Learning directed acyclic graph (DAG) that describes the causality of observed data is a very challenging but important task. Due to the limited quantity and quality of observed data, and non-identifiability of causal graph, it is almost impossible to infer a single precise DAG. Some methods approximate the posterior distribution of DAGs to explore the DAG space via Markov chain Monte Carlo (MCMC), but the DAG space is over the nature of super-exponential growth, accurately characterizing the whole distribution over DAGs is very intractable. In this paper, we propose {Reinforcement Causal Structure Learning on Order Graph} (RCL-OG) that uses order graph instead of MCMC to model different DAG topological orderings and to reduce the problem size. RCL-OG first defines reinforcement learning with a new reward mechanism to approximate the posterior distribution of orderings in an efficacy way, and uses deep Q-learning to update and transfer rewards between nodes. Next, it obtains the probability transition model of nodes on order graph, and computes the posterior probability of different orderings. In this way, we can sample on this model to obtain the ordering with high probability. Experiments on synthetic and benchmark datasets show that RCL-OG provides accurate posterior probability approximation and achieves better results than competitive causal discovery algorithms.

Probabilistic circuits (PCs) are a tractable representation of probability distributions allowing for exact and efficient computation of likelihoods and marginals. There has been significant recent progress on improving the scale and expressiveness of PCs. However, PC training performance plateaus as model size increases. We discover that most capacity in existing large PC structures is wasted: fully-connected parameter layers are only sparsely used. We propose two operations: pruning and growing, that exploit the sparsity of PC structures. Specifically, the pruning operation removes unimportant sub-networks of the PC for model compression and comes with theoretical guarantees. The growing operation increases model capacity by increasing the size of the latent space. By alternatingly applying pruning and growing, we increase the capacity that is meaningfully used, allowing us to significantly scale up PC learning. Empirically, our learner achieves state-of-the-art likelihoods on MNIST-family image datasets and on Penn Tree Bank language data compared to other PC learners and less tractable deep generative models such as flow-based models and variational autoencoders (VAEs).

We tackle the problem of cooperative visual exploration where multiple agents need to jointly explore unseen regions as fast as possible based on visual signals. Classical planning-based methods often suffer from expensive computation overhead at each step and a limited expressiveness of complex cooperation strategy. By contrast, reinforcement learning (RL) has recently become a popular paradigm for tackling this challenge due to its modeling capability of arbitrarily complex strategies and minimal inference overhead. In this paper, we extend the state-of-the-art single-agent visual navigation method, Active Neural SLAM (ANS), to the multi-agent setting by introducing a novel RL-based planning module, Multi-agent Spatial Planner (MSP).MSP leverages a transformer-based architecture, Spatial-TeamFormer, which effectively captures spatial relations and intra-agent interactions via hierarchical spatial self-attentions. In addition, we also implement a few multi-agent enhancements to process local information from each agent for an aligned spatial representation and more precise planning. Finally, we perform policy distillation to extract a meta policy to significantly improve the generalization capability of final policy. We call this overall solution, Multi-Agent Active Neural SLAM (MAANS). MAANS substantially outperforms classical planning-based baselines for the first time in a photo-realistic 3D simulator, Habitat. Code and videos can be found at https://sites.google.com/view/maans.

Data availability has dramatically increased in recent years, driving model-based control methods to exploit learning techniques for improving the system description, and thus control performance. Two key factors that hinder the practical applicability of learning methods in control are their high computational complexity and limited generalization capabilities to unseen conditions. Meta-learning is a powerful tool that enables efficient learning across a finite set of related tasks, easing adaptation to new unseen tasks. This paper makes use of a meta-learning approach for adaptive model predictive control, by learning a system model that leverages data from previous related tasks, while enabling fast fine-tuning to the current task during closed-loop operation. The dynamics is modeled via Gaussian process regression and, building on the Karhunen-Lo{\`e}ve expansion, can be approximately reformulated as a finite linear combination of kernel eigenfunctions. Using data collected over a set of tasks, the eigenfunction hyperparameters are optimized in a meta-training phase by maximizing a variational bound for the log-marginal likelihood. During meta-testing, the eigenfunctions are fixed, so that only the linear parameters are adapted to the new unseen task in an online adaptive fashion via Bayesian linear regression, providing a simple and efficient inference scheme. Simulation results are provided for autonomous racing with miniature race cars adapting to unseen road conditions.

The paper covers the design and analysis of experiments to discriminate between two Gaussian process models, such as those widely used in computer experiments, kriging, sensor location and machine learning. Two frameworks are considered. First, we study sequential constructions, where successive design (observation) points are selected, either as additional points to an existing design or from the beginning of observation. The selection relies on the maximisation of the difference between the symmetric Kullback Leibler divergences for the two models, which depends on the observations, or on the mean squared error of both models, which does not. Then, we consider static criteria, such as the familiar log-likelihood ratios and the Fr\'echet distance between the covariance functions of the two models. Other distance-based criteria, simpler to compute than previous ones, are also introduced, for which, considering the framework of approximate design, a necessary condition for the optimality of a design measure is provided. The paper includes a study of the mathematical links between different criteria and numerical illustrations are provided.

Chain event graphs (CEGs) are a recent family of probabilistic graphical models that generalise the popular Bayesian networks (BNs) family. Crucially, unlike BNs, a CEG is able to embed, within its graph and its statistical model, asymmetries exhibited by a process. These asymmetries might be in the conditional independence relationships or in the structure of the graph and its underlying event space. Structural asymmetries are common in many domains, and can occur naturally (e.g. a defendant vs prosecutor's version of events) or by design (e.g. a public health intervention). However, there currently exists no software that allows a user to leverage the theoretical developments of the CEG model family in modelling processes with structural asymmetries. This paper introduces cegpy, the first Python package for learning and analysing complex processes using CEGs. The key feature of cegpy is that it is the first CEG package in any programming language that can model processes with symmetric as well as asymmetric structures. cegpy contains an implementation of Bayesian model selection and probability propagation algorithms for CEGs. We illustrate the functionality of cegpy using a structurally asymmetric dataset.

Normalizing flow (NF) has gained popularity over traditional maximum likelihood based methods due to its strong capability to model complex data distributions. However, the standard approach, which maps the observed data to a normal distribution, has difficulty in handling data distributions with multiple relatively isolated modes. To overcome this issue, we propose a new framework based on variational latent representation to improve the practical performance of NF. The idea is to replace the standard normal latent variable with a more general latent representation, jointly learned via Variational Bayes. For example, by taking the latent representation as a discrete sequence, our framework can learn a Transformer model that generates the latent sequence and an NF model that generates continuous data distribution conditioned on the sequence. The resulting method is significantly more powerful than the standard normalization flow approach for generating data distributions with multiple modes. Extensive experiments have shown the advantages of NF with variational latent representation.

Random forests (RFs) [Bre01] are machine learning models with various applications in areas like E-commerce, Finance and Medicine. They consist of multiple decision trees that use different subsets of the available features. Given an input, every tree makes an individual decision and the output of the random forest is obtained by a majority vote. They have low risk of overfitting; support both classification and regression tasks and come equipped with some feature importance measures [Bre01]. However, feature importance measures can be too simplistic as they can represent neither joint effects of features (e.g., multi-drug interactions) nor non-monotonicity (e.g., increasing the weight may be healthy for an underweight person, but not for an overweight person). In recent years, a variety of other explanation methods has been proposed. Modelagnostic feature importance measures like LIME [RSG16], SHAP [LL17] and MAPLE [PMT18] have similar limitations like the feature importance measures defined for random forests.

Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or discrete, including in high-dimensions. However, in many applications data span variables of different types (e.g. continuous, count, binary, ordinal, etc.), whose principled joint analysis is nontrivial. Latent Gaussian copula models, in which all variables are modeled as transformations of underlying jointly Gaussian variables, represent a useful approach. Recent advances have shown how the binary-continuous case can be tackled, but the general mixed variable type regime remains challenging. In this work, we make the simple yet useful observation that classical ideas concerning polychoric and polyserial correlations can be leveraged in a latent Gaussian copula framework. Building on this observation we propose flexible and scalable methodology for data with variables of entirely general mixed type. We study the key properties of the approaches theoretically and empirically, via extensive simulations as well an illustrative application to data from the UK Biobank concerning COVID-19 risk factors.

Deep reinforcement learning (DRL) is one of the most popular algorithms to realize an autonomous driving (AD) system. The key success factor of DRL is that it embraces the perception capability of deep neural networks which, however, have been proven vulnerable to Trojan attacks. Trojan attacks have been widely explored in supervised learning (SL) tasks (e.g., image classification), but rarely in sequential decision-making tasks solved by DRL. Hence, in this paper, we explore Trojan attacks on DRL for AD tasks. First, we propose a spatio-temporal DRL algorithm based on the recurrent neural network and attention mechanism to prove that capturing spatio-temporal traffic features is the key factor to the effectiveness and safety of a DRL-augment AD system. We then design a spatial-temporal Trojan attack on DRL policies, where the trigger is hidden in a sequence of spatial and temporal traffic features, rather than a single instant state used in existing Trojan on SL and DRL tasks. With our Trojan, the adversary acts as a surrounding normal vehicle and can trigger attacks via specific spatial-temporal driving behaviors, rather than physical or wireless access. Through extensive experiments, we show that while capturing spatio-temporal traffic features can improve the performance of DRL for different AD tasks, they suffer from Trojan attacks since our designed Trojan shows high stealthy (various spatio-temporal trigger patterns), effective (less than 3.1\% performance variance rate and more than 98.5\% attack success rate), and sustainable to existing advanced defenses.