Among machine learning problems, matrix factorization (MF) is significant because MF appears in many applications such as recommendation system, signal processing, etc. We restrict ourselves to sparse MF problem in this article, where either factorized matrix must be sparse. This is originally discussed as sparse coding in neuroscience [1, 2], and recognized as a significant problem in neuronal information processing in the brain. It also appears in sparse modeling in information science such as dictionary learning [3, 4] or sparse principal component analysis (sparse PCA) [5, 6]. Many attempts have been made so far for understanding theoretical aspects of MF, and analytical tools for random systems in statistical physics are found to be useful, e.g. Markov chain Monte Carlo method [7], replica analysis [8, 9, 10, 11, 12], and message passing [9, 10, 11, 12, 13, 14], where some works are not limited to sparse matrix case.

We introduce Graph-Induced Sum-Product Networks (GSPNs), a new probabilistic framework for graph representation learning that can tractably answer probabilistic queries. Inspired by the computational trees induced by vertices in the context of message-passing neural networks, we build hierarchies of sum-product networks (SPNs) where the parameters of a parent SPN are learnable transformations of the a-posterior mixing probabilities of its children's sum units. Due to weight sharing and the tree-shaped computation graphs of GSPNs, we obtain the efficiency and efficacy of deep graph networks with the additional advantages of a purely probabilistic model. We show the model's competitiveness on scarce supervision scenarios, handling missing data, and graph classification in comparison to popular neural models. We complement the experiments with qualitative analyses on hyper-parameters and the model's ability to answer probabilistic queries.

We present a novel approach for black-box VI that bypasses the difficulties of stochastic gradient ascent, including the task of selecting step-sizes. Our approach involves using a sequence of sample average approximation (SAA) problems. SAA approximates the solution of stochastic optimization problems by transforming them into deterministic ones. We use quasi-Newton methods and line search to solve each deterministic optimization problem and present a heuristic policy to automate hyperparameter selection. Our experiments show that our method simplifies the VI problem and achieves faster performance than existing methods.

Bayesian networks (BN) are directed acyclic graphical (DAG) models that have been adopted into many fields for their strengths in transparency, interpretability, probabilistic reasoning, and causal modeling. Given a set of data, one hurdle towards using BNs is in building the network graph from the data that properly handles dependencies, whether correlated or causal. In this paper, we propose an initial methodology for discovering network structures using Tsetlin Machines.

Two performance criteria are commonly used for infinitehorizon MDPs: 1) the discounted-reward setting, where Robust Markov decision processes (MDPs) address the reward is discounted exponentially with time; and 2) the challenge of model uncertainty by optimizing the average-reward setting, where the long-term averagereward the worst-case performance over an uncertainty over time is of interest. For systems that operate for set of MDPs. In this paper, we focus on the an extended period of time, e.g., queue control, inventory robust average-reward MDPs under the modelfree management in supply chains, or communication networks, setting. We first theoretically characterize it is more important to optimize the average-reward since the structure of solutions to the robust averagereward policies obtained from the discounted-reward setting may Bellman equation, which is essential for be myopic and have poor long-term performance (Kazemi our later convergence analysis.

Most works on multi-agent reinforcement learning focus on scenarios where the state of the environment is fully observable. In this work, we consider a cooperative policy evaluation task in which agents are not assumed to observe the environment state directly. Instead, agents can only have access to noisy observations and to belief vectors. It is well-known that finding global posterior distributions under multi-agent settings is generally NP-hard. As a remedy, we propose a fully decentralized belief forming strategy that relies on individual updates and on localized interactions over a communication network. In addition to the exchange of the beliefs, agents exploit the communication network by exchanging value function parameter estimates as well. We analytically show that the proposed strategy allows information to diffuse over the network, which in turn allows the agents' parameters to have a bounded difference with a centralized baseline. A multi-sensor target tracking application is considered in the simulations.

Accessibility is one of the most important features in the design of robots and their interfaces. This thesis proposes methods that improve the accessibility of robots for three different target audiences: consumers, researchers, and learners. In order for humans and robots to work together effectively, they both must be able to communicate with each other. We tackle the problem of generating route instructions that are readily understandable by novice humans for the navigation of a priori unknown indoor environments. We then move on to the related problem of enabling robots to understand natural language utterances in the context of learning to operate articulated objects (e.g., fridges, drawers) by leveraging kinematic models. Next, we turn our focus to the development of accessible and reproducible robotic platforms for scientific research. We propose a new concept for reproducible robotics research that integrates development and benchmarking, so that reproducibility is obtained "by design" from the beginning of the research and development process. We then propose a framework called SHARC (SHared Autonomy for Remote Collaboration), to improve accessibility for underwater robotic intervention operations. SHARC allows multiple remote scientists to efficiently plan and execute high-level sampling procedures using an underwater manipulator while deferring low-level control to the robot. Lastly, we developed the first hardware-based MOOC in AI and robotics. This course allows learners to study autonomy hands-on by making real robots make their own decisions and accomplish broadly defined tasks. We design a new robotic platform from the ground up to support this new learning experience. A fully browser-based interface, based on leading tools and technologies for code development, testing, validation, and deployment serves to maximize the accessibility of these educational resources.

Understanding the causal relationships among the variables of a system is paramount to explain and control its behaviour. Inferring the causal graph from observational data without interventions, however, requires a lot of strong assumptions that are not always realistic. Even for domain experts it can be challenging to express the causal graph. Therefore, metrics that quantitatively assess the goodness of a causal graph provide helpful checks before using it in downstream tasks. Existing metrics provide an absolute number of inconsistencies between the graph and the observed data, and without a baseline, practitioners are left to answer the hard question of how many such inconsistencies are acceptable or expected. Here, we propose a novel consistency metric by constructing a surrogate baseline through node permutations. By comparing the number of inconsistencies with those on the surrogate baseline, we derive an interpretable metric that captures whether the DAG fits significantly better than random. Evaluating on both simulated and real data sets from various domains, including biology and cloud monitoring, we demonstrate that the true DAG is not falsified by our metric, whereas the wrong graphs given by a hypothetical user are likely to be falsified.

Humans use semantic concepts such as spatial relations between objects to describe scenes and communicate tasks such as "Put the tea to the right of the cup" or "Move the plate between the fork and the spoon." Just as children, assistive robots must be able to learn the sub-symbolic meaning of such concepts from human demonstrations and instructions. We address the problem of incrementally learning geometric models of spatial relations from few demonstrations collected online during interaction with a human. Such models enable a robot to manipulate objects in order to fulfill desired spatial relations specified by verbal instructions. At the start, we assume the robot has no geometric model of spatial relations. Given a task as above, the robot requests the user to demonstrate the task once in order to create a model from a single demonstration, leveraging cylindrical probability distribution as generative representation of spatial relations. We show how this model can be updated incrementally with each new demonstration without access to past examples in a sample-efficient way using incremental maximum likelihood estimation, and demonstrate the approach on a real humanoid robot.

Value decomposition methods have gained popularity in the field of cooperative multi-agent reinforcement learning. However, almost all existing methods follow the principle of Individual Global Max (IGM) or its variants, which limits their problem-solving capabilities. To address this, we propose a dual self-awareness value decomposition framework, inspired by the notion of dual self-awareness in psychology, that entirely rejects the IGM premise. Each agent consists of an ego policy for action selection and an alter ego value function to solve the credit assignment problem. The value function factorization can ignore the IGM assumption by utilizing an explicit search procedure. On the basis of the above, we also suggest a novel anti-ego exploration mechanism to avoid the algorithm becoming stuck in a local optimum. As the first fully IGM-free value decomposition method, our proposed framework achieves desirable performance in various cooperative tasks.