Regularizing Portfolio Optimization

The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification "pressure". This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade-off between the two, depending on the size of the available data set

Closed-Loop Statistical Verification of Stochastic Nonlinear Systems Subject to Parametric Uncertainties

This paper proposes a statistical verification framework using Gaussian processes (GPs) for simulation-based verification of stochastic nonlinear systems with parametric uncertainties. Given a small number of stochastic simulations, the proposed framework constructs a GP regression model and predicts the system's performance over the entire set of possible uncertainties. Included in the framework is a new metric to estimate the confidence in those predictions based on the variance of the GP's cumulative distribution function. This variance-based metric forms the basis of active sampling algorithms that aim to minimize prediction error through careful selection of simulations. In three case studies, the new active sampling algorithms demonstrate up to a 35% improvement in prediction error over other approaches and are able to correctly identify regions with low prediction confidence through the variance metric.Comment: 8 pages, submitted to ACC 201

Visual and Contextual Modeling for the Detection of Repeated Mild Traumatic Brain Injury.

Currently, there is a lack of computational methods for the evaluation of mild traumatic brain injury (mTBI) from magnetic resonance imaging (MRI). Further, the development of automated analyses has been hindered by the subtle nature of mTBI abnormalities, which appear as low contrast MR regions. This paper proposes an approach that is able to detect mTBI lesions by combining both the high-level context and low-level visual information. The contextual model estimates the progression of the disease using subject information, such as the time since injury and the knowledge about the location of mTBI. The visual model utilizes texture features in MRI along with a probabilistic support vector machine to maximize the discrimination in unimodal MR images. These two models are fused to obtain a final estimate of the locations of the mTBI lesion. The models are tested using a novel rodent model of repeated mTBI dataset. The experimental results demonstrate that the fusion of both contextual and visual textural features outperforms other state-of-the-art approaches. Clinically, our approach has the potential to benefit both clinicians by speeding diagnosis and patients by improving clinical care