Learning compositional structures
Freitag, 8.11.19, 12:00-13:00, Raum 403, Ernst-Zermelo-Str. 1
Many data problems, in particular in biogenetics, often come with a highly complex underlying structure. This often makes is difficult to extract interpretable information. In this talk we want to demonstrate that often these complex structures are well approximated by a composition of a few simple parts, which provides very descriptive insights into the underlying data generating process. We demonstrate this with two examples.\n \nIn the first example, the single components are finite alphabet vectors (e.g., binary components), which encode some discrete information. For instance, in genetics a binary vector of length n can encode whether or not a mutation (e.g., a SNP) is present at location i = 1,…,n in the genome. On the population level studying genetic variations is often highly complex, as various groups of mutations are present simultaneously. However, in many settings a population might be well approximated by a composition of a few dominant groups. Examples are Evolve&Resequence experiments where the outer supply of genetic variation is limited and thus, over time, only a few haplotypes survive. Similar, in a cancer tumor, often only a few competing groups of cancer cells (clones) come out on top. \n \nIn the second example, the single components relate to separate branches of a tree structure. Tree structures, showing hierarchical relationships between samples, are ubiquitous in genomic and biomedical sciences. A common question in many studies is whether there is an association between a response variable and the latent group structure represented by the tree. Such a relation can be highly complex, in general. However, often it is well approximated by a simple composition of relations associated with a few branches of the tree. \n \nFor both of these examples we first study theoretical aspects of the underlying compositional structure, such as identifiability of single components and optimal statistical procedures under probabilistic data model. Based on this, we find insights into practical aspects of the problem, namely how to actually recover such components from data.
How implicit regularization of Neural Networks affects the learned function
Freitag, 6.12.19, 12:00-13:00, Raum 404, Ernst-Zermelo-Str. 1
Today, various forms of neural networks are trained to perform approximation tasks in many fields. However, the solutions obtained are not wholly understood. Empirical results suggest that the training favors regularized solutions.\nThese observations motivate us to analyze properties of the solutions found by the gradient descent algorithm frequently employed to perform the training task. As a starting point, we consider one dimensional (shallow) neural networks in which weights are chosen randomly and only the terminal layer is trained. We show, that the resulting solution converges to the smooth spline interpolation of the training data as the number of hidden nodes tends to infinity. This might give valuable insight on the properties of the solutions obtained using gradient descent methods in general settings.
Design risk of Constant Proportion Portfolio Insurance
Freitag, 31.1.20, 12:00-13:00, Raum 404, Ernst-Zermelo-Str. 1
This paper introduces the notion of design risk into the portfolio insurance literature. It focus on the evaluation of path–dependency/independency of the most widespread portfolio insurance strategies. In particular, we look at constant proportion portfolio insurance (CPPI) structures and compare them to both the classical option based portfolio insurance (OBPI) and naïve strategies such as stop-loss portfolio insurance (SLPI), or a CPPI with a multiplier of one. The paper is based upon conditional Monte Carlo simulations to control for the terminal value of the underlying. We show that even in scenarios where the terminal value of the underlying is several times higher its initial value, CPPIs can get cash-locked. The likelihood of ending up cash-locked increases with the size of the multiplier and the maturity, more than on the properties of the risky underlying’s dynamics. This cash-lock problem is specific of CPPIs, it goes against the European-style nature of traded CPPIs, and it adds to the strategy a risk that is unrelated to the underlying risky asset – a design risk. Design risk does not occur for path-independent portfolio insurance strategies, like in OBPI strategies, nor in naïve strategies. This study contributes to reinforce the idea that bad designing of structure products or investments strategies, may expose investors to undesired risks.\n\nJoint work with João Carvalho and João Beleza Sousa.\n