Related papers: Polytopes and Machine Learning

We describe algorithms which address two classical problems in lattice geometry: the lattice covering and the simultaneous lattice packing-covering problem. Theoretically our algorithms solve the two problems in any fixed dimension d in the…

We study the typical learning properties of the recently proposed Support Vectors Machines. The generalization error on linearly separable tasks, the capacity, the typical number of Support Vectors, the margin, and the robustness or noise…

Recently, the use of machine learning in meteorology has increased greatly. While many machine learning methods are not new, university classes on machine learning are largely unavailable to meteorology students and are not required to…

The last decade has seen an explosive growth of interest in exploiting developments in machine learning to accelerate lattice QCD calculations. On the sampling side, generative models are a promising approach to mitigating critical slowing…

Ladder polymers, known for their rigid, ladder-like structures, exhibit exceptional thermal stability and mechanical strength, positioning them as candidates for advanced applications. However, accurately determining their structure from…

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…

Estimating the number of vertices of a two dimensional projection, called a shadow, of a polytope is a fundamental tool for understanding the performance of the shadow simplex method for linear programming among other applications. We prove…

The main purpose of this paper is to report on the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes. Using the polymake system we explore various algorithms and…

We make a connection between classical polytopes called zonotopes and Support Vector Machine (SVM) classifiers. We combine this connection with the ellipsoid method to give some new theoretical results on training SVMs. We also describe…

For a d-dimensional convex lattice polytope P, a formula for the boundary volume is derived in terms of the number of boundary lattice points on the first $\floor{d/2}$ dilations of P. As an application we give a necessary and sufficient…

We propose a new learning-based approach for 3D particle field imaging using holography. Our approach uses a U-net architecture incorporating residual connections, Swish activation, hologram preprocessing, and transfer learning to cope with…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…

This thesis reviews numerical optimization methods with machine learning problems in mind. Since machine learning models are highly parametrized, we focus on methods suited for high dimensional optimization. We build intuition on quadratic…

We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…

Over the past decade the use of machine learning in meteorology has grown rapidly. Specifically neural networks and deep learning have been used at an unprecedented rate. In order to fill the dearth of resources covering neural networks…

We introduce an efficient method for learning linear models from uncertain data, where uncertainty is represented as a set of possible variations in the data, leading to predictive multiplicity. Our approach leverages abstract…

Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…

Many machine learning problems and methods are combinations of three components: data, hypothesis space and loss function. Different machine learning methods are obtained as combinations of different choices for the representation of data,…

3D geometry is a very informative cue when interacting with and navigating an environment. This writing proposes a new approach to 3D reconstruction and scene understanding, which implicitly learns 3D geometry from depth maps pairing a deep…