Structural risk assessment and aircraft fleet maintenance

In the present analysis, deterministic flaw growth analysis is used to project the failure distributions from inspection data. Inspection data is reported for each critical point in the aircraft. The data will indicate either a crack of a specific size or no crack. The crack length may be either less than, equal to, or greater than critical size for that location. Non-critical length cracks are projected to failure using the crack growth characteristics for that location to find the life when it will be at critical length. Greater-than-critical length cracks are projected back to determine the life at failure, that is, when it was at critical length. The same process is used as in the case of a non-critical crack except that the projection goes the other direction. These points, along with the critical length cracks are used to determine the failure distribution. To be able to use data from different aircraft to build a common failure distribution, a consistent life variable must be used. Aircraft life varies with the severity of the usage; therefore the number of flight hours for a particular aircraft must be modified by its usage factor to obtain a normalized life which can be compared with that from other aircraft

A structural risk-neutral model of electricity prices

The objective of this paper is to present a model for electricity spot prices and the corresponding forward contracts, which relies on the underlying fuels markets, thus avoiding the electricity non-storability restriction. The structural aspect of our model comes from the fact that the electricity spot prices depend on the dynamic of the electricity demand at the maturity $T$, and on the random available capacity of each production means. Our model allows to explain, in a stylized fact, how the different fuels prices together with the demand combine to produce electricity prices. This modeling methodology allows to transfer to electricity prices the risk-neutral probabilities of the fuels market and under the hypothesis of independence between demand, outages filtrations on one hand, and fuels prices filtration on the other hand, it provides a regression-type relation between electricity forward prices and fuels forward prices. Moreover, the model produces, by nature, the well-known peaks observed on electricity market data. In our model, spikes occur when the producer has to switch from one technology to the lowest cost available one. Numerical tests performed on a very crude approximation of the French electricity market using only two fuels (gas and oil) provide an illustration of the potential interest of this model.energy markets; electricity prices; fuels prices; risk-neutral probability; no-arbitrage pricing; forward contracts

A structural risk-neutral model of electricity prices

The objective of this paper is to present a model for electricity spot prices and the corresponding forward contracts, which relies on the underlying market of fuels, thus avoiding the electricity non-storability restriction. The structural aspect of our model comes from the fact that the electricity spot prices depend on the dynamics of the electricity demand at the maturity $T$, and on the random available capacity of each production means. Our model explains, in a stylized fact, how the prices of different fuels together with the demand combine to produce electricity prices. This modeling methodology allows one to transfer to electricity prices the risk-neutral probabilities of the market of fuels and under the hypothesis of independence between demand and outages on one hand, and prices of fuels on the other hand, it provides a regression-type relation between electricity forward prices and forward prices of fuels. Moreover, the model produces, by nature, the well-known peaks observed on electricity market data. In our model, spikes occur when the producer has to switch from one technology to the lowest cost available one. Numerical tests performed on a very crude approximation of the French electricity market using only two fuels (gas and oil) provide an illustration of the potential interest of this model.energy markets; electricity prices; fuel prices; risk-neutral probability; no-arbitrage pricing; forward contracts

Empirical Risk Minimization with Approximations of Probabilistic Grammars

Probabilistic grammars are generative statistical models that are useful for compositional and sequential structures. We present a framework, reminiscent of structural risk minimization, for empirical risk minimization of the parameters of a fixed probabilistic grammar using the log-loss. We derive sample complexity bounds in this framework that apply both to the supervised setting and the unsupervised setting.

Lasso type classifiers with a reject option

We consider the problem of binary classification where one can, for a particular cost, choose not to classify an observation. We present a simple proof for the oracle inequality for the excess risk of structural risk minimizers using a lasso type penalty.Comment: Published at http://dx.doi.org/10.1214/07-EJS058 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Support Vector Machines in High Energy Physics

This lecture will introduce the Support Vector algorithms for classification and regression. They are an application of the so called kernel trick, which allows the extension of a certain class of linear algorithms to the non linear case. The kernel trick will be introduced and in the context of structural risk minimization, large margin algorithms for classification and regression will be presented. Current applications in high energy physics will be discussed.Comment: 11 pages, 12 figures. Part of the proceedings of the Track 'Computational Intelligence for HEP Data Analysis' at iCSC 200

Structural Risk Minimization for Learning Nonlinear Dynamics

Recent advances in learning or identification of nonlinear dynamics focus on learning a suitable model within a pre-specified model class. However, a key difficulty that remains is the choice of the model class from which the dynamics will be learned. The fundamental challenge is trading the richness of the model class with the learnability within the model class. Toward addressing the so-called model selection problem, we introduce a novel notion of Structural Risk Minimization (SRM) for learning nonlinear dynamics. Inspired by classical SRM for classification, we minimize a bound on the true prediction error over hierarchies of model classes. The class selected by our SRM scheme is shown to achieve a nearly optimal learning guarantee among all model classes contained in the hierarchy. Employing the proposed scheme along with computable model class complexity bounds, we derive explicit SRM schemes for learning nonlinear dynamics under hierarchies of: i) norm-constrained Reproducing Kernel Hilbert Spaces, and ii) norm-constrained Neural Network classes. We empirically show that even though too loose to be used as absolute estimates, our SRM bounds on the true prediction error are able to track its relative behavior across different model classes of the hierarchy