Imitation learning addresses the challenge of learning by observing an expert's demonstrations without access to reward signals from environments. Most existing imitation learning methods that do not require interacting with environments either model the expert distribution as the conditional probability p(a|s) (e.g., behavioral cloning, BC) or the joint probability p(s, a). Despite its simplicity, modeling the conditional probability with BC usually struggles with generalization. While modeling the joint probability can improve generalization performance, the inference procedure is often time-consuming, and the model can suffer from manifold overfitting. This work proposes an imitation learning framework that benefits from modeling both the conditional and joint probability of the expert distribution. Our proposed diffusion model-augmented behavioral cloning (DBC) employs a diffusion model trained to model expert behaviors and learns a policy to optimize both the BC loss (conditional) and our proposed diffusion model loss (joint). DBC outperforms baselines in various continuous control tasks in navigation, robot arm manipulation, dexterous manipulation, and locomotion. We design additional experiments to verify the limitations of modeling either the conditional probability or the joint probability of the expert distribution, as well as compare different generative models. Ablation studies justify the effectiveness of our design choices. Recently, the success of deep reinforcement learning (DRL) (Mnih et al., 2015; Lillicrap et al., 2016; Arulkumaran et al., 2017) has inspired the research community to develop DRL frameworks to control robots, aiming to automate the process of designing sensing, planning, and control algorithms by letting the robot learn in an end-to-end fashion. Yet, acquiring complex skills through trial and error can still lead to undesired behaviors even with sophisticated reward design (Christiano et al., 2017; Leike et al., 2018; Lee et al., 2019). Moreover, the exploring process could damage expensive robotic platforms or even be dangerous to humans (Garcıa and Fernández, 2015; Levine et al., 2020). To overcome this issue, imitation learning (i.e., learning from demonstration) (Schaal, 1997; Osa et al., 2018) has received growing attention, whose aim is to learn a policy from expert demonstrations, which are often more accessible than appropriate reward functions for reinforcement learning. Among various imitation learning directions, adversarial imitation learning (Ho and Ermon, 2016; Zolna et al., 2021; Kostrikov et al., 2019) and inverse reinforcement learning (Ng and Russell, 2000; Abbeel and Ng, 2004) have achieved encouraging results in a variety of domains. Yet, these methods require interacting with environments, which can still be expensive or even dangerous. On the other hand, behavioral cloning (BC) (Pomerleau, 1989; Bain and Sammut, 1995) does not require interacting with environments.

Gaussian denoising has emerged as a powerful principle for constructing simulation-free continuous normalizing flows for generative modeling. Despite their empirical successes, theoretical properties of these flows and the regularizing effect of Gaussian denoising have remained largely unexplored. In this work, we aim to address this gap by investigating the well-posedness of simulation-free continuous normalizing flows built on Gaussian denoising. Through a unified framework termed Gaussian interpolation flow, we establish the Lipschitz regularity of the flow velocity field, the existence and uniqueness of the flow, and the Lipschitz continuity of the flow map and the time-reversed flow map for several rich classes of target distributions. This analysis also sheds light on the auto-encoding and cycle-consistency properties of Gaussian interpolation flows. Additionally, we delve into the stability of these flows in source distributions and perturbations of the velocity field, using the quadratic Wasserstein distance as a metric. Our findings offer valuable insights into the learning techniques employed in Gaussian interpolation flows for generative modeling, providing a solid theoretical foundation for end-to-end error analyses of learning GIFs with empirical observations.

Information geometry and Wasserstein geometry are two main structures introduced in a manifold of probability distributions, and they capture its different characteristics. We study characteristics of Wasserstein geometry in the framework of Li and Zhao (2023) for the affine deformation statistical model, which is a multi-dimensional generalization of the location-scale model. We compare merits and demerits of estimators based on information geometry and Wasserstein geometry. The shape of a probability distribution and its affine deformation are separated in the Wasserstein geometry, showing its robustness against the waveform perturbation in exchange for the loss in Fisher efficiency. We show that the Wasserstein estimator is the moment estimator in the case of the elliptically symmetric affine deformation model. It coincides with the information-geometrical estimator (maximum-likelihood estimator) when and only when the waveform is Gaussian. The role of the Wasserstein efficiency is elucidated in terms of robustness against waveform change.

With the rise of electronic data, particularly Earth observation data, data-based geospatial modelling using machine learning (ML) has gained popularity in environmental research. Accurate geospatial predictions are vital for domain research based on ecosystem monitoring and quality assessment and for policy-making and action planning, considering effective management of natural resources. The accuracy and computation speed of ML has generally proved efficient. However, many questions have yet to be addressed to obtain precise and reproducible results suitable for further use in both research and practice. A better understanding of the ML concepts applicable to geospatial problems enhances the development of data science tools providing transparent information crucial for making decisions on global challenges such as biosphere degradation and climate change. This survey reviews common nuances in geospatial modelling, such as imbalanced data, spatial autocorrelation, prediction errors, model generalisation, domain specificity, and uncertainty estimation. We provide an overview of techniques and popular programming tools to overcome or account for the challenges. We also discuss prospects for geospatial Artificial Intelligence in environmental applications. To date, obtaining spatial predictions is an essential step in the monitoring, assessment, and prognosis tasks applicable to all kinds of Earth systems on both local and global scales (Figure 1).

The power-law distribution plays a crucial role in complex networks as well as various applied sciences. Investigating whether the degree distribution of a network follows a power-law distribution is an important concern. The commonly used inferential methods for estimating the model parameters often yield biased estimates, which can lead to the rejection of the hypothesis that a model conforms to a power-law. In this paper, we discuss improved methods that utilize Bayesian inference to obtain accurate estimates and precise credibility intervals. The inferential methods are derived for both continuous and discrete distributions. These methods reveal that objective Bayesian approaches return nearly unbiased estimates for the parameters of both models. Notably, in the continuous case, we identify an explicit posterior distribution. This work enhances the power of goodness-of-fit tests, enabling us to accurately discern whether a network or any other dataset adheres to a power-law distribution. We apply the proposed approach to fit degree distributions for more than 5,000 synthetic networks and over 3,000 real networks. The results indicate that our method is more suitable in practice, as it yields a frequency of acceptance close to the specified nominal level.

The concept of updating a probability distribution in the light of new evidence lies at the heart of statistics and machine learning. Pearl's and Jeffrey's rule are two natural update mechanisms which lead to different outcomes, yet the similarities and differences remain mysterious. This paper clarifies their relationship in several ways: via separate descriptions of the two update mechanisms in terms of probabilistic programs and sampling semantics, and via different notions of likelihood (for Pearl and for Jeffrey). Moreover, it is shown that Jeffrey's update rule arises via variational inference. In terms of categorical probability theory, this amounts to an analysis of the situation in terms of the behaviour of the multiset functor, extended to the Kleisli category of the distribution monad.

This paper addresses a gap in the current state of the art by providing a solution for modeling causal relationships that evolve over time and occur at different time scales. Specifically, we introduce the multiscale non-stationary directed acyclic graph (MN-DAG), a framework for modeling multivariate time series data. Our contribution is twofold. Firstly, we expose a probabilistic generative model by leveraging results from spectral and causality theories. Our model allows sampling an MN-DAG according to user-specified priors on the time-dependence and multiscale properties of the causal graph. Secondly, we devise a Bayesian method named Multiscale Non-stationary Causal Structure Learner (MN-CASTLE) that uses stochastic variational inference to estimate MN-DAGs. The method also exploits information from the local partial correlation between time series over different time resolutions. The data generated from an MN-DAG reproduces well-known features of time series in different domains, such as volatility clustering and serial correlation. Additionally, we show the superior performance of MN-CASTLE on synthetic data with different multiscale and non-stationary properties compared to baseline models. Finally, we apply MN-CASTLE to identify the drivers of the natural gas prices in the US market. Causal relationships have strengthened during the COVID-19 outbreak and the Russian invasion of Ukraine, a fact that baseline methods fail to capture. MN-CASTLE identifies the causal impact of critical economic drivers on natural gas prices, such as seasonal factors, economic uncertainty, oil prices, and gas storage deviations.

Compute Continuum (CC) systems comprise a vast number of devices distributed over computational tiers. Evaluating business requirements, i.e., Service Level Objectives (SLOs), requires collecting data from all those devices; if SLOs are violated, devices must be reconfigured to ensure correct operation. If done centrally, this dramatically increases the number of devices and variables that must be considered, while creating an enormous communication overhead. To address this, we (1) introduce a causality filter based on Markov blankets (MB) that limits the number of variables that each device must track, (2) evaluate SLOs decentralized on a device basis, and (3) infer optimal device configuration for fulfilling SLOs. We evaluated our methodology by analyzing video stream transformations and providing device configurations that ensure the Quality of Service (QoS). The devices thus perceived their environment and acted accordingly -- a form of decentralized intelligence.

To engage human users in meaningful conversation, open-domain dialogue agents are required to generate diverse and contextually coherent dialogue. Despite recent advancements, which can be attributed to the usage of pretrained language models, the generation of diverse and coherent dialogue remains an open research problem. A popular approach to address this issue involves the adaptation of variational frameworks. However, while these approaches successfully improve diversity, they tend to compromise on contextual coherence. Hence, we propose the Bayesian Open-domain Dialogue with Empirical Bayes (BODEB) framework, an empirical bayes framework for constructing an Bayesian open-domain dialogue agent by leveraging pretrained parameters to inform the prior and posterior parameter distributions. Empirical results show that BODEB achieves better results in terms of both diversity and coherence compared to variational frameworks.

The recent success of large language models gives new urgency to the question of how model performance should be evaluated. In many tasks, models can be evaluated for the accuracy of their outputs. However, models can also be evaluated along other important dimensions. For example, we can assess models for the transparency or interpretability of their judgments (Creel 2020; Vredenburgh 2022). We can also assess models for the presence of problematic biases (Kelly 2023; Johnson 2020). Most work on biases in large language models focuses on a conception of bias closely tied to unfairness, especially as affecting marginalized social groups. However, recent work has alleged that large language models also show a number of classic cognitive biases familiar from work in the psychology of reasoning, behavioral economics, and judgment and decisionmaking (Dasgupta et al. 2022; Lin and Ng 2023; Jones and Steinhardt 2022). This development is exciting because it raises the possibility of using cognitive bias as a novel metric by which to evaluate the performance of large language models.