Who Learns Better Bayesian Network Structures: Accuracy and Speed of Structure Learning Algorithms

Three classes of algorithms to learn the structure of Bayesian networks from data are common in the literature: constraint-based algorithms, which use conditional independence tests to learn the dependence structure of the data; score-based algorithms, which use goodness-of-fit scores as objective functions to maximise; and hybrid algorithms that combine both approaches. Constraint-based and score-based algorithms have been shown to learn the same structures when conditional independence and goodness of fit are both assessed using entropy and the topological ordering of the network is known (Cowell, 2001). In this paper, we investigate how these three classes of algorithms perform outside the assumptions above in terms of speed and accuracy of network reconstruction for both discrete and Gaussian Bayesian networks. We approach this question by recognising that structure learning is defined by the combination of a statistical criterion and an algorithm that determines how the criterion is applied to the data. Removing the confounding effect of different choices for the statistical criterion, we find using both simulated and real-world complex data that constraint-based algorithms are often less accurate than score-based algorithms, but are seldom faster (even at large sample sizes); and that hybrid algorithms are neither faster nor more accurate than constraint-based algorithms. This suggests that commonly held beliefs on structure learning in the literature are strongly influenced by the choice of particular statistical criteria rather than just by the properties of the algorithms themselves.Comment: 27 pages, 8 figure

Verifying Controllers Against Adversarial Examples with Bayesian Optimization

Recent successes in reinforcement learning have lead to the development of complex controllers for real-world robots. As these robots are deployed in safety-critical applications and interact with humans, it becomes critical to ensure safety in order to avoid causing harm. A first step in this direction is to test the controllers in simulation. To be able to do this, we need to capture what we mean by safety and then efficiently search the space of all behaviors to see if they are safe. In this paper, we present an active-testing framework based on Bayesian Optimization. We specify safety constraints using logic and exploit structure in the problem in order to test the system for adversarial counter examples that violate the safety specifications. These specifications are defined as complex boolean combinations of smooth functions on the trajectories and, unlike reward functions in reinforcement learning, are expressive and impose hard constraints on the system. In our framework, we exploit regularity assumptions on individual functions in form of a Gaussian Process (GP) prior. We combine these into a coherent optimization framework using problem structure. The resulting algorithm is able to provably verify complex safety specifications or alternatively find counter examples. Experimental results show that the proposed method is able to find adversarial examples quickly.Comment: Proc. of the IEEE International Conference on Robotics and Automation, 201

A Common-Factor Approach for Multivariate Data Cleaning with an Application to Mars Phoenix Mission Data

Data quality is fundamentally important to ensure the reliability of data for stakeholders to make decisions. In real world applications, such as scientific exploration of extreme environments, it is unrealistic to require raw data collected to be perfect. As data miners, when it is infeasible to physically know the why and the how in order to clean up the data, we propose to seek the intrinsic structure of the signal to identify the common factors of multivariate data. Using our new data driven learning method, the common-factor data cleaning approach, we address an interdisciplinary challenge on multivariate data cleaning when complex external impacts appear to interfere with multiple data measurements. Existing data analyses typically process one signal measurement at a time without considering the associations among all signals. We analyze all signal measurements simultaneously to find the hidden common factors that drive all measurements to vary together, but not as a result of the true data measurements. We use common factors to reduce the variations in the data without changing the base mean level of the data to avoid altering the physical meaning.Comment: 12 pages, 10 figures, 1 tabl

Bayesian Nonparametric Inverse Reinforcement Learning

Inverse reinforcement learning (IRL) is the task of learning the reward function of a Markov Decision Process (MDP) given the transition function and a set of observed demonstrations in the form of state-action pairs. Current IRL algorithms attempt to find a single reward function which explains the entire observation set. In practice, this leads to a computationally-costly search over a large (typically infinite) space of complex reward functions. This paper proposes the notion that if the observations can be partitioned into smaller groups, a class of much simpler reward functions can be used to explain each group. The proposed method uses a Bayesian nonparametric mixture model to automatically partition the data and find a set of simple reward functions corresponding to each partition. The simple rewards are interpreted intuitively as subgoals, which can be used to predict actions or analyze which states are important to the demonstrator. Experimental results are given for simple examples showing comparable performance to other IRL algorithms in nominal situations. Moreover, the proposed method handles cyclic tasks (where the agent begins and ends in the same state) that would break existing algorithms without modification. Finally, the new algorithm has a fundamentally different structure than previous methods, making it more computationally efficient in a real-world learning scenario where the state space is large but the demonstration set is small

Reprint of The new paradigm of economic complexity

Economic complexity offers a potentially powerful paradigm to understand key societal issues and challenges of our time. The underlying idea is that growth, development, technological change, income inequality, spatial disparities, and resilience are the visible outcomes of hidden systemic interactions. The study of economic complexity seeks to understand the structure of these interactions and how they shape various socioeconomic processes. This emerging field relies heavily on big data and machine learning techniques. This brief introduction to economic complexity has three aims. The first is to summarize key theoretical foundations and principles of economic complexity. The second is to briefly review the tools and metrics developed in the economic complexity literature that exploit information encoded in the structure of the economy to find new empirical patterns. The final aim is to highlight the insights from economic complexity to improve prediction and political decision-making. Institutions including the World Bank, the European Commission, the World Economic Forum, the OECD, and a range of national and regional organizations have begun to embrace the principles of economic complexity and its analytical framework. We discuss policy implications of this field, in particular the usefulness of building recommendation systems for major public investment decisions in a complex world