Goal-conditioned Hierarchical Reinforcement Learning (HRL) is a promising approach for scaling up reinforcement learning (RL) techniques. However, it often suffers from training inefficiency as the action space of the high-level, i.e., the goal space, is large. Searching in a large goal space poses difficulty for both high-level subgoal generation and low-level policy learning. In this paper, we show that this problem can be effectively alleviated by restricting the high-level action space from the whole goal space to a $k$-step adjacent region of the current state using an adjacency constraint. We theoretically prove that in a deterministic Markov Decision Process (MDP), the proposed adjacency constraint preserves the optimal hierarchical policy, while in a stochastic MDP the adjacency constraint induces a bounded state-value suboptimality determined by the MDP's transition structure. We further show that this constraint can be practically implemented by training an adjacency network that can discriminate between adjacent and non-adjacent subgoals. Experimental results on discrete and continuous control tasks including challenging simulated robot locomotion and manipulation tasks show that incorporating the adjacency constraint significantly boosts the performance of state-of-the-art goal-conditioned HRL approaches.

In most existing studies on large-scale multi-agent coordination, the control methods aim to learn discrete policies for agents with finite choices. They rarely consider selecting actions directly from continuous action spaces to provide more accurate control, which makes them unsuitable for more complex tasks. To solve the control issue due to large-scale multi-agent systems with continuous action spaces, we propose a novel MARL coordination control method that derives stable continuous policies. By optimizing policies with maximum entropy learning, agents improve their exploration in execution and acquire an excellent performance after training. We also employ hierarchical graph attention networks (HGAT) and gated recurrent units (GRU) to improve the scalability and transferability of our method. The experiments show that our method consistently outperforms all baselines in large-scale multi-agent cooperative reconnaissance tasks.

We propose a new sparse Granger-causal learning framework for temporal event data. We focus on a specific class of point processes called the Hawkes process. We begin by pointing out that most of the existing sparse causal learning algorithms for the Hawkes process suffer from a singularity in maximum likelihood estimation. As a result, their sparse solutions can appear only as numerical artifacts. In this paper, we propose a mathematically well-defined sparse causal learning framework based on a cardinality-regularized Hawkes process, which remedies the pathological issues of existing approaches. We leverage the proposed algorithm for the task of instance-wise causal event analysis, where sparsity plays a critical role. We validate the proposed framework with two real use-cases, one from the power grid and the other from the cloud data center management domain.

We introduce a probabilistic model with implicit norm regularization for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent variables associated with each data dimension. The nonnegativity constraint for the latent factors is handled by choosing priors with support on the nonnegative subspace, e.g., exponential density or distribution based on exponential function. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including Genomics of Drug Sensitivity in Cancer (GDSC $IC_{50}$) and Gene body methylation with different sizes and dimensions, and show that the proposed Bayesian NMF GL$_2^2$ and GL$_\infty$ models lead to robust predictions for different data values and avoid overfitting compared with competitive Bayesian NMF approaches.

Discovering and parameterising latent confounders represent important and challenging problems in causal structure learning and density estimation respectively. In this paper, we focus on both discovering and learning the distribution of latent confounders. This task requires solutions that come from different areas of statistics and machine learning. We combine elements of variational Bayesian methods, expectation-maximisation, hill-climbing search, and structure learning under the assumption of causal insufficiency. We propose two learning strategies; one that maximises model selection accuracy, and another that improves computational efficiency in exchange for minor reductions in accuracy. The former strategy is suitable for small networks and the latter for moderate size networks. Both learning strategies perform well relative to existing solutions. Keywords: Ancestral graphs; EM algorithm; greedy search; hill-climbing search; hidden variables; probabilistic graphical models; variational inference.

Learning a Bayesian network is an NP-hard problem and with an increase in the number of nodes, classical algorithms for learning the structure of Bayesian networks become inefficient. In recent years, some methods and algorithms for learning Bayesian networks with a high number of nodes (more than 50) were developed. But these solutions have their disadvantages, for instance, they only operate one type of data (discrete or continuous) or their algorithm has been created to meet a specific nature of data (medical, social, etc.). The article presents a BigBraveBN algorithm for learning large Bayesian Networks with a high number of nodes (over 100). The algorithm utilizes the Brave coefficient that measures the mutual occurrence of instances in several groups. To form these groups, we use the method of nearest neighbours based on the Mutual information (MI) measure. In the experimental part of the article, we compare the performance of BigBraveBN to other existing solutions on multiple data sets both discrete and continuous. The experimental part also represents tests on real data. The aforementioned experimental results demonstrate the efficiency of the BigBraveBN algorithm in structure learning of Bayesian Networks.

Variational autoencoders (VAEs) often suffer from posterior collapse, which is a phenomenon in which the learned latent space becomes uninformative. This is often related to the hyperparameter resembling the data variance. It can be shown that an inappropriate choice of this hyperparameter causes the oversmoothness in the linearly approximated case and can be empirically verified for the general cases. Moreover, determining such appropriate choice becomes infeasible if the data variance is non-uniform or conditional. Therefore, we propose VAE extensions with generalized parameterizations of the data variance and incorporate maximum likelihood estimation into the objective function to adaptively regularize the decoder smoothness. The images generated from proposed VAE extensions show improved Fr\'echet inception distance (FID) on MNIST and CelebA datasets.

Early classification algorithms help users react faster to their machine learning model's predictions. Early warning systems in hospitals, for example, let clinicians improve their patients' outcomes by accurately predicting infections. While early classification systems are advancing rapidly, a major gap remains: existing systems do not consider irregular time series, which have uneven and often-long gaps between their observations. Such series are notoriously pervasive in impactful domains like healthcare. We bridge this gap and study early classification of irregular time series, a new setting for early classifiers that opens doors to more real-world problems. Our solution, Stop&Hop, uses a continuous-time recurrent network to model ongoing irregular time series in real time, while an irregularity-aware halting policy, trained with reinforcement learning, predicts when to stop and classify the streaming series. By taking real-valued step sizes, the halting policy flexibly decides exactly when to stop ongoing series in real time. This way, Stop&Hop seamlessly integrates information contained in the timing of observations, a new and vital source for early classification in this setting, with the time series values to provide early classifications for irregular time series. Using four synthetic and three real-world datasets, we demonstrate that Stop&Hop consistently makes earlier and more-accurate predictions than state-of-the-art alternatives adapted to this new problem. Our code is publicly available at https://github.com/thartvigsen/StopAndHop.

Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically. This tutorial provides an in-depth introduction to Markov chains, and explores their connection to graphs and random walks. We utilize tools from linear algebra and graph theory to describe the transition matrices of different types of Markov chains, with a particular focus on exploring properties of the eigenvalues and eigenvectors corresponding to these matrices. The results presented are relevant to a number of methods in machine learning and data mining, which we describe at various stages. Rather than being a novel academic study in its own right, this text presents a collection of known results, together with some new concepts. Moreover, the tutorial focuses on offering intuition to readers rather than formal understanding, and only assumes basic exposure to concepts from linear algebra and probability theory. It is therefore accessible to students and researchers from a wide variety of disciplines.

Sight and hearing are two senses that play a vital role in human communication and scene understanding. To mimic human perception ability, audio-visual learning, aimed at developing computational approaches to learn from both audio and visual modalities, has been a flourishing field in recent years. A comprehensive survey that can systematically organize and analyze studies of the audio-visual field is expected. Starting from the analysis of audio-visual cognition foundations, we introduce several key findings that have inspired our computational studies. Then, we systematically review the recent audio-visual learning studies and divide them into three categories: audio-visual boosting, cross-modal perception and audio-visual collaboration. Through our analysis, we discover that, the consistency of audio-visual data across semantic, spatial and temporal support the above studies. To revisit the current development of the audio-visual learning field from a more macro view, we further propose a new perspective on audio-visual scene understanding, then discuss and analyze the feasible future direction of the audio-visual learning area. Overall, this survey reviews and outlooks the current audio-visual learning field from different aspects. We hope it can provide researchers with a better understanding of this area. A website including constantly-updated survey is released: \url{https://gewu-lab.github.io/audio-visual-learning/}.