A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new method for Bayesian optimization uses Voronoi tessellation candidates to reduce search time.
Quantized Variational Inference improves ELBO optimization with fast convergence.
Accurate taxi demand-supply forecasting is a challenging application of ITS (Intelligent Transportation Systems), due to the complex spatial and temporal patterns. We investigate the impact of different spatial partitioning techniques on the prediction performance of an LSTM (Long Short-Term Memory) network, in the con…
Bayesian model captures mean and variance of response variables.
Constructs an explicit cycle in arithmetic group cohomology.
A Riemannian symmetric space is a Riemannian manifold in which it is possible to reflect all geodesics through a point by an isometry of the space. On such spaces, we introduce the notion of a distributional lattice, generalizing the notion of lattice. Distributional lattices exist in any Riemannian symmetric space: th…
The paper proves actions of lattices in higher rank groups have cost one.
A new method learns quantization boundaries in continuous space using tessellation.
The Delaunay tessellation of a locally finite subset of hyperbolic space is constructed using convex hulls in Euclidean space of one higher dimension. For finite and lattice-invariant sets it is proven to be a polyhedral decomposition, and versions (necessarily modified from the Euclidean setting) of the empty circumsp…
New upper bound for Cheeger constant of hyperbolic surfaces.
New method uses geometric properties for better density estimation.
Develops a new non-adversarial framework for better generative models.
In this paper, we investigate the significance of choosing an appropriate tessellation strategy for a spatio-temporal taxi demand-supply modeling framework. Our study compares (i) the variable-sized polygon based Voronoi tessellation, and (ii) the fixed-sized grid based Geohash tessellation, using taxi demand-supply GP…
A key problem in location-based modeling and forecasting lies in identifying suitable spatial and temporal resolutions. In particular, judicious spatial partitioning can play a significant role in enhancing the performance of location-based forecasting models. In this work, we investigate two widely used tessellation s…
The article describes how decorations on hyperbolic surfaces lead to unique tessellations and decompositions.
In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to the Delaunay triangulation. Advantage is taken from this fact calculating the p…
The paper analyzes how companies' investments before crises affect their performance after crises.
rMCL improves on MCL by preserving diversity in predictions for regression problems.
s-RBFN integrates multiple hypotheses for efficient and diverse prediction.
New matching estimators correct bias in multivariate settings without smoothing parameters.
We propose Dirichlet Simplex Nest, a class of probabilistic models suitable for a variety of data types, and develop fast and provably accurate inference algorithms by accounting for the model's convex geometry and low dimensional simplicial structure. By exploiting the connection to Voronoi tessellation and properties…
FiberNet integrates geometry into machine learning for clearer classification.
In our physically inspired in-tree (IT) based clustering algorithm and the series after it, there is only one free parameter involved in computing the potential value of each point. In this work, based on the Delaunay Triangulation or its dual Voronoi tessellation, we propose a nonparametric process to compute potentia…
Generative adversarial networks (GANs) are the state of the art in generative modeling. Unfortunately, most GAN methods are susceptible to mode collapse, meaning that they tend to capture only a subset of the modes of the true distribution. A possible way of dealing with this problem is to use an ensemble of GANs, wher…
We introduce \texttt{pycobra}, a Python library devoted to ensemble learning (regression and classification) and visualisation. Its main assets are the implementation of several ensemble learning algorithms, a flexible and generic interface to compare and blend any existing machine learning algorithm available in Pytho…
Estimates BV functions from noisy data using Voronoi diagrams.
Neural message passing on molecular graphs is one of the most promising methods for predicting formation energy and other properties of molecules and materials. In this work we extend the neural message passing model with an edge update network which allows the information exchanged between atoms to depend on the hidde…
This paper analyzes the connection between innovation activities of companies -- implemented before crisis -- and their performance -- measured at time of crisis. The companies listed in the STAR Market Segment of the Italian Stock Exchange are analyzed. Innovation is measured through the level of investments in total …
New algorithm optimizes tessellated kernels for larger datasets and improved performance.
In this thesis we study sets of points in the plane and their Voronoi diagrams, in particular when the points coincide. We bring together two ways of studying point sets that have received a lot of attention in recent years: Voronoi diagrams and compactifications of configuration spaces. We study moving and colliding p…
Study higher rank inner products and their tilings to describe tori degenerations.
Tessellations cover planes without gaps or overlaps.
A hex sphere is a singular Euclidean sphere with four cones points whose cone angles are (integer) multiples of 2*pi/3 but less than 2*pi. Given a hex sphere M, we consider its Voronoi decomposition centered at the two cone points with greatest cone angles. In this paper we use elementary Euclidean geometry to describe…
Up to isomorphism there are six fixed-point free crystallographic groups in Euclidean Space generated by twists (screw motions). In each case, an orientable 3-manifold is obtained as the quotient of E3 by such a group. The cubic tessellation of E3 induces tessellations on each such manifold. These tessellations of the …
Proof of existence and uniqueness of weighted Voronoi-Delaunay on polyhedral surfaces.
By regular tessellation, we mean any hyperbolic 3-manifold tessellated by ideal Platonic solids such that the symmetry group acts transitively on oriented flags. A regular tessellation has an invariant we call the cusp modulus. For small cusp modulus, we classify all regular tessellations. For large cusp modulus, we pr…
New method calculates cut locus on surfaces without boundary.
This paper is the second part of a two-part study of an elementary functorial construction of tesselated surfaces from finite groups. This elementary construction was discussed in the first part and generally results in a large collection of tesselated surfaces per group, for example when the construction is applied to…
We present an explicit algorithm for tessellating the algebraic surfaces (real 4-manifolds) F(n) embedded in CP3 defined by the equation z0^n + z1^n + z2^n + z3^n = 0 in the standard homogeneous coordinates [z0, z1, z2, z3], where n is any positive integer. Note that F(4) in particular is a K3 surface. Our tessellation…
Deviance Voronoi residuals improve earthquake insurance risk assessment.
This paper is the first part in a 2 part study of an elementary functorial construction from the category of finite non-abelian groups to a category of singular compact, oriented 2-manifolds. After a desingularization process this construction results in a collection of compact, connected, oriented tesselated smooth su…
The paper generalizes Farey tessellation to 3D hyperbolic space.
Hexagonal tilings minimize perimeter with unequal volumes.
New random forest variants achieve optimal performance in high dimensions.
Proposes a new adversarial model to avoid accuracy vs. adversarial accuracy tradeoff.
Algorithm finds adversarial examples for k-NN classifiers using Voronoi diagrams.
Consider a finite connected graph possibly with multiple edges and loops. In discrete geometric analysis, Kotani and Sunada constructed the crystal associated to the graph as a standard realization of the maximal abelian covering of the graph. As an application of what the author showed in an earlier paper with Seshadr…
For every half-translation surface with marked points , we construct an associated tessellation of the Poincaré upper half plane whose tiles have finitely many sides and area at most . The tessellation is equivariant with respect to the action of , and invariant w…