Conditional distribution modeling for estimating and exploiting uncertainty in control systems

This paper presents a general methodology for estimating and incorporating uncertainty in the controller and forward models for noisy nonlinear control problems. Conditional distribution modeling in a neural network context is used to estimate uncertainty around the prediction of neural network outputs. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localize the possible control solutions to consider. A nonlinear multivariable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non Gaussian distributions of control signal as well as processes with hysteresis

In All Likelihood, Deep Belief Is Not Enough

Statistical models of natural stimuli provide an important tool for researchers in the fields of machine learning and computational neuroscience. A canonical way to quantitatively assess and compare the performance of statistical models is given by the likelihood. One class of statistical models which has recently gained increasing popularity and has been applied to a variety of complex data are deep belief networks. Analyses of these models, however, have been typically limited to qualitative analyses based on samples due to the computationally intractable nature of the model likelihood. Motivated by these circumstances, the present article provides a consistent estimator for the likelihood that is both computationally tractable and simple to apply in practice. Using this estimator, a deep belief network which has been suggested for the modeling of natural image patches is quantitatively investigated and compared to other models of natural image patches. Contrary to earlier claims based on qualitative results, the results presented in this article provide evidence that the model under investigation is not a particularly good model for natural image

Optimal estimation for Large-Eddy Simulation of turbulence and application to the analysis of subgrid models

The tools of optimal estimation are applied to the study of subgrid models for Large-Eddy Simulation of turbulence. The concept of optimal estimator is introduced and its properties are analyzed in the context of applications to a priori tests of subgrid models. Attention is focused on the Cook and Riley model in the case of a scalar field in isotropic turbulence. Using DNS data, the relevance of the beta assumption is estimated by computing (i) generalized optimal estimators and (ii) the error brought by this assumption alone. Optimal estimators are computed for the subgrid variance using various sets of variables and various techniques (histograms and neural networks). It is shown that optimal estimators allow a thorough exploration of models. Neural networks are proved to be relevant and very efficient in this framework, and further usages are suggested