Decision trees have found widespread application within the machine learning community due to their flexibility and interpretability. This paper is directed towards learning decision trees from data using a Bayesian approach, which is challenging due to the potentially enormous parameter space required to span all tree models. Several approaches have been proposed to combat this challenge, with one of the more successful being Markov chain Monte Carlo (MCMC) methods. The efficacy and efficiency of MCMC methods fundamentally rely on the quality of the so-called proposals, which is the focus of this paper. In particular, this paper investigates using a Hamiltonian Monte Carlo (HMC) approach to explore the posterior of Bayesian decision trees more efficiently by exploiting the geometry of the likelihood within a global update scheme. Two implementations of the novel algorithm are developed and compared to existing methods by testing against standard datasets in the machine learning and Bayesian decision tree literature. HMC-based methods are shown to perform favourably with respect to predictive test accuracy, acceptance rate, and tree complexity.

The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown parameter vector in a group of cooperative estimators. Utilizing kernel density estimation and buffering some intermediate estimations, the prior distribution and conditional likelihood of the parameters vector in each node are calculated. Pseudo Huber loss function is used for designing the likelihood function. Also, an error thresholding function is defined to reduce the computational overhead as well as more relaxation against noise, which stops the update every time an error is less than a predefined threshold. The performance of the proposed algorithm is examined in the stationary and non-stationary scenarios in the presence of Gaussian and non-Gaussian noise. Results show the robustness of the proposed algorithm in the presence of different noise types.

We explore the idea of aligning an AI assistant by inverting a model of users' (unknown) preferences from observed interactions. To validate our proposal, we run proof-of-concept simulations in the economic ultimatum game, formalizing user preferences as policies that guide the actions of simulated players. We find that the AI assistant accurately aligns its behavior to match standard policies from the economic literature (e.g., selfish, altruistic). However, the assistant's learned policies lack robustness and exhibit limited generalization in an out-of-distribution setting when confronted with a currency (e.g., grams of medicine) that was not included in the assistant's training distribution. Additionally, we find that when there is inconsistency in the relationship between language use and an unknown policy (e.g., an altruistic policy combined with rude language), the assistant's learning of the policy is slowed. Overall, our preliminary results suggest that developing simulation frameworks in which AI assistants need to infer preferences from diverse users can provide a valuable approach for studying practical alignment questions.

In many fields of scientific research and real-world applications, unbiased estimation of causal effects from non-experimental data is crucial for understanding the mechanism underlying the data and for decision-making on effective responses or interventions. A great deal of research has been conducted to address this challenging problem from different angles. For estimating causal effect in observational data, assumptions such as Markov condition, faithfulness and causal sufficiency are always made. Under the assumptions, full knowledge such as, a set of covariates or an underlying causal graph, is typically required. A practical challenge is that in many applications, no such full knowledge or only some partial knowledge is available. In recent years, research has emerged to use search strategies based on graphical causal modelling to discover useful knowledge from data for causal effect estimation, with some mild assumptions, and has shown promise in tackling the practical challenge. In this survey, we review these data-driven methods on causal effect estimation for a single treatment with a single outcome of interest and focus on the challenges faced by data-driven causal effect estimation. We concisely summarise the basic concepts and theories that are essential for data-driven causal effect estimation using graphical causal modelling but are scattered around the literature. We identify and discuss the challenges faced by data-driven causal effect estimation and characterise the existing methods by their assumptions and the approaches to tackling the challenges. We analyse the strengths and limitations of the different types of methods and present an empirical evaluation to support the discussions. We hope this review will motivate more researchers to design better data-driven methods based on graphical causal modelling for the challenging problem of causal effect estimation.

Accurate uncertainty quantification in graph neural networks (GNNs) is essential, especially in high-stakes domains where GNNs are frequently employed. Conformal prediction (CP) offers a promising framework for quantifying uncertainty by providing $\textit{valid}$ prediction sets for any black-box model. CP ensures formal probabilistic guarantees that a prediction set contains a true label with a desired probability. However, the size of prediction sets, known as $\textit{inefficiency}$, is influenced by the underlying model and data generating process. On the other hand, Bayesian learning also provides a credible region based on the estimated posterior distribution, but this region is $\textit{well-calibrated}$ only when the model is correctly specified. Building on a recent work that introduced a scaling parameter for constructing valid credible regions from posterior estimate, our study explores the advantages of incorporating a temperature parameter into Bayesian GNNs within CP framework. We empirically demonstrate the existence of temperatures that result in more efficient prediction sets. Furthermore, we conduct an analysis to identify the factors contributing to inefficiency and offer valuable insights into the relationship between CP performance and model calibration.

The aim of this paper is to establish a causal link between the policies implemented by technology companies and the outcomes they yield within intricate temporal and/or spatial dependent experiments. We propose a novel temporal/spatio-temporal Varying Coefficient Decision Process (VCDP) model, capable of effectively capturing the evolving treatment effects in situations characterized by temporal and/or spatial dependence. Our methodology encompasses the decomposition of the Average Treatment Effect (ATE) into the Direct Effect (DE) and the Indirect Effect (IE). We subsequently devise comprehensive procedures for estimating and making inferences about both DE and IE. Additionally, we provide a rigorous analysis of the statistical properties of these procedures, such as asymptotic power. To substantiate the effectiveness of our approach, we carry out extensive simulations and real data analyses.

Learning from noisy labels is an important and long-standing problem in machine learning for real applications. One of the main research lines focuses on learning a label corrector to purify potential noisy labels. However, these methods typically rely on strict assumptions and are limited to certain types of label noise. In this paper, we reformulate the label-noise problem from a generative-model perspective, $\textit{i.e.}$, labels are generated by gradually refining an initial random guess. This new perspective immediately enables existing powerful diffusion models to seamlessly learn the stochastic generative process. Once the generative uncertainty is modeled, we can perform classification inference using maximum likelihood estimation of labels. To mitigate the impact of noisy labels, we propose the $\textbf{L}$abel-$\textbf{R}$etrieval-$\textbf{A}$ugmented (LRA) diffusion model, which leverages neighbor consistency to effectively construct pseudo-clean labels for diffusion training. Our model is flexible and general, allowing easy incorporation of different types of conditional information, $\textit{e.g.}$, use of pre-trained models, to further boost model performance. Extensive experiments are conducted for evaluation. Our model achieves new state-of-the-art (SOTA) results on all the standard real-world benchmark datasets. Remarkably, by incorporating conditional information from the powerful CLIP model, our method can boost the current SOTA accuracy by 10-20 absolute points in many cases.

Task planning for embodied AI has been one of the most challenging problems where the community does not meet a consensus in terms of formulation. In this paper, we aim to tackle this problem with a unified framework consisting of an end-to-end trainable method and a planning algorithm. Particularly, we propose a task-agnostic method named 'planning as in-painting'. In this method, we use a Denoising Diffusion Model (DDM) for plan generation, conditioned on both language instructions and perceptual inputs under partially observable environments. Partial observation often leads to the model hallucinating the planning. Therefore, our diffusion-based method jointly models both state trajectory and goal estimation to improve the reliability of the generated plan, given the limited available information at each step. To better leverage newly discovered information along the plan execution for a higher success rate, we propose an on-the-fly planning algorithm to collaborate with the diffusion-based planner. The proposed framework achieves promising performances in various embodied AI tasks, including vision-language navigation, object manipulation, and task planning in a photorealistic virtual environment. The code is available at: https://github.com/joeyy5588/planning-as-inpainting.

Linear partial differential equations (PDEs) are an important, widely applied class of mechanistic models, describing physical processes such as heat transfer, electromagnetism, and wave propagation. In practice, specialized numerical methods based on discretization are used to solve PDEs. They generally use an estimate of the unknown model parameters and, if available, physical measurements for initialization. Such solvers are often embedded into larger scientific models with a downstream application and thus error quantification plays a key role. However, by ignoring parameter and measurement uncertainty, classical PDE solvers may fail to produce consistent estimates of their inherent approximation error. In this work, we approach this problem in a principled fashion by interpreting solving linear PDEs as physics-informed Gaussian process (GP) regression. Our framework is based on a key generalization of the Gaussian process inference theorem to observations made via an arbitrary bounded linear operator. Crucially, this probabilistic viewpoint allows to (1) quantify the inherent discretization error; (2) propagate uncertainty about the model parameters to the solution; and (3) condition on noisy measurements. Demonstrating the strength of this formulation, we prove that it strictly generalizes methods of weighted residuals, a central class of PDE solvers including collocation, finite volume, pseudospectral, and (generalized) Galerkin methods such as finite element and spectral methods. This class can thus be directly equipped with a structured error estimate. In summary, our results enable the seamless integration of mechanistic models as modular building blocks into probabilistic models by blurring the boundaries between numerical analysis and Bayesian inference.

For safe operation, a robot must be able to avoid collisions in uncertain environments. Existing approaches for motion planning under uncertainties often assume parametric obstacle representations and Gaussian uncertainty, which can be inaccurate. While visual perception can deliver a more accurate representation of the environment, its use for safe motion planning is limited by the inherent miscalibration of neural networks and the challenge of obtaining adequate datasets. To address these limitations, we propose to employ ensembles of deep semantic segmentation networks trained with massively augmented datasets to ensure reliable probabilistic occupancy information. To avoid conservatism during motion planning, we directly employ the probabilistic perception in a scenario-based path planning approach. A velocity scheduling scheme is applied to the path to ensure a safe motion despite tracking inaccuracies. We demonstrate the effectiveness of the massive data augmentation in combination with deep ensembles and the proposed scenario-based planning approach in comparisons to state-of-the-art methods and validate our framework in an experiment with a human hand as an obstacle.