Related papers: Projection pursuit for discrete data
Training diffusion models requires large datasets. However, acquiring large volumes of high-quality data can be challenging, for example, collecting large numbers of high-resolution images and long videos. On the other hand, there are many…
This paper presents an algorithm for the preprocessing of observation data aimed at improving the robustness of orbit determination tools. Two objectives are fulfilled: obtain a refined solution to the initial orbit determination problem…
Computational photography involves sophisticated capture methods. A new trend is to capture projection of higher dimensional visual signals such as videos, multi-spectral data and lightfields on lower dimensional sensors. Carefully designed…
Discrete diffusion models are a class of generative models that produce samples from an approximated data distribution within a discrete state space. Often, there is a need to target specific regions of the data distribution. Current…
Users of a personalised recommendation system face a dilemma: recommendations can be improved by learning from data, but only if the other users are willing to share their private information. Good personalised predictions are vitally…
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…
This paper presents a novel mathematical framework for understanding pixel-driven approaches for the parallel beam Radon transform as well as for the fanbeam transform, showing that with the correct discretization strategy, convergence -…
Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional…
Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…
We propose a Deep RObust Goal-Oriented trajectory prediction Network (DROGON) for accurate vehicle trajectory prediction by considering behavioral intentions of vehicles in traffic scenes. Our main insight is that the behavior (i.e.,…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
We introduce a representation learning framework for spatial trajectories. We represent partial observations of trajectories as probability distributions in a learned latent space, which characterize the uncertainty about unobserved parts…
In the literature, two series of models have been proposed to address prediction problems including classification and regression. Simple models, such as generalized linear models, have ordinary performance but strong interpretability on a…
High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…
We establish a mixed norm estimate for the Radon transform in the plane when the set of directions has fractional dimension. This estimate is used to prove a result about an exceptional set of directions connected with projections of planar…
We present a method which allows to extract theoretical informations out of a limited set of experimental data and observables, forming up in general an under- constrained system. It has been applied to the field of nucleon structure, in…
The merit of projecting data onto linear subspaces is well known from, e.g., dimension reduction. One key aspect of subspace projections, the maximum preservation of variance (principal component analysis), has been thoroughly researched…
Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…
The big data trend has inspired feature-driven learning tasks, which cannot be handled by conventional machine learning models. Unstructured data produces very large binary matrices with millions of columns when converted to vector form.…
This paper presents a formal framework and proposes algorithms to extend forecast reconciliation to discrete-valued data to extend forecast reconciliation to discrete-valued data, including low counts. A novel method is introduced based on…