Henryk Gzyl

Abel Rodriguez, Henryk Gzyl, German Molina et al.

Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility models that uses opening and closing prices along with the minimum and maximum prices within a trading period to infer the dynamics underlying the volatility process of asset prices and compares it with similar models that have been previously presented in the literature. The paper also discusses sequential Monte Carlo algorithms to fit this class of models and illustrates its features using both a simulation study and data form the SP500 index.

Argimiro Arratia, Mahmoud El Daou, Henryk Gzyl

We consider the following classification problem: Given a population of individuals characterized by a set of attributes represented as a vector in ${\mathbb R}^N$, the goal is to find a hyperplane in ${\mathbb R}^N$ that separates two sets of points corresponding to two distinct classes. This problem, with a history dating back to the perceptron model, remains central to machine learning. In this paper we propose a novel approach by searching for a vector of parameters in a bounded $N$-dimensional hypercube centered at the origin and a positive vector in ${\mathbb R}^M$, obtained through the minimization of an entropy-based function defined over the space of unknown variables. The method extends to polynomial surfaces, allowing the separation of data points by more complex decision boundaries. This provides a robust alternative to traditional linear or quadratic optimization techniques, such as support vector machines and gradient descent. Numerical experiments demonstrate the efficiency and versatility of the method in handling diverse classification tasks, including linear and non-linear separability.

Erika Gomes-Gonçalves, Henryk Gzyl, Frank Nielsen

Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its codebook Voronoi diagrams, and report on experimental performances of partition-based, hierarchical, and soft clustering algorithms with respect to these Riemann-Bregman distances.