Causal discovery algorithms aim at untangling complex causal relationships from data. Here, we study causal discovery and inference methods based on staged tree models, which can represent complex and asymmetric causal relationships between categorical variables. We provide a first graphical representation of the equivalence class of a staged tree, by looking only at a specific subset of its underlying independences. We further define a new pre-metric, inspired by the widely used structural intervention distance, to quantify the closeness between two staged trees in terms of their corresponding causal inference statements. A simulation study highlights the efficacy of staged trees in uncovering complexes, asymmetric causal relationships from data, and real-world data applications illustrate their use in practical causal analysis.

Online learning has gained increasing interest due Online optimization methods can directly be applied to update to its capability of tracking real-world streaming models that are fully specified by a certain value of its data. Although it has been widely studied in the parameters. Beyond such models, there is another class of setting of frequentist statistics, few works have models known as Bayesian models that treat the parameters considered online learning with the Bayesian sampling as random variables, thus giving an output also as a random problem. In this paper, we study an Online variable (often the expectation is taken as the final output on Particle-based Variational Inference (OPVI) algorithm par with the conventional case). The stochasticity enables that updates a set of particles to gradually Bayesian models to provide diverse outputs, characterize approximate the Bayesian posterior. To reduce prediction uncertainty, and be more robust to adversarial the gradient error caused by the use of stochastic attacks (Hernández-Lobato and Adams, 2015; Li and Gal, approximation, we include a sublinear increasing 2017; Yoon et al., 2018; Zhang et al., 2019; Tolpin et al., batch-size method to reduce the variance.

Many problems arising in control require the determination of a mathematical model of the application. This has often to be performed starting from input-output data, leading to a task known as system identification in the engineering literature. One emerging topic in this field is estimation of networks consisting of several interconnected dynamic systems. We consider the linear setting assuming that system outputs are the result of many correlated inputs, hence making system identification severely ill-conditioned. This is a scenario often encountered when modeling complex cybernetics systems composed by many sub-units with feedback and algebraic loops. We develop a strategy cast in a Bayesian regularization framework where any impulse response is seen as realization of a zero-mean Gaussian process. Any covariance is defined by the so called stable spline kernel which includes information on smooth exponential decay. We design a novel Markov chain Monte Carlo scheme able to reconstruct the impulse responses posterior by efficiently dealing with collinearity. Our scheme relies on a variation of the Gibbs sampling technique: beyond considering blocks forming a partition of the parameter space, some other (overlapping) blocks are also updated on the basis of the level of collinearity of the system inputs. Theoretical properties of the algorithm are studied obtaining its convergence rate. Numerical experiments are included using systems containing hundreds of impulse responses and highly correlated inputs.

Abstract-- After many researchers observed fruitfulness from the recent diffusion probabilistic model, its effectiveness in image generation is actively studied these days. In this paper, our objective is to evaluate the potential of diffusion probabilistic models for 3D human motion-related tasks. To this end, this paper presents a study of employing diffusion probabilistic models to predict future 3D human motion(s) from the previously observed motion. Based on the Human 3.6M and HumanEva-I datasets, our results show that diffusion probabilistic models are competitive for both single (deterministic) and multiple (stochastic) 3D motion prediction tasks, after finishing a single training process. In addition, we find out that diffusion probabilistic models can offer an attractive compromise, since they can strike the right balance between the likelihood and diversity of the predicted future motions.

This paper introduces a new sparse Bayesian learning (SBL) algorithm that jointly recovers a temporal sequence of edge maps from noisy and under-sampled Fourier data. The new method is cast in a Bayesian framework and uses a prior that simultaneously incorporates intra-image information to promote sparsity in each individual edge map with inter-image information to promote similarities in any unchanged regions. By treating both the edges as well as the similarity between adjacent images as random variables, there is no need to separately form regions of change. Thus we avoid both additional computational cost as well as any information loss resulting from pre-processing the image. Our numerical examples demonstrate that our new method compares favorably with more standard SBL approaches.

The rising growth of deep neural networks (DNNs) and datasets in size motivates the need for efficient solutions for simultaneous model selection and training. Many methods for hyperparameter optimization (HPO) of iterative learners, including DNNs, attempt to solve this problem by querying and learning a response surface while searching for the optimum of that surface. However, many of these methods make myopic queries, do not consider prior knowledge about the response structure, and/or perform a biased cost-aware search, all of which exacerbate identifying the best-performing model when a total cost budget is specified. This paper proposes a novel approach referred to as {\bf B}udget-{\bf A}ware {\bf P}lanning for {\bf I}terative Learners (BAPI) to solve HPO problems under a constrained cost budget. BAPI is an efficient non-myopic Bayesian optimization solution that accounts for the budget and leverages the prior knowledge about the objective function and cost function to select better configurations and to take more informed decisions during the evaluation (training). Experiments on diverse HPO benchmarks for iterative learners show that BAPI performs better than state-of-the-art baselines in most cases.

Numerous neuro-symbolic approaches have recently been proposed typically with the goal of adding symbolic knowledge to the output layer of a neural network. Ideally, such losses maximize the probability that the neural network's predictions satisfy the underlying domain. Unfortunately, this type of probabilistic inference is often computationally infeasible. Neuro-symbolic approaches therefore commonly resort to fuzzy approximations of this probabilistic objective, sacrificing sound probabilistic semantics, or to sampling which is very seldom feasible. We approach the problem by first assuming the constraint decomposes conditioned on the features learned by the network. We iteratively strengthen our approximation, restoring the dependence between the constraints most responsible for degrading the quality of the approximation. This corresponds to computing the mutual information between pairs of constraints conditioned on the network's learned features, and may be construed as a measure of how well aligned the gradients of two distributions are. We show how to compute this efficiently for tractable circuits. We test our approach on three tasks: predicting a minimum-cost path in Warcraft, predicting a minimum-cost perfect matching, and solving Sudoku puzzles, observing that it improves upon the baselines while sidestepping intractability.

Learning energy-based models (EBMs) is known to be difficult especially on discrete data where gradient-based learning strategies cannot be applied directly. Although ratio matching is a sound method to learn discrete EBMs, it suffers from expensive computation and excessive memory requirements, thereby resulting in difficulties in learning EBMs on high-dimensional data. Motivated by these limitations, in this study, we propose ratio matching with gradient-guided importance sampling (RMwGGIS). Particularly, we use the gradient of the energy function w.r.t. the discrete data space to approximately construct the provably optimal proposal distribution, which is subsequently used by importance sampling to efficiently estimate the original ratio matching objective. We perform experiments on density modeling over synthetic discrete data, graph generation, and training Ising models to evaluate our proposed method. The experimental results demonstrate that our method can significantly alleviate the limitations of ratio matching, perform more effectively in practice, and scale to high-dimensional problems. Our implementation is available at https://github.com/divelab/RMwGGIS.

Within this study, we propose a new approach for natural language processing using Bayesian networks to predict and analyze the context and how this approach can be applied to the Community Question Answering domain. We discuss how Bayesian networks can detect semantic relationships and dependencies between entities, and this is connected to different score-based approaches of structure-learning. We compared the Bayesian networks with different score metrics, such as the BIC, BDeu, K2 and Chow-Liu trees. Our proposed approach out-performs the baseline model at the precision metric. We also discuss the influence of penalty terms on the structure of Bayesian networks and how they can be used to analyze the relationships between entities. In addition, we examine the visualization of directed acyclic graphs to analyze semantic relationships. The article further identifies issues with detecting certain semantic classes that are separated in the structure of directed acyclic graphs. Finally, we evaluate potential improvements for the Bayesian network approach.

Autonomous vehicles (AVs) need to reason about the multimodal behavior of neighboring agents while planning their own motion. Many existing trajectory planners seek a single trajectory that performs well under \emph{all} plausible futures simultaneously, ignoring bi-directional interactions and thus leading to overly conservative plans. Policy planning, whereby the ego agent plans a policy that reacts to the environment's multimodal behavior, is a promising direction as it can account for the action-reaction interactions between the AV and the environment. However, most existing policy planners do not scale to the complexity of real autonomous vehicle applications: they are either not compatible with modern deep learning prediction models, not interpretable, or not able to generate high quality trajectories. To fill this gap, we propose Tree Policy Planning (TPP), a policy planner that is compatible with state-of-the-art deep learning prediction models, generates multistage motion plans, and accounts for the influence of ego agent on the environment behavior. The key idea of TPP is to reduce the continuous optimization problem into a tractable discrete Markov Decision Process (MDP) through the construction of two tree structures: an ego trajectory tree for ego trajectory options, and a scenario tree for multi-modal ego-conditioned environment predictions. We demonstrate the efficacy of TPP in closed-loop simulations based on real-world nuScenes dataset and results show that TPP scales to realistic AV scenarios and significantly outperforms non-policy baselines.