Unwrapping black box models: a case study in credit risk

The past two decades have witnessed the rapid development of machine learning techniques, which have proven to be powerful tools for the construction of predictive models, such as those used in credit risk management. A considerable volume of published work has looked at the utility of machine learning for this purpose, the increased predictive capacities delivered and how new types of data can be exploited. However, these benefits come at the cost of increased complexity, which may render the models uninterpretable. To overcome this issue a new field has emerged under the name of explainable artificial intelligence, with numerous tools being proposed to gain an insight into the inner workings of these models. This type of understanding is fundamental in credit risk in order to ensure compliance with the existing regulatory requirements and to comprehend the factors driving the predictions and their macro-economic implications. This paper studies the effectiveness of some of the most widely-used interpretability techniques on a neural network trained on real data. These techniques are found to be useful for understanding the model, even though some limitations have been encountered.En las dos últimas décadas se ha observado un rápido desarrollo de las técnicas de aprendizaje automático, que han demostrado ser herramientas muy potentes para elaborar modelos de predicción, como los utilizados en la gestión del riesgo de crédito. En un volumen considerable de trabajos publicados se analizan la utilidad del aprendizaje automático para este fin, las mayores capacidades predictivas que ofrece y la forma en la que se pueden explotar nuevos tipos de datos. Sin embargo, estas ventajas llevan aparejada una mayor complejidad, que puede imposibilitar la interpretación de los modelos. Para solventar este punto ha surgido un nuevo campo de investigación, denominado «inteligencia artificial explicable» (del inglés explicable artificial intelligence), en el que se proponen numerosas herramientas para obtener información relativa al funcionamiento interno de estos modelos. Este tipo de conocimiento es fundamental en materia de riesgo de crédito para garantizar que se cumplen los requerimientos regulatorios existentes y para comprender los factores determinantes de las predicciones y sus implicaciones macroeconómicas. En este artículo se estudia la eficacia de algunas de las técnicas de interpretabilidad más utilizadas en una red neuronal entrenada con datos reales. Estas técnicas se consideran útiles para la comprensión del modelo, pese a que se han detectado algunas limitaciones

The offence of stalking : a domcatic and jurisprudential analysis

Máster Universitario en Acceso a la Profesión de Abogado (M155

On the method of Bukhgeim for two-dimensional inverse problems

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de lectura: 22-02-201

Percentiles of sums of heavy-tailed random variables: Beyond the single-loss approximation

The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-013-9376-6A perturbative approach is used to derive approximations of arbitrary order to estimate high percentiles of sums of positive independent random variables that exhibit heavy tails. Closed-form expressions for the successive approximations are obtained both when the number of terms in the sum is deterministic and when it is random. The zeroth order approximation is the percentile of the maximum term in the sum. Higher orders in the perturbative series involve the right-truncated moments of the individual random variables that appear in the sum. These censored moments are always finite. As a result, and in contrast to previous approximations proposed in the literature, the perturbative series has the same form regardless of whether these random variables have a finite mean or not. For high percentiles, and specially for heavier tails, the quality of the estimate improves as more terms are included in the series, up to a certain order. Beyond that order the convergence of the series deteriorates. Nevertheless, the approximations obtained by truncating the perturbative series at intermediate orders are remarkably accurate for a variety of distributions in a wide range of parameters.The authors thank the anonymous reviewers for their valuable comments and suggestions. A.S. acknowledges financial support from the Spanish Dirección General de Investigación, project TIN2010-21575-C02-02

A bankable method for the field testingor a CPV plant

The bankability of CPV projects is an important issue to pave the way toward a swift and sustained growth in this technology. The bankability of a PV plant is generally addressed through the modeling of its energy yield under a b aseline loss scenario, followed by an on-site measurement campaign aimed at verifying its energetic behavior. The main difference between PV and CPV resides in the proper CPV modules, in particular in the inclusion of optical lements and III-V multijunction cells that are much more sensitive to spectral variations than xSi cells, while the rest of the system behaves in a way that possesses many common points with xSi technology. The modeling of the DC power output of a CPV system thus requires several impo rtant second order parameters to be considered, mainly related to optics, spectral direct solar radiation, wind speed, tracker accuracy and heat dissipation of cells