# Seminars in Statistics

• Date: –12:00
• Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 4004
• Organiser: Matematiska institutionen
• Contact person: Erik Ekström

9.15 Benny Avelin: Generalisation estimates of deep neural networks

Abstract: Neural networks is a specific type of regression functions arising in statistical learning, that has gained widespread attention in real world applications, for instance image analysis and control problems. Little is however known about this class of regression functions, and classical VC theory fails to explain why they still generalize in the over-parametrized regime. In this talk we will cover known generalization estimates and how we attempt to improve them by considering the deep limit of neural networks, as well as some recent results in this direction.

10.15 Hiba Nassa: Empirically driven orthonormal bases for functional data analysis

Abstract: There is a strong relation between high-dimensional data and functional data. One can convert the densely observed high-dimensional data to functional data by defining a set of functional bases, then set up the coefficients to define the functional data as a linear combination of these bases. Typically, the choice of the bases is not data-driven with a notable exception to the number of dimensions, that often can be derived by cross-validations. As a consequence, several standard bases such as Fourier and related bases, wavelets, splines etc. are typically used to transform observed functional data. Through such a prior and rather arbitrary decision on the basis selection the problem is transformed to a finite-dimensional space of basis coefficients and formally is losing its infinite dimensional character.

We propose a strictly data-driven method of basis selection. Since the method is algorithmic and searches the data to find an effective representation of the basis by minimizing overall mean square error across functional samples, the functional basis is strictly tied to the functional character of the data and loses arbitrariness of common approaches. The method itself uses B-splines and O-splines in the machine learning style of functional data mining to find efficiently placed knots. Due to machine learning character of data processing, the method has the potential to further numerically improve and extend beyond the considered scope.

11.15 Liam Solus: Discrete Geometry in Model Discovery

Abstract: In the today's world, where data is an abundant resource, there is a strong interest in data-driven algorithms for model discovery that are both efficient and reliable. Of particular interest are such algorithms for learning probabilistic, or even causal, DAG models. Historically, the combinatorics of graphs has played a central role in the development of DAG model learning algorithms. However, ideas from contemporary geometric and algebraic combinatorics were previously uninvolved. In this talk, we will discuss a new method for DAG model discovery. This method arises as a simplex-type algorithm over convex polytopes known as generalized permutohedra, which are central to the field of algebraic and geometric combinatorics.  We will see that, when compared with the state-of-the-art, these methods perform competitively, are provably more reliable, and even shed some restricting parametric assumptions.