arXiv research

Conformal Prediction Regions match Imprecise Highest Density Regions under consonance.

The study proves optimal isoperimetric regions in manifolds with density.

Study shows how near crushing singularities, Kasner-like regions can exist.

Contrast uses normalizing flows to create precise prediction regions for multi-dimensional outputs.

We completely characterize isoperimetric regions in R^n with density e^h, where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isoperimetric regions of any given volume, proving the Log-Convex Density Conjecture due to Kenneth Brakke.

This work introduces a novel nonparametric density index defined on graphs, the Sum-over-Forests (SoF) density index. It is based on a clear and intuitive idea: high-density regions in a graph are characterized by the fact that they contain a large amount of low-cost trees with high outdegrees while low-density regions…

We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive stability conditions, which lead to the conjecture that for a radial log-convex density…

Bayesian model averaging under predictor redundancy

Study on bit threads and their locking properties in holographic spacetimes.

SDG uses optimal control to improve classifier guidance in low-density regions.

A new method for time-series data provides guaranteed coverage and adapts to non-exchangeable data.

Density-based clustering is the task of discovering high-density regions of entities (clusters) that are separated from each other by contiguous regions of low-density. DBSCAN is, arguably, the most popular density-based clustering algorithm. However, its cluster recovery capabilities depend on the combination of the t…

A new method improves flow matching by dynamically weighting density estimates.

SLS optimizes minimum-volume regions for conditional quantiles, bypassing density estimation.

The two most extended density-based approaches to clustering are surely mixture model clustering and modal clustering. In the mixture model approach, the density is represented as a mixture and clusters are associated to the different mixture components. In modal clustering, clusters are understood as regions of high d…

A new method improves quantile regression for high-dimensional data.

A new method detects small holes in noisy data.

We show that the unique isoperimetric hypersurfaces in $\mathbb{R}^n$ with density $r^p$ for $n \ge 3$ and $p>0$ are spheres that pass through the origin.

Neural network accuracy improves with denser training samples.

We leverage recent breakthroughs in neural density estimation to propose a new unsupervised anomaly detection technique (ANODE). By estimating the probability density of the data in a signal region and in sidebands, and interpolating the latter into the signal region, a likelihood ratio of data vs. background can be co…

New method calibrates reference distributions for bounded support.

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is …

Study identifies high-density anomalies in normal data regions.

In the knowledge that the ex-post performance of Markowitz efficient portfolios is inferior to that implied ex-ante, we make two contributions to the portfolio selection literature. Firstly, we propose a methodology to identify the region of risk-expected return space where ex-post performance matches ex-ante estimates…

New method improves Gaussian Mixture Model fitting speed.

The paper introduces a new method to find meaningful data subsets in multivariate probability density functions.

As one type of efficient unsupervised learning methods, clustering algorithms have been widely used in data mining and knowledge discovery with noticeable advantages. However, clustering algorithms based on density peak have limited clustering effect on data with varying density distribution (VDD), equilibrium distribu…

Density mode clustering is a nonparametric clustering method. The clusters are the basins of attraction of the modes of a density estimator. We study the risk of mode-based clustering. We show that the clustering risk over the cluster cores --- the regions where the density is high --- is very small even in high dimens…

Method uses normalizing flows to efficiently sample from complex target densities.

Optimizes noisy IS with better proposal densities.

We present a new algorithm for stochastic variational inference that targets at models with non-differentiable densities. One of the key challenges in stochastic variational inference is to come up with a low-variance estimator of the gradient of a variational objective. We tackle the challenge by generalizing the repa…

Study on packing links with geometric constraints.

The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our understanding of the formation and evolution of galaxies. The density range of clusters, wa…

Method detects new physics signals without prior knowledge.

The study calculates Weyl entropy in spacetime regions and shows its monotonic behavior.

Improves generation of minority samples using diffusion models.

Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We propose a novel hyperplane classifier for clustering and semi-supervised classificati…

MD-split+ creates locally valid prediction regions for complex data.

VSPS creates flexible prediction regions for multi-target regression with guaranteed coverage.

OneFlow detects anomalies by finding a minimal volume region, outperforming other methods.

We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor $Y$. Assuming the data in question is invariant under an $S^1$-action (locally around $Y$) we prove that this density function has a distri…

A fast Modal EM algorithm for Gaussian mixtures.

While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel density estimator (KDE). As with other estimators, a robust version of the KDE is u…

New method uses dynamic sampling to improve PINNs efficiency.

Neural samplers such as variational autoencoders (VAEs) or generative adversarial networks (GANs) approximate distributions by transforming samples from a simple random source---the latent space---to samples from a more complex distribution represented by a dataset. While the manifold hypothesis implies that the densit…

We define and compute plausible counterfactual explanations using density constraints.

The problem of inhomogeneous cluster densities has been a long-standing issue for distance-based and density-based algorithms in clustering and anomaly detection. These algorithms implicitly assume that all clusters have approximately the same density. As a result, they often exhibit a bias towards dense clusters in th…

Deep metric learning algorithms have been utilized to learn discriminative and generalizable models which are effective for classifying unseen classes. In this paper, a novel noise tolerant deep metric learning algorithm is proposed. The proposed method, termed as Density Aware Metric Learning, enforces the model to le…