Ensuring safe operation of safety-critical complex systems interacting with their environment poses significant challenges, particularly when the system's world model relies on machine learning algorithms to process the perception input. A comprehensive safety argumentation requires knowledge of how faults or functional insufficiencies propagate through the system and interact with external factors, to manage their safety impact. While statistical analysis approaches can support the safety assessment, associative reasoning alone is neither sufficient for the safety argumentation nor for the identification and investigation of safety measures. A causal understanding of the system and its interaction with the environment is crucial for safeguarding safety-critical complex systems. It allows to transfer and generalize knowledge, such as insights gained from testing, and facilitates the identification of potential improvements. This work explores using causal Bayesian networks to model the system's causalities for safety analysis, and proposes measures to assess causal influences based on Pearl's framework of causal inference. We compare the approach of causal Bayesian networks to the well-established fault tree analysis, outlining advantages and limitations. In particular, we examine importance metrics typically employed in fault tree analysis as foundation to discuss suitable causal metrics. An evaluation is performed on the example of a perception system for automated driving. Overall, this work presents an approach for causal reasoning in safety analysis that enables the integration of data-driven and expert-based knowledge to account for uncertainties arising from complex systems operating in open environments.

Recently developed quasi-Bayesian (QB) methods \cite{fong2023martingale} proposed a stimulating change of paradigm in Bayesian computation by directly constructing the Bayesian predictive distribution through recursion, removing the need for expensive computations involved in sampling the Bayesian posterior distribution. This has proved to be data-efficient for univariate predictions, however, existing constructions for higher dimensional densities are only possible by relying on restrictive assumptions on the model's multivariate structure. Here, we propose a wholly different approach to extend Quasi-Bayesian prediction to high dimensions through the use of Sklar's theorem, by decomposing the predictive distribution into one-dimensional predictive marginals and a high-dimensional copula. We use the efficient recursive QB construction for the one-dimensional marginals and model the dependence using highly expressive vine copulas. Further, we tune hyperparameters using robust divergences (eg.

Data point selection (DPS) is becoming a critical topic in deep learning due to the ease of acquiring uncurated training data compared to the difficulty of obtaining curated or processed data. Existing approaches to DPS are predominantly based on a bi-level optimisation (BLO) formulation, which is demanding in terms of memory and computation, and exhibits some theoretical defects regarding minibatches.Thus, we propose a novel Bayesian approach to DPS. We view the DPS problem as posterior inference in a novel Bayesian model where the posterior distributions of the instance-wise weights and the main neural network parameters are inferred under a reasonable prior and likelihood model.We employ stochastic gradient Langevin MCMC sampling to learn the main network and instance-wise weights jointly, ensuring convergence even with minibatches. Our update equation is comparable to the widely used SGD and much more efficient than existing BLO-based methods. Through controlled experiments in both the vision and language domains, we present the proof-of-concept.

In this paper, we consider the problem of learning a sparse graph from the Laplacian constrained Gaussian graphical model. This problem can be formulated as a penalized maximum likelihood estimation of the precision matrix under Laplacian structural constraints. Like in the classical graphical lasso problem, recent works made use of the \ell_1 -norm with the goal of promoting sparsity in the Laplacian constrained precision matrix estimation. However, through empirical evidence, we observe that the \ell_1 -norm is not effective in imposing a sparse solution in this problem. From a theoretical perspective, we prove that a large regularization parameter will surprisingly lead to a solution representing a fully connected graph instead of a sparse graph.

We present high quality image synthesis results using diffusion probabilistic models, a class of latent variable models inspired by considerations from nonequilibrium thermodynamics. Our best results are obtained by training on a weighted variational bound designed according to a novel connection between diffusion probabilistic models and denoising score matching with Langevin dynamics, and our models naturally admit a progressive lossy decompression scheme that can be interpreted as a generalization of autoregressive decoding. On the unconditional CIFAR10 dataset, we obtain an Inception score of 9.46 and a state-of-the-art FID score of 3.17. On 256x256 LSUN, we obtain sample quality similar to ProgressiveGAN.

We propose a novel neural networks based approach to efficiently answer arbitrary Most Probable Explanation (MPE) queries--a well-known NP-hard task--in large probabilistic models such as Bayesian and Markov networks, probabilistic circuits, and neural auto-regressive models. By arbitrary MPE queries, we mean that there is no predefined partition of variables into evidence and non-evidence variables. The key idea is to distill all MPE queries over a given probabilistic model into a neural network and then use the latter for answering queries, eliminating the need for time-consuming inference algorithms that operate directly on the probabilistic model. We improve upon this idea by incorporating inference-time optimization with self-supervised loss to iteratively improve the solutions and employ a teacher-student framework that provides a better initial network, which in turn, helps reduce the number of inference-time optimization steps. The teacher network utilizes a self-supervised loss function optimized for getting the exact MPE solution, while the student network learns from the teacher's near-optimal outputs through supervised loss.

Value function approximation has demonstrated phenomenal empirical success in reinforcement learning (RL). Nevertheless, despite a handful of recent progress on developing theory for RL with linear function approximation, the understanding of \emph{general} function approximation schemes largely remains missing. In this paper, we establish the first provably efficient RL algorithm with general value function approximation. We show that if the value functions admit an approximation with a function class \mathcal{F}, our algorithm achieves a regret bound of \widetilde{O}(\mathrm{poly}(dH)\sqrt{T}) where d is a complexity measure of \mathcal{F} that depends on the eluder dimension [Russo and Van Roy, 2013] and log-covering numbers, H is the planning horizon, and T is the number interactions with the environment. Moreover, our algorithm is model-free and provides a framework to justify the effectiveness of algorithms used in practice.

The construction and theoretical analysis of the most popular universally consistent nonparametric density estimators hinge on one functional property: smoothness. In this paper we investigate the theoretical implications of incorporating a multi-view latent variable model, a type of low-rank model, into nonparametric density estimation. To do this we perform extensive analysis on histogram-style estimators that integrate a multi-view model. Our analysis culminates in showing that there exists a universally consistent histogram-style estimator that converges to any multi-view model with a finite number of Lipschitz continuous components at a rate of \widetilde{O}(1/\sqrt[3]{n}) in L 1 error. We also introduce a new nonparametric latent variable model based on the Tucker decomposition.

Simulation-Based Inference (SBI) is a common name for an emerging family of approaches that infer the model parameters when the likelihood is intractable. Existing SBI methods either approximate the likelihood, such as Approximate Bayesian Computation (ABC) or directly model the posterior, such as Sequential Neural Posterior Estimation (SNPE). While ABC is efficient on low-dimensional problems, on higher-dimensional tasks, it is generally outperformed by SNPE, which leverages function approximation. In this paper, we propose Pseudo-Likelihood Inference (PLI), a new method that brings neural approximation into ABC, making it competitive on challenging Bayesian system identification tasks. By utilizing integral probability metrics, we introduce a smooth likelihood kernel with an adaptive bandwidth that is updated based on information-theoretic trust regions.

Denoising Diffusion Probabilistic Models (DDPM) have recently gained significant attention. DDPMs compose a Markovian process that begins in the data domain and gradually adds noise until reaching pure white noise. DDPMs generate high-quality samples from complex data distributions by defining an inverse process and training a deep neural network to learn this mapping. However, these models are inefficient because they require many diffusion steps to produce aesthetically pleasing samples. Additionally, unlike generative adversarial networks (GANs), the latent space of diffusion models is less interpretable.