understanding of the environmental context characteristics limits the dynamics generalization ability of the world model. Since the changes in dynamics are not observable and can only be inferred from the observation sequence, for tasks with high-dimensional sensor inputs, dynamics generalization remains challenging.

Deep generative models have become useful for synthetic data generation, particularly population synthesis. The models implicitly learn the probability distribution of a dataset and can draw samples from a distribution. Several models have been proposed, but their performance is only tested on a single cross-sectional sample. The implementation of population synthesis on single datasets is seen as a drawback that needs further studies to explore the robustness of the models on multiple datasets. While comparing with the real data can increase trust and interpretability of the models, techniques to evaluate deep generative models' robustness for population synthesis remain underexplored. In this study, we present bootstrap confidence interval for the deep generative models, an approach that computes efficient confidence intervals for mean errors predictions to evaluate the robustness of the models to multiple datasets. Specifically, we adopt the tabular-based Composite Travel Generative Adversarial Network (CTGAN) and Variational Autoencoder (VAE), to estimate the distribution of the population, by generating agents that have tabular data using several samples over time from the same study area. The models are implemented on multiple travel diaries of Montreal Origin- Destination Survey of 2008, 2013, and 2018 and compare the predictive performance under varying sample sizes from multiple surveys. Results show that the predictive errors of CTGAN have narrower confidence intervals indicating its robustness to multiple datasets of the varying sample sizes when compared to VAE. Again, the evaluation of model robustness against varying sample size shows a minimal decrease in model performance with decrease in sample size. This study directly supports agent-based modelling by enabling finer synthetic generation of populations in a reliable environment.

Compared with model-based control and optimization methods, reinforcement learning (RL) provides a data-driven, learning-based framework to formulate and solve sequential decision-making problems. The RL framework has become promising due to largely improved data availability and computing power in the aviation industry. Many aviation-based applications can be formulated or treated as sequential decision-making problems. Some of them are offline planning problems, while others need to be solved online and are safety-critical. In this survey paper, we first describe standard RL formulations and solutions. Then we survey the landscape of existing RL-based applications in aviation. Finally, we summarize the paper, identify the technical gaps, and suggest future directions of RL research in aviation.

Recent research in robust optimization has shown an overfitting-like phenomenon in which models trained against adversarial attacks exhibit higher robustness on the training set compared to the test set. Although previous work provided theoretical explanations for this phenomenon using a robust PAC-Bayesian bound over the adversarial test error, related algorithmic derivations are at best only loosely connected to this bound, which implies that there is still a gap between their empirical success and our understanding of adversarial robustness theory. To close this gap, in this paper we consider a different form of the robust PAC-Bayesian bound and directly minimize it with respect to the model posterior. The derivation of the optimal solution connects PAC-Bayesian learning to the geometry of the robust loss surface through a Trace of Hessian (TrH) regularizer that measures the surface flatness. In practice, we restrict the TrH regularizer to the top layer only, which results in an analytical solution to the bound whose computational cost does not depend on the network depth. Finally, we evaluate our TrH regularization approach over CIFAR-10/100 and ImageNet using Vision Transformers (ViT) and compare against baseline adversarial robustness algorithms. Experimental results show that TrH regularization leads to improved ViT robustness that either matches or surpasses previous state-of-the-art approaches while at the same time requires less memory and computational cost.