Predictive Models for Min-Entropy Estimation

Random numbers are essential for cryptography. In most real-world systems, these values come from a cryptographic pseudorandom number generator (PRNG), which in turn is seeded by an entropy source. The security of the entire cryptographic system then relies on the accuracy of the claimed amount of entropy provided by the source. If the entropy source provides less unpredictability than is expected, the security of the cryptographic mechanisms is undermined. For this reason, correctly estimating the amount of entropy available from a source is critical. In this paper, we develop a set of tools for estimating entropy, based on mechanisms that attempt to predict the next sample in a sequence based on all previous samples. These mechanisms are called predictors. We develop a framework for using predictors to estimate entropy, and test them experimentally against both simulated and real noise sources. For comparison, we subject the entropy estimates defined in the August 2012 draft of NIST Special Publication 800-90B to the same tests, and compare their performance

Entropy-Based Financial Asset Pricing

We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return - entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behaviour of the beta along with entropy.Comment: 21 pages, 6 figures, 3 tables and 4 supporting file

On the Effect of Inter-observer Variability for a Reliable Estimation of Uncertainty of Medical Image Segmentation

Uncertainty estimation methods are expected to improve the understanding and quality of computer-assisted methods used in medical applications (e.g., neurosurgical interventions, radiotherapy planning), where automated medical image segmentation is crucial. In supervised machine learning, a common practice to generate ground truth label data is to merge observer annotations. However, as many medical image tasks show a high inter-observer variability resulting from factors such as image quality, different levels of user expertise and domain knowledge, little is known as to how inter-observer variability and commonly used fusion methods affect the estimation of uncertainty of automated image segmentation. In this paper we analyze the effect of common image label fusion techniques on uncertainty estimation, and propose to learn the uncertainty among observers. The results highlight the negative effect of fusion methods applied in deep learning, to obtain reliable estimates of segmentation uncertainty. Additionally, we show that the learned observers' uncertainty can be combined with current standard Monte Carlo dropout Bayesian neural networks to characterize uncertainty of model's parameters.Comment: Appears in Medical Image Computing and Computer Assisted Interventions (MICCAI), 201

Predicting trend reversals using market instantaneous state

Collective behaviours taking place in financial markets reveal strongly correlated states especially during a crisis period. A natural hypothesis is that trend reversals are also driven by mutual influences between the different stock exchanges. Using a maximum entropy approach, we find coordinated behaviour during trend reversals dominated by the pairwise component. In particular, these events are predicted with high significant accuracy by the ensemble's instantaneous state.Comment: 18 pages, 15 figure