Short-time near-the-money skew in rough fractional stochastic volatility models
Friday, 28.4.17, 11:00-12:00, Raum 232, Eckerstr. 1
We consider rough stochastic volatility models where the driving noise of volatility\nhas fractional scaling, in the rough regime of Hurst parameter H < 1/2. This regime\nrecently attracted a lot of attention both from the statistical and option pricing\npoint of view. With focus on the latter, we sharpen the large deviation results of\nForde-Zhang (2017) in a way that allows us to zoom-in around the money while\nmaintaining full analytical tractability. More precisely, this amounts to proving\nhigher order moderate deviation estimates, only recently introduced in the option\npricing context. This in turn allows us to push the applicability range of known at-\nthe-money skew approximation formulae from CLT type log-moneyness deviations\nof order t1/2 (recent works of Alo‘s, Le ?on Vives and Fukasawa) to the wider\nmoderate deviations regime.\nThis is work in collaboration with C. Bayer, P. Friz, A. Gulsashvili and B. Stemper
A General Framework for Uncovering Dependence Networks
Friday, 28.4.17, 12:00-13:00, Raum 404, Eckerstr. 1
Dependencies in multivariate observations are a unique gateway to uncovering relationships among processes. An approach that has proved particularly successful in modeling and visualizing such dependence structures is the use of graphical models. However, whereas graphical models have been formulated for finite count data and Gaussian-type data, many other data types prevalent in the sciences have not been accounted for. For example, it is believed that insights into microbial interactions in human habitats, such as the gut or the oral cavity, can be deduced\nfrom analyzing the dependencies in microbial abundance data, a data type that is not amenable to standard classes of graphical models. We present a novel framework that unifies existing classes of graphical models and provides other classes that extend the concept of graphical models to a broad variety of discrete and continuous data, both in low- and high-dimensional settings. Moreover, we present a corresponding set of statistical methods and theoretical guarantees that allows for efficient estimation and inference in the framework.
Statistical methodology for comparing curves
Friday, 12.5.17, 12:00-13:00, Raum 404, Eckerstr. 1
An important problem in drug development is to establish the similarity between two dose response curves (bridging studies). We propose new statistical methodology improving the current state of the art in at least two directions. On the one hand efficient designs are constructed minimizing the width of the confidence band for the difference between the regression functions, which is currently used for a test of similarity. The use of the new designs yields a reduction of the width of the confidence band by more than 50 percent and consequently to a substantially more powerful test. On the other hand – and more importantly – we propose new and substantially more powerful tests for the hypothesis of ”similarity”. In particular, we develop some non-standard parametric bootstrap procedure and prove its consistency. We also explain some not so well known results about classical goodness of fit tests (such as Kolmogorov-Smirnov-tests) under fixed alternatives.\n\n\n\n
Deep Learning
Friday, 2.6.17, 12:00-13:00, Raum 404, Eckerstr. 1
Deep learning has been getting large attention in science and the media. In my talk I will show results mainly from computer vision that explain this attention and indicates how things could go on in the future. The talk will consist of three main parts. In the first part, I will give a brief introduction into the fundamentals of deep learning, such as common network architectures and the basic back-propagation algorithm for optimization of their parameters. In the second part, I will show recent results from my group, which developed for the first time learning formulations for 3D computer vision. In the third part, I will list mathematical challenges in deep learning, the solution of which would probably largely improve the state of the art.
(Localized) learning with kernels
Friday, 16.6.17, 12:00-13:00, Raum 404, Eckerstr. 1
Using reproducing kernel Hilbert spaces in non-parametric approaches\nfor regression and classification has a long-standing history. In\nthe first part of this talk, I will introduce these kernel-based learning\n(KBL) methods and discuss some existing statistical guarantees for them.\nIn the second part I will present a localization approach that addresses\nthe super-linear computational requirements of KBLs in terms of the number\nof training samples. I will further provide a statistical analysis that\nshows that the "local KBL" achieves the same learning rates as the original,\nglobal KBL. Furthermore, I will report from some large scale experiments\nshowing that the local KBL achieves essentially the same test performance\nas the global KBL, but for a fraction of the computational requirements.\nIn addition, it turns out that the computational requirements for the local\nKBLs are similar to those of a vanilla random chunk approach, while the\nachieved test errors are in most cases significantly better. Finally, if time\npermits, I will briefly explain, how these methods are being made available\nin a recent software package.
Computational Models as Drivers of Cardiac Research
Friday, 30.6.17, 12:00-13:00, Raum 404, Eckerstr. 1
What are models? What is their role in biological research? Can they be relied on? Can computer simulations replace experiments on living animals? When will we have an all-inclusive model of [...insert system of choice...]? Questions like this are frequently raised in professional and lay discussions. This lecture will attempt to address some aspects, using illustrations 'from the heart'.\n
Forensic DNA Phenotyping
Friday, 14.7.17, 12:00-13:00, Raum 404, Eckerstr. 1
Forensic DNA Phenotyping (FDP) is a relatively new development in the field of forensic genetics. It aims at predicting selected so-called externally visible characteristics (EVCs) of a trace donor from their DNA as left behind at the crime scene. The best results for FDP were achieved for eye colour where the IrisPlex DNA test system was developed (Walsh et al. 2011), which includes six SNPs in six different genes, and was found to obtain relatively high levels of prediction. The second best predictable EVC after eye colour is hair colour.\n In the first part of this talk, results of a study investigating the prediction of the pigmentation phenotypes eye, hair and skin colour in a Northern German population will be presented (Caliebe et al. 2016). With this study, we aimed at answering the following research questions: (1) do existing models allow good prediction of high-quality phenotypes in a genetically similar albeit more homogeneous population? (2) Would a model specifically set up for the more homogeneous population perform notably better than existing models? (3) Can the number of markers included in existing models be reduced without compromising their predictive capability in the more homogenous population?\nIn the second part of the talk we differentiate FDP from trace donor identification problems. In the latter, it has become widely accepted in forensics that, owing to a lack of sensible priors, the evidential value of matching DNA profiles is most sensibly communicated in the form of a likelihood ratio (LR). This agreement is not in contradiction to the fact that the posterior odds (PO) would be the preferred basis for returning a verdict. A completely different situation holds for FDP. The statistical models underlying FDP typically yield PO for an individual possessing a certain EVC. This apparent discrepancy has led to confusion as to when LR or PO is the appropriate outcome of forensic DNA analysis to be communicated. We thus set out to clarify the distinction between LR and PO in the context of forensic DNA profiling and FDP from a statistical point of view (Caliebe et al. 2017). \nCaliebe, A., M. Harder, R. Schuett, M. Krawczak, A. Nebel and N. von Wurmb-Schwark, 2016. The more the merrier? How a few SNPs predict pigmentation phenotypes in the Northern German population. Eur. J. Hum. Genet. 24: 739-747.\nCaliebe, A., S. Walsh, F. Liu, M. Kayser and M. Krawczak, 2017. Likelihood ratio and posterior odds in forensic genetics: Two sides of the same coin. Forensic Sci Int Genet 28: 203-210.\nWalsh, S., F. Liu, K. N. Ballantyne, M. van Oven, O. Lao and M. Kayser, 2011. IrisPlex: a sensitive DNA tool for accurate prediction of blue and brown eye colour in the absence of ancestry information. Forensic Sci Int Genet 5: 170-180.
Time-delay reservoir computers: nonlinear stability of functional differential systems and optimal nonlinear information processing capacity. Applications to stochastic nonlinear time series forecasting.
Friday, 14.7.17, 13:00-14:00, Raum 404, Eckerstr. 1
Reservoir computing is a recently introduced brain-inspired\nmachine learning paradigm capable of excellent performances in the processing of empirical data. We focus on a particular kind of time-delay based reservoir computers that have been physically implemented using optical and electronic systems and have shown unprecedented data processing rates. Reservoir computing is well-known for the ease of the associated training scheme but also for the problematic sensitivity of its performance to architecture parameters.\nThis talk addresses the reservoir design problem, which remains the biggest challenge in the applicability of this information processing scheme. More specifically, we use the information available regarding the optimal reservoir working regimes to construct a functional link between the reservoir parameters and its performance. This function is\nused to explore various properties of the device and to choose the optimal reservoir architecture, thus replacing the tedious and time consuming parameter scanning used so far in the literature.\n
Linking differential equation modeling to population statistics in metabolomics - insights from general population data for statistical analyses and study design of metabolome wide association analyses
Friday, 28.7.17, 12:00-13:00, Raum 404, Eckerstr. 1
Metabolomics has developed fast in the last decade, presenting promising results, both in terms of improving the understanding of physiological and pathophysiological processes and in terms of predictive and diagnostic models aiming at personalized medicine. However, statistical modeling has been relying almost exclusively on linear models like partial least squares or ordinary least squares regression analyses, despite them being physiologically implausible in a wide range of scenarios. Here, by using data from the large general population cohort Study of Health in Pomerania (SHIP, n=4068), we show that differential equation modeling can be utilized to inform and refine statistical regression models on the population level, describing successfully important features of one-time metabolome measures. As shown, the information derived from differential equation modeling can then be used to modify and optimize several steps of metabolome wide association analyses from data sampling (e.g. which factors should be sampled or controlled) and data preparation (e.g normalization of urine data) to model specification (e.g. correct adjustment for important confounder) and data interpretation (e.g. metabolite-phenotype interactions). In conclusion, we demonstrate that metabolome data contain more information than usually extracted and that theoretical modelling via differential equations can be helpful in understanding attributes of one-time metabolomic measurements, paving the way for better applications of metabolomics in the clinical sciences.\n