Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov Chain Monte Carlo (MCMC) methods, namely, Hamiltonian Monte Carlo (HMC). The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the art methods

An efficient anti-optimization approach for uncertainty analysis in composite laminates

This work presents an efficient approach to quantify uncertainties in composite laminates using the interval analysis, anti-optimization technique, and the α-cut procedure. The solutions are compared with the traditional and robust Monte Carlo method in 3 cases scenarios: natural frequencies, buckling, and strength safe factor. For natural frequencies and buckling loads, the presented Interval based methodology showed 2.5% to 4.5% larger error values when compared to the Monte Carlo method using the same number of function calls. This implies a larger uncertain area, and hence, a better solution. For the strength test using Tsai-Wu failure theory, the error values are even greater: 22% to 46%. A violation of the failure limit was detected by the proposed Interval based approach, but not detected by Monte Carlo method. The solutions show that the presented methodology yields a safer and more precise analysis when compared to the traditional Monte Carlo approach

Monte Carlo optimization approach for decentralized estimation networks under communication constraints

We consider designing decentralized estimation schemes over bandwidth limited communication links with a particular interest in the tradeoff between the estimation accuracy and the cost of communications due to, e.g., energy consumption. We take two classes of in–network processing strategies into account which yield graph representations through modeling the sensor platforms as the vertices and the communication links by edges as well as a tractable Bayesian risk that comprises the cost of transmissions and penalty for the estimation errors. This approach captures a broad range of possibilities for “online” processing of observations as well as the constraints imposed and enables a rigorous design setting in the form of a constrained optimization problem. Similar schemes as well as the structures exhibited by the solutions to the design problem has been studied previously in the context of decentralized detection. Under reasonable assumptions, the optimization can be carried out in a message passing fashion. We adopt this framework for estimation, however, the corresponding optimization schemes involve integral operators that cannot be evaluated exactly in general. We develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both classes of in–network processing strategies and their optimization. The proposed Monte Carlo optimization procedures operate in a scalable and efficient fashion and, owing to the non-parametric nature, can produce results for any distributions provided that samples can be produced from the marginals. In addition, this approach exhibits graceful degradation of the estimation accuracy asymptotically as the communication becomes more costly, through a parameterized Bayesian risk

Monte Carlo optimization approach for decentralized estimation networks under communication constraints

We consider designing decentralized estimation schemes over bandwidth limited communication links with a particular interest in the tradeoff between the estimation accuracy and the cost of communications due to, e.g., energy consumption. We take two classes of in–network processing strategies into account which yield graph representations through modeling the sensor platforms as the vertices and the communication links by edges as well as a tractable Bayesian risk that comprises the cost of transmissions and penalty for the estimation errors. This approach captures a broad range of possibilities for “online” processing of observations as well as the constraints imposed and enables a rigorous design setting in the form of a constrained optimization problem. Similar schemes as well as the structures exhibited by the solutions to the design problem has been studied previously in the context of decentralized detection. Under reasonable assumptions, the optimization can be carried out in a message passing fashion. We adopt this framework for estimation, however, the corresponding optimization schemes involve integral operators that cannot be evaluated exactly in general. We develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both classes of in–network processing strategies and their optimization. The proposed Monte Carlo optimization procedures operate in a scalable and efficient fashion and, owing to the non-parametric nature, can produce results for any distributions provided that samples can be produced from the marginals. In addition, this approach exhibits graceful degradation of the estimation accuracy asymptotically as the communication becomes more costly, through a parameterized Bayesian risk

Monte Carlo optimization of decentralized estimation networks over directed acyclic graphs under communication constraints

Motivated by the vision of sensor networks, we consider decentralized estimation networks over bandwidth–limited communication links, and are particularly interested in the tradeoff between the estimation accuracy and the cost of communications due to, e.g., energy consumption. We employ a class of in–network processing strategies that admits directed acyclic graph representations and yields a tractable Bayesian risk that comprises the cost of communications and estimation error penalty. This perspective captures a broad range of possibilities for processing under network constraints and enables a rigorous design problem in the form of constrained optimization. A similar scheme and the structures exhibited by the solutions have been previously studied in the context of decentralized detection. Under reasonable assumptions, the optimization can be carried out in a message passing fashion. We adopt this framework for estimation, however, the corresponding optimization scheme involves integral operators that cannot be evaluated exactly in general. We develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both the in–network processing strategies and their optimization. The proposed Monte Carlo optimization procedure operates in a scalable and efficient fashion and, owing to the non-parametric nature, can produce results for any distributions provided that samples can be produced from the marginals. In addition, this approach exhibits graceful degradation of the estimation accuracy asymptotically as the communication becomes more costly, through a parameterized Bayesian risk

MS

thesisGeometric constraint problems appear in many situations, including CAD systems, robotics, and computational biology. The complexity of these problems inspires the search for efficient solutions. We have developed a method to solve geometric constraint problems in the areas of geometric computation and robot path planning using configuration space subdivision. In this approach the configuration space, or parameter space, is subdivided and conservatively tested to find collision-free regions, which are then numerically searched for specific path solutions. This thesis presents a new more general approach to this last solution search step, using Monte Carlo optimization. In this new search approach, within a single subdivided area of configuration space, space is randomly sampled and then iteratively resampled based on importance weighting, until convergence to a solution with an acceptable error. We show that by using Monte Carlo optimization to extend configuration space subdivision we can solve higher dimensional problems more efficiently than configuration space subdivision by itself

Efficient Object Manipulation Planning with Monte Carlo Tree Search

This paper presents an efficient approach to object manipulation planning using Monte Carlo Tree Search (MCTS) to find contact sequences and an efficient ADMM-based trajectory optimization algorithm to evaluate the dynamic feasibility of candidate contact sequences. To accelerate MCTS, we propose a methodology to learn a goal-conditioned policy-value network to direct the search towards promising nodes. Further, manipulation-specific heuristics enable to drastically reduce the search space. Systematic object manipulation experiments in a physics simulator and on real hardware demonstrate the efficiency of our approach. In particular, our approach scales favorably for long manipulation sequences thanks to the learned policy-value network, significantly improving planning success rate

Quasi-Monte Carlo, Monte Carlo, and regularized gradient optimization methods for source characterization of atmospheric releases

An inversion technique based on MC/QMC search and regularized gradient optimization was developed to solve the atmospheric source characterization problem. The Gaussian Plume Model was adopted as the forward operator and QMC/MC search was implemented in order to find good starting points for the gradient optimization. This approach was validated on the Copenhagen Tracer Experiments. The QMC approach with the utilization of clasical and scrambled Halton, Hammersley and Sobol points was shown to be 10-100 times more efficient than the Mersenne Twister Monte Carlo generator. Further experiments are needed for different data sets. Computational complexity analysis needs to be carried out

Robust topology optimization of continuum structures using Monte Carlo method and Kriging models

El objetivo de este trabajo es presentar una nueva metodología eficiente y precisa llamada Monte Carlo y Kriging (MCK) para la optimización de topología robusta. El objetivo es minimizar el valor esperado de la compliance considerando la existencia de incertidumbre con cargas concentradas. La incertidumbre en la carga puede presentarse en la magnitud, en la dirección y/o en la posición. La evaluación de la función objetivo se realiza utilizando el método de simulación de Monte Carlo en combinación con un modelo Kriging. Para estimar el valor esperado de la compliance, se transforma el problema probabilístico en otro determinístico sujeto a múltiples estados de carga mediante el Método de Monte Carlo pero empleando un reducido número de evaluaciones del modelo de simulación. Para ello es necesario construir un modelo Kriging del modelo de simulación a partir de una pequeña muestra obtenida con un hipercubo latino del espacio de diseño y predecir la compliance en cada uno de los puntos utilizados por la simulación de Monte Carlo. Dos ejemplos demuestran la precisión y eficiencia del algoritmo. Para verificar el algoritmo propuesto, los problemas también se resuelven mediante el método de Monte Carlo estándar.The aim of this paper is to introduce an efficient and accurate new approach called Monte Carlo and Kriging (MCK) to robust topology optimization. The objective is to minimize the expected value of compliance under concentrated loading uncertainty. The loading uncertainty may occur in magnitude, direction and/or position. The Monte Carlo simulation method and Kriging model are used to evaluate the objective function. To evaluate the expected value of compliance the probabilistic problem is transformed into a multiple loading deterministic one using of Monte Carlo method but with a reduced evaluations number of simulation model. A small sample obtained with a Latin Hypercube is used to build a Kriging model of the simulation model. This is utilized to estimate the compliance in those points used by Monte Carlo simulation method. Two problems are solved to demonstrate the efficiency and accuracy of the approach. The examples are solved again using a standard Monte Carlo simulation to check the proposed approach.Peer Reviewe