Rigorous finite-time guarantees for optimization on continuous domains by simulated annealing

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

Simulated Annealing: Rigorous finite-time guarantees for optimization on continuous domains

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

Reinforcement learning for parameter estimation in statistical spoken dialogue systems

Reinforcement techniques have been successfully used to maximise the expected cumulative reward of statistical dialogue systems. Typically, reinforcement learning is used to estimate the parameters of a dialogue policy which selects the system's responses based on the inferred dialogue state. However, the inference of the dialogue state itself depends on a dialogue model which describes the expected behaviour of a user when interacting with the system. Ideally the parameters of this dialogue model should be also optimised to maximise the expected cumulative reward. This article presents two novel reinforcement algorithms for learning the parameters of a dialogue model. First, the Natural Belief Critic algorithm is designed to optimise the model parameters while the policy is kept fixed. This algorithm is suitable, for example, in systems using a handcrafted policy, perhaps prescribed by other design considerations. Second, the Natural Actor and Belief Critic algorithm jointly optimises both the model and the policy parameters. The algorithms are evaluated on a statistical dialogue system modelled as a Partially Observable Markov Decision Process in a tourist information domain. The evaluation is performed with a user simulator and with real users. The experiments indicate that model parameters estimated to maximise the expected reward function provide improved performance compared to the baseline handcrafted parameters. © 2011 Elsevier Ltd. All rights reserved.

Phrase-based statistical language generation using graphical models and active learning

Most previous work on trainable language generation has focused on two paradigms: (a) using a statistical model to rank a set of generated utterances, or (b) using statistics to inform the generation decision process. Both approaches rely on the existence of a handcrafted generator, which limits their scalability to new domains. This paper presents BAGEL, a statistical language generator which uses dynamic Bayesian networks to learn from semantically-aligned data produced by 42 untrained annotators. A human evaluation shows that BAGEL can generate natural and informative utterances from unseen inputs in the information presentation domain. Additionally, generation performance on sparse datasets is improved significantly by using certainty-based active learning, yielding ratings close to the human gold standard with a fraction of the data. © 2010 Association for Computational Linguistics.

Natural actor and belief critic: Reinforcement algorithm for learning parameters of dialogue systems modelled as POMDPs

This article presents a novel algorithm for learning parameters in statistical dialogue systems which are modeled as Partially Observable Markov Decision Processes (POMDPs). The three main components of a POMDP dialogue manager are a dialogue model representing dialogue state information; a policy that selects the system's responses based on the inferred state; and a reward function that specifies the desired behavior of the system. Ideally both the model parameters and the policy would be designed to maximize the cumulative reward. However, while there are many techniques available for learning the optimal policy, no good ways of learning the optimal model parameters that scale to real-world dialogue systems have been found yet. The presented algorithm, called the Natural Actor and Belief Critic (NABC), is a policy gradient method that offers a solution to this problem. Based on observed rewards, the algorithm estimates the natural gradient of the expected cumulative reward. The resulting gradient is then used to adapt both the prior distribution of the dialogue model parameters and the policy parameters. In addition, the article presents a variant of the NABC algorithm, called the Natural Belief Critic (NBC), which assumes that the policy is fixed and only the model parameters need to be estimated. The algorithms are evaluated on a spoken dialogue system in the tourist information domain. The experiments show that model parameters estimated to maximize the expected cumulative reward result in significantly improved performance compared to the baseline hand-crafted model parameters. The algorithms are also compared to optimization techniques using plain gradients and state-of-the-art random search algorithms. In all cases, the algorithms based on the natural gradient work significantly better. © 2011 ACM.

Statistical inference for single- and multi-band probabilistic amplitude demodulation.

Amplitude demodulation is an ill-posed problem and so it is natural to treat it from a Bayesian viewpoint, inferring the most likely carrier and envelope under probabilistic constraints. One such treatment is Probabilistic Amplitude Demodulation (PAD), which, whilst computationally more intensive than traditional approaches, offers several advantages. Here we provide methods for estimating the uncertainty in the PAD-derived envelopes and carriers, and for learning free-parameters like the time-scale of the envelope. We show how the probabilistic approach can naturally handle noisy and missing data. Finally, we indicate how to extend the model to signals which contain multiple modulators and carriers.

Learning based automatic face annotation for arbitrary poses and expressions from frontal images only

Statistical approaches for building non-rigid deformable models, such as the Active Appearance Model (AAM), have enjoyed great popularity in recent years, but typically require tedious manual annotation of training images. In this paper, a learning based approach for the automatic annotation of visually deformable objects from a single annotated frontal image is presented and demonstrated on the example of automatically annotating face images that can be used for building AAMs for fitting and tracking. This approach employs the idea of initially learning the correspondences between landmarks in a frontal image and a set of training images with a face in arbitrary poses. Using this learner, virtual images of unseen faces at any arbitrary pose for which the learner was trained can be reconstructed by predicting the new landmark locations and warping the texture from the frontal image. View-based AAMs are then built from the virtual images and used for automatically annotating unseen images, including images of different facial expressions, at any random pose within the maximum range spanned by the virtually reconstructed images. The approach is experimentally validated by automatically annotating face images from three different databases. © 2009 IEEE.

Active learning of model evidence using Bayesian quadrature

Numerical integration is a key component of many problems in scientific computing, statistical modelling, and machine learning. Bayesian Quadrature is a modelbased method for numerical integration which, relative to standard Monte Carlo methods, offers increased sample efficiency and a more robust estimate of the uncertainty in the estimated integral. We propose a novel Bayesian Quadrature approach for numerical integration when the integrand is non-negative, such as the case of computing the marginal likelihood, predictive distribution, or normalising constant of a probabilistic model. Our approach approximately marginalises the quadrature model's hyperparameters in closed form, and introduces an active learning scheme to optimally select function evaluations, as opposed to using Monte Carlo samples. We demonstrate our method on both a number of synthetic benchmarks and a real scientific problem from astronomy.