Query DAGs: A Practical Paradigm for Implementing Belief-Network Inference

We describe a new paradigm for implementing inference in belief networks, which consists of two steps: (1) compiling a belief network into an arithmetic expression called a Query DAG (Q-DAG); and (2) answering queries using a simple evaluation algorithm. Each node of a Q-DAG represents a numeric operation, a number, or a symbol for evidence. Each leaf node of a Q-DAG represents the answer to a network query, that is, the probability of some event of interest. It appears that Q-DAGs can be generated using any of the standard algorithms for exact inference in belief networks (we show how they can be generated using clustering and conditioning algorithms). The time and space complexity of a Q-DAG generation algorithm is no worse than the time complexity of the inference algorithm on which it is based. The complexity of a Q-DAG evaluation algorithm is linear in the size of the Q-DAG, and such inference amounts to a standard evaluation of the arithmetic expression it represents. The intended value of Q-DAGs is in reducing the software and hardware resources required to utilize belief networks in on-line, real-world applications. The proposed framework also facilitates the development of on-line inference on different software and hardware platforms due to the simplicity of the Q-DAG evaluation algorithm. Interestingly enough, Q-DAGs were found to serve other purposes: simple techniques for reducing Q-DAGs tend to subsume relatively complex optimization techniques for belief-network inference, such as network-pruning and computation-caching.Comment: See http://www.jair.org/ for any accompanying file

Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models

We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such that unrestricted label sets determine which edges can be deleted from the underlying directed acyclic graph (DAG) for a given context. Several properties of these models are derived, including a generalization of the concept of Markov equivalence classes. Efficient Bayesian learning of LDAGs is enabled by introducing an LDAG-based factorization of the Dirichlet prior for the model parameters, such that the marginal likelihood can be calculated analytically. In addition, we develop a novel prior distribution for the model structures that can appropriately penalize a model for its labeling complexity. A non-reversible Markov chain Monte Carlo algorithm combined with a greedy hill climbing approach is used for illustrating the useful properties of LDAG models for both real and synthetic data sets.Comment: 26 pages, 17 figure

Attractor Dynamics in Feedforward Neural Networks

We study the probabilistic generative models parameterized by feedforward neural networks. An attractor dynamics for probabilistic inference in these models is derived from a mean field approximation for large, layered sigmoidal networks. Fixed points of the dynamics correspond to solutions of the mean field equations, which relate the statistics of each unit to those of its Markov blanket. We establish global convergence of the dynamics by providing a Lyapunov function and show that the dynamics generate the signals required for unsupervised learning. Our results for feedforward networks provide a counterpart to those of Cohen-Grossberg and Hopfield for symmetric networks. 1 Introduction Attractor neural networks lend a computational purpose to continuous dynamical systems. Celebrated uses of these networks include the storage of associative memories (Amit, 1989), the reconstruction of noisy images (Koch et al, 1986), and the search for shortest paths in the traveling salesman proble..

Query-driven adaptive sampling

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2022.Automated information gathering allows exploration of environments where data is limited and gathering observations introduces risk, such as underwater and planetary exploration. Typically, exploration has been performed in service of a query, with a unique algorithm developed for each mission. Yet this approach does not allow scientists to respond to novel questions as they are raised. In this thesis, we develop a single approach for a broad range of adaptive sampling missions with risk and limited prior knowledge. To achieve this, we present contributions in planning adaptive missions in service of queries, and modeling multi-attribute environments. First, we define a query language suitable for specifying diverse goals in adaptive sampling. The language fully encompasses objectives from previous adaptive sampling approaches, and significantly extends the possible range of objectives. We prove that queries expressible in this language are not biased in a way that avoids information. We then describe a Monte Carlo tree search approach to plan for all queries in our language, using sample based objective estimators embedded within tree search. This approach outperforms methods that maximize information about all variables in hydrocarbon seep search and fire escape scenarios. Next, we show how to plan when the policy must bound risk as a function of reward. By solving approximating problems, we guarantee risk bounds on policies with large numbers of actions and continuous observations, ensuring that risks are only taken when justified by reward. Exploration is limited by the quality of the environment model, so we introduce Gaussian process models with directed acyclic structure to improve model accuracy under limited data. The addition of interpretable structure allows qualitative expert knowledge of the environment to be encoded through structure and parameter constraints. Since expert knowledge may be incomplete, we introduce efficient structure learning over structural models using A* search with bounding conflicts. By placing bounds on likelihood of substructures, we limit the number of structures that are trained, significantly accelerating search. Experiments modeling geographic data show that our model produces more accurate predictions than existing Gaussian process methods, and using bounds allows structure to be learned in 50% of the time.The work in this thesis was supported by the Exxon Mobil Corporation as part of the MIT Energy Initiative under the project ‘Autonomous System for Deep Sea Hydrocarbon Detection and Monitoring’, NASA’s PSTAR program under the project ‘Cooperative Exploration with Under-actuated Autonomous Vehicles in Hazardous Environments’, and the Vulcan Machine Learning Center for Impact under the project ‘Machine Learning Based Persistent Autonomous Underwater Scientific Studies’