Program

Ghuru Ganeshan

Extracting High Quality Data Subsets Using Monte-Carlo Search

Often, big or imbalanced datasets are subject to undersampling in order to improve the overall accuracy of the underlying predictive model. In this paper, we study undersampling from the perspective of information content and propose and analyze a Monte-Carlo search methodology to obtain high quality, low redundancy data subsets from large datasets. Our strategy is to transform the data redundancy structure into a graph theoretic format and assign importance to each data point in terms of vertex degrees. We then extract low redundancy data points via iteration, allowing for random exploration in the intermediate steps. Our simulation results indicate that if the redundancy graph is sufficiently sparse, then there is a non-trivial exploration probability that maximizes the quality of the final dataset. We illustrate our methodologies using the zoo animal dataset available in Kaggle and also discuss theoretical questions for potential future research, regarding the properties of the optimal exploration probability.

Vincent Grande

Point-Level Topological Representation Learning on Point Clouds

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description of the global structure of the point cloud. However, common machine learning applications like classification require point-level information and features to be available. In this paper, we bridge this gap and propose a novel method to extract node-level topological features from complex point clouds using discrete variants of concepts from algebraic topology and differential geometry. We verify the effectiveness of these topological point features (TOPF) on both synthetic and real-world data and study their robustness under noise and heterogeneous sampling.

Wojciech Chachólski, Christina Kapatsori and Björn Wehlin

Random Complexes in the Metric Space Setting

We are interested in random complexes in arbitrary metric spaces. Our focus is on these complexes which have certain homotopical properties allowing for control of their homotopy-invariant features in a probabilistic setting. We will share some of our early progress and candidate definitions in this context. For example, we illustrate how these homotopical aspects imply measurability of associated random variables. This is joint work with Christina Kapatsori and Wojciech Chachólski.

Christian Hirsch and Martina Petráková

Large-Deviation Analysis for Canonical Gibbs Measures

In this poster, we present a large deviation theory developed for functionals of binomial Gibbs processes with fixed intensity in increasing windows. Our method relies on the traditional large deviation result for the Poisson point process noting that the binomial point process is obtained from the Poisson point process by conditioning on the point number. Our main methodological contribution is the development of coupling constructions that allow us to handle delicate and unlikely pathological events. The presented results cover a broad class of both the interaction function (possibly unbounded) and the functionals (given as a sum of possibly unbounded local score functions). The poster is based on a joint work with Christian Hirsch.