We study the matrix completion problem that leverages hierarchical similarity graphs as side information in the context of recommender systems. Under a hierarchical stochastic block model that well respects practically-relevant social graphs and a low-rank rating matrix model, we characterize the exact information-theoretic limit on the number of observed matrix entries (i.e., optimal sample complexity) by proving sharp upper and lower bounds on the sample complexity. In the achievability proof, we demonstrate that probability of error of the maximum likelihood estimator vanishes for sufficiently large number of users and items, if all sufficient conditions are satisfied. On the other hand, the converse (impossibility) proof is based on the genie-aided maximum likelihood estimator. Under each necessary condition, we present examples of a genie-aided estimator to prove that the probability of error does not vanish for sufficiently large number of users and items. One important consequence of this result is that exploiting the hierarchical structure of social graphs yields a substantial gain in sample complexity relative to the one that simply identifies different groups without resorting to the relational structure across them. More specifically, we analyze the optimal sample complexity and identify different regimes whose characteristics rely on quality metrics of side information of the hierarchical similarity graph. Finally, we present simulation results to corroborate our theoretical findings and show that the characterized information-theoretic limit can be asymptotically achieved. N recent years, personalized recommender systems have emerged in an extensive range of Web applications to predict the preferences of its users and provide them with new and relevant items based on the scarce data about the users and/or items [2]. There are two major paradigms of recommender systems: (i) content-based filtering systems; (ii) collaborative filtering systems. Content-based filtering approach exploits a profile of users' preferences and/or properties of the items to carry out the recommendation task.

Mixed-membership (MM) models such as Latent Dirichlet Allocation (LDA) have been applied to microbiome compositional data to identify latent subcommunities of microbial species. However, microbiome compositional data, especially those collected from the gut, typically display substantial cross-sample heterogeneities in the subcommunity composition which current MM methods do not account for. To address this limitation, we incorporate the logistic-tree normal (LTN) model -- using the phylogenetic tree structure -- into the LDA model to form a new MM model. This model allows variation in the composition of each subcommunity around some ``centroid'' composition. Incorporation of auxiliary P\'olya-Gamma variables enables a computationally efficient collapsed blocked Gibbs sampler to carry out Bayesian inference under this model. We compare the new model and LDA and show that in the presence of large cross-sample heterogeneity, under the LDA model the resulting inference can be extremely sensitive to the specification of the total number of subcommunities as it does not account for cross-sample heterogeneity. As such, the popular strategy in other applications of MM models of overspecifying the number of subcommunities -- and hoping that some meaningful subcommunities will emerge among artificial ones -- can lead to highly misleading conclusions in the microbiome context. In contrast, by accounting for such heterogeneity, our MM model restores the robustness of the inference in the specification of the number of subcommunities and again allows meaningful subcommunities to be identified under this strategy.

Causal inference using observational text data is becoming increasingly popular in many research areas. This paper presents the Bayesian Topic Regression (BTR) model that uses both text and numerical information to model an outcome variable. It allows estimation of both discrete and continuous treatment effects. Furthermore, it allows for the inclusion of additional numerical confounding factors next to text data. To this end, we combine a supervised Bayesian topic model with a Bayesian regression framework and perform supervised representation learning for the text features jointly with the regression parameter training, respecting the Frisch-Waugh-Lovell theorem. Our paper makes two main contributions. First, we provide a regression framework that allows causal inference in settings when both text and numerical confounders are of relevance. We show with synthetic and semi-synthetic datasets that our joint approach recovers ground truth with lower bias than any benchmark model, when text and numerical features are correlated. Second, experiments on two real-world datasets demonstrate that a joint and supervised learning strategy also yields superior prediction results compared to strategies that estimate regression weights for text and non-text features separately, being even competitive with more complex deep neural networks.

Driving is an intuitive task that requires skills, constant alertness and vigilance for unexpected events. The driving task also requires long concentration spans focusing on the entire task for prolonged periods, and sophisticated negotiation skills with other road users, including wild animals. These requirements are particularly important when approaching intersections, overtaking, giving way, merging, turning and while adhering to the vast body of road rules. Modern motor vehicles now include an array of smart assistive and autonomous driving systems capable of subsuming some, most, or in limited cases, all of the driving task. The UK Department of Transport's response to the Safe Use of Automated Lane Keeping System consultation proposes that these systems are tested for compliance with relevant traffic rules. Building these smart automotive systems requires software developers with highly technical software engineering skills, and now a lawyer's in-depth knowledge of traffic legislation as well. These skills are required to ensure the systems are able to safely perform their tasks while being observant of the law. This paper presents an approach for deconstructing the complicated legalese of traffic law and representing its requirements and flow. The approach (de)constructs road rules in legal terminology and specifies them in structured English logic that is expressed as Boolean logic for automation and Lawmaps for visualisation. We demonstrate an example using these tools leading to the construction and validation of a Bayesian Network model. We strongly believe these tools to be approachable by programmers and the general public, and capable of use in developing Artificial Intelligence to underpin motor vehicle smart systems, and in validation to ensure these systems are considerate of the law when making decisions.

Out of the numerous hazards posing a threat to sustainable environmental conditions in the 21st century, only a few have a graver impact than air pollution. Its importance in determining the health and living standards in urban settings is only expected to increase with time. Various factors ranging from emissions from traffic and power plants, household emissions, natural causes are known to be primary causal agents or influencers behind rising air pollution levels. However, the lack of large scale data involving the major factors has hindered the research on the causes and relations governing the variability of the different air pollutants. Through this work, we introduce a large scale city-wise dataset for exploring the relationships among these agents over a long period of time. We analyze and explore the dataset to bring out inferences which we can derive by modeling the data. Also, we provide a set of benchmarks for the problem of estimating or forecasting pollutant levels with a set of diverse models and methodologies. Through our paper, we seek to provide a ground base for further research into this domain that will demand critical attention of ours in the near future.

Extracting moral sentiment from text is a vital component in understanding public opinion, social movements, and policy decisions. The Moral Foundation Theory identifies five moral foundations, each associated with a positive and negative polarity. However, moral sentiment is often motivated by its targets, which can correspond to individuals or collective entities. In this paper, we introduce morality frames, a representation framework for organizing moral attitudes directed at different entities, and come up with a novel and high-quality annotated dataset of tweets written by US politicians. Then, we propose a relational learning model to predict moral attitudes towards entities and moral foundations jointly. We do qualitative and quantitative evaluations, showing that moral sentiment towards entities differs highly across political ideologies.

Knowing the position of the robot in the world is crucial for navigation. Nowadays, Bayesian filters, such as Kalman and particle-based, are standard approaches in mobile robotics. Recently, end-to-end learning has allowed for scaling-up to high-dimensional inputs and improved generalization. However, there are still limitations to providing reliable laser navigation. Here we show a proof-of-concept of the predictive processing-inspired approach to perception applied for localization and navigation using laser sensors, without the need for odometry. We learn the generative model of the laser through self-supervised learning and perform both online state-estimation and navigation through stochastic gradient descent on the variational free-energy bound. We evaluated the algorithm on a mobile robot (TIAGo Base) with a laser sensor (SICK) in Gazebo. Results showed improved state-estimation performance when comparing to a state-of-the-art particle filter in the absence of odometry. Furthermore, conversely to standard Bayesian estimation approaches our method also enables the robot to navigate when providing the desired goal by inferring the actions that minimize the prediction error.

Probabilistic generative models are attractive for scientific modeling because their inferred parameters can be used to generate hypotheses and design experiments. This requires that the learned model provide an accurate representation of the input data and yield a latent space that effectively predicts outcomes relevant to the scientific question. Supervised Variational Autoencoders (SVAEs) have previously been used for this purpose, where a carefully designed decoder can be used as an interpretable generative model while the supervised objective ensures a predictive latent representation. Unfortunately, the supervised objective forces the encoder to learn a biased approximation to the generative posterior distribution, which renders the generative parameters unreliable when used in scientific models. This issue has remained undetected as reconstruction losses commonly used to evaluate model performance do not detect bias in the encoder. We address this previously-unreported issue by developing a second order supervision framework (SOS-VAE) that influences the decoder to induce a predictive latent representation. This ensures that the associated encoder maintains a reliable generative interpretation. We extend this technique to allow the user to trade-off some bias in the generative parameters for improved predictive performance, acting as an intermediate option between SVAEs and our new SOS-VAE. We also use this methodology to address missing data issues that often arise when combining recordings from multiple scientific experiments. We demonstrate the effectiveness of these developments using synthetic data and electrophysiological recordings with an emphasis on how our learned representations can be used to design scientific experiments.

Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models have been proposed that can be easily embedded within a hierarchical modeling framework to carry out Bayesian inference. While the focus of statistical research has mostly been directed toward innovative and more complex model development, relatively limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article discusses how point-referenced spatial process models can be cast as a conjugate Bayesian linear regression that can rapidly deliver inference on spatial processes. The approach allows exact sampling directly (avoids iterative algorithms such as Markov chain Monte Carlo) from the joint posterior distribution of regression parameters, the latent process and the predictive random variables, and can be easily implemented on statistical programming environments such as R.

As an important step to fulfill the Paris Agreement and achieve net-zero emissions by 2050, the European Commission adopted the most ambitious package of climate impact measures in April 2021 to improve the flow of capital towards sustainable activities. For these and other international measures to be successful, reliable data is key. The ability to see the carbon footprint of companies around the world will be critical for investors to comply with the measures. However, with only a small portion of companies volunteering to disclose their greenhouse gas (GHG) emissions, it is nearly impossible for investors to align their investment strategies with the measures. By training a machine learning model on disclosed GHG emissions, we are able to estimate the emissions of other companies globally who do not disclose their emissions. In this paper, we show that our model provides accurate estimates of corporate GHG emissions to investors such that they are able to align their investments with the regulatory measures and achieve net-zero goals.