21,417 research outputs found
Probabilistic Methodology and Techniques for Artefact Conception and Development
The purpose of this paper is to make a state of the art on probabilistic methodology and techniques for artefact conception and development. It is the 8th deliverable of the BIBA (Bayesian Inspired Brain and Artefacts) project. We first present the incompletness problem as the central difficulty that both living creatures and artefacts have to face: how can they perceive, infer, decide and act efficiently with incomplete and uncertain knowledge?. We then introduce a generic probabilistic formalism called Bayesian Programming. This formalism is then used to review the main probabilistic methodology
and techniques. This review is organized in 3 parts: first the probabilistic models from Bayesian networks to Kalman filters and from sensor fusion to CAD systems, second the inference techniques and finally the learning and model acquisition and comparison methodologies. We conclude with the perspectives of the BIBA project as they rise from this state of the art
Efficient Bayes-Adaptive Reinforcement Learning using Sample-Based Search
Bayesian model-based reinforcement learning is a formally elegant approach to
learning optimal behaviour under model uncertainty, trading off exploration and
exploitation in an ideal way. Unfortunately, finding the resulting
Bayes-optimal policies is notoriously taxing, since the search space becomes
enormous. In this paper we introduce a tractable, sample-based method for
approximate Bayes-optimal planning which exploits Monte-Carlo tree search. Our
approach outperformed prior Bayesian model-based RL algorithms by a significant
margin on several well-known benchmark problems -- because it avoids expensive
applications of Bayes rule within the search tree by lazily sampling models
from the current beliefs. We illustrate the advantages of our approach by
showing it working in an infinite state space domain which is qualitatively out
of reach of almost all previous work in Bayesian exploration.Comment: 14 pages, 7 figures, includes supplementary material. Advances in
Neural Information Processing Systems (NIPS) 201
Maximum a Posteriori Estimation by Search in Probabilistic Programs
We introduce an approximate search algorithm for fast maximum a posteriori
probability estimation in probabilistic programs, which we call Bayesian ascent
Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with
varying number of mutually dependent finite, countable, and continuous random
variables. BaMC is an anytime MAP search algorithm applicable to any
combination of random variables and dependencies. We compare BaMC to other MAP
estimation algorithms and show that BaMC is faster and more robust on a range
of probabilistic models.Comment: To appear in proceedings of SOCS1
Parallel hierarchical sampling:a general-purpose class of multiple-chains MCMC algorithms
This paper introduces the Parallel Hierarchical Sampler (PHS), a class of Markov chain Monte Carlo algorithms using several interacting chains having the same target distribution but different mixing properties. Unlike any single-chain MCMC algorithm, upon reaching stationarity one of the PHS chains, which we call the “mother” chain, attains exact Monte Carlo sampling of the target distribution of interest. We empirically show that this translates in a dramatic improvement in the sampler’s performance with respect to single-chain MCMC algorithms. Convergence of the PHS joint transition kernel is proved and its relationships with single-chain samplers, Parallel Tempering (PT) and variable augmentation algorithms are discussed. We then provide two illustrative examples comparing the accuracy of PHS with
Sampling decomposable graphs using a Markov chain on junction trees
Full Bayesian computational inference for model determination in undirected
graphical models is currently restricted to decomposable graphs, except for
problems of very small scale. In this paper we develop new, more efficient
methodology for such inference, by making two contributions to the
computational geometry of decomposable graphs. The first of these provides
sufficient conditions under which it is possible to completely connect two
disconnected complete subsets of vertices, or perform the reverse procedure,
yet maintain decomposability of the graph. The second is a new Markov chain
Monte Carlo sampler for arbitrary positive distributions on decomposable
graphs, taking a junction tree representing the graph as its state variable.
The resulting methodology is illustrated with numerical experiments on three
specific models.Comment: 22 pages, 7 figures, 1 table. V2 as V1 except that Fig 1 was
corrected. V3 has significant edits, dropping some figures and including
additional examples and a discussion of the non-decomposable case. V4 is
further edited following review, and includes additional reference
Better Optimism By Bayes: Adaptive Planning with Rich Models
The computational costs of inference and planning have confined Bayesian
model-based reinforcement learning to one of two dismal fates: powerful
Bayes-adaptive planning but only for simplistic models, or powerful, Bayesian
non-parametric models but using simple, myopic planning strategies such as
Thompson sampling. We ask whether it is feasible and truly beneficial to
combine rich probabilistic models with a closer approximation to fully Bayesian
planning. First, we use a collection of counterexamples to show formal problems
with the over-optimism inherent in Thompson sampling. Then we leverage
state-of-the-art techniques in efficient Bayes-adaptive planning and
non-parametric Bayesian methods to perform qualitatively better than both
existing conventional algorithms and Thompson sampling on two contextual
bandit-like problems.Comment: 11 pages, 11 figure
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