Related papers: The Gerrymandering Jumble: Map Projections Permute…
We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. We show that these random projections retain the functionality of their underlying adjacency matrices while having extra…
A plethora of dimensionality reduction techniques have emerged over the past decades, leaving researchers and analysts with a wide variety of choices for reducing their data, all the more so given some techniques come with additional…
Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…
The evaluation of probabilistic forecasts plays a central role both in the interpretation and in the use of forecast systems and their development. Probabilistic scores (scoring rules) provide statistical measures to assess the quality of…
We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or {\L}ojasiewicz properties. These geometrical notions are usually local by nature, and may…
Using the recently introduced declination function, we estimate the net number of seats won in the US House of Representatives due to asymmetries in vote distributions. Such asymmetries can arise from combinations of partisan gerrymandering…
We propose in this paper a general framework for deriving loss functions for structured prediction. In our framework, the user chooses a convex set including the output space and provides an oracle for projecting onto that set. Given that…
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…
Here is an English summary of the abstract: This research investigates a geometric dynamical mechanism within a specific class of domains that contain a fixed convex core. By using a radial structure that links the boundaries of the core…
Gerrymandering is the practice of drawing biased electoral maps that manipulate the voter population to gain an advantage. The most recent time gerrymandering became an issue was 2019 when the U.S. Federal Supreme Court decided that the…
Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which…
Projections (or dimensionality reduction) methods $P$ aim to map high-dimensional data to typically 2D scatterplots for visual exploration. Inverse projection methods $P^{-1}$ aim to map this 2D space to the data space to support tasks such…
The ROC curve is widely used to assess the quality of prediction/classification/ranking algorithms, and its properties have been extensively studied. The precision-recall (PR) curve has become the de facto replacement for the ROC curve in…
Scoring rules are an important tool for evaluating the performance of probabilistic forecasting schemes. In the binary case, scoring rules (which are strictly proper) allow for a decomposition into terms related to the resolution and to the…
The parameter-free reconstruction of the surface-mass density of clusters of galaxies is one of the principal applications of weak gravitational lensing. From the observable ellipticities of images of background galaxies, the tidal…
Driven by an increasing prevalence of trackers, ever more IoT sensors, and the declining cost of computing power, geospatial information has come to play a pivotal role in contemporary predictive models. While enhancing prognostic…
We form a "map of tournaments" by adapting the map framework from the world of elections. By a tournament we mean a complete directed graph where the nodes are the players and an edge points from a winner of a game to the loser (with no…
Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…
The aim of this note is to give a quick algebraic proof of (the combinatorial part of) the classification theorem for compact real surfaces, whose classical proofs (as in the Massey book and in the Conway ZIP proof) are based on surgery…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…