arXiv research

For a density $f$ on ${\mathbb R}^d$, a {\it high-density cluster} is any connected component of $\{x: f(x) \geq λ\}$, for some $λ> 0$. The set of all high-density clusters forms a hierarchy called the {\it cluster tree} of $f$. We present two procedures for estimating the cluster tree given samples from $f$. The first…

Study identifies high-density anomalies in normal data regions.

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

We provide initial seedings to the Quick Shift clustering algorithm, which approximate the locally high-density regions of the data. Such seedings act as more stable and expressive cluster-cores than the singleton modes found by Quick Shift. We establish statistical consistency guarantees for this modification. We then…

Paper proposes MMC to avoid high-density bias in clustering.

New DL approach reveals feature construction in dense samples.

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

L-Cool improves image and language translation by cooling low-density samples.

In implicit models, one often interpolates between sampled points in latent space. As we show in this paper, care needs to be taken to match-up the distributional assumptions on code vectors with the geometry of the interpolating paths. Otherwise, typical assumptions about the quality and semantics of in-between points…

In this paper, we study how the mean shift algorithm can be used to denoise a dataset. We introduce a new framework to analyze the mean shift algorithm as a denoising approach by viewing the algorithm as an operator on a distribution function. We investigate how the mean shift algorithm changes the distribution and sho…

Improves GAN sample quality by refining the training dataset.

Air traffic control is a real-time safety-critical decision making process in highly dynamic and stochastic environments. In today's aviation practice, a human air traffic controller monitors and directs many aircraft flying through its designated airspace sector. With the fast growing air traffic complexity in traditi…

This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data. These tools can be used to detect outliers and clusters. Both our prediction bands and clustering trees provide prediction sets for the underlying stochastic process with a guaranteed fi…

Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be inaccurate and/or very slow. In this work we introduce deep network architectures tra…

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…

A new graph-based sampling method improves classification of imbalanced COVID-19 datasets.

Adaptive stopping in MCMC using classifier-based dynamics

New findings suggest deep generative models can misclassify outliers, requiring new evaluation methods.

The contractive auto-encoder learns a representation of the input data that captures the local manifold structure around each data point, through the leading singular vectors of the Jacobian of the transformation from input to representation. The corresponding singular values specify how much local variation is plausib…

A new method detects small holes in noisy data.

A new method samples from multi-modal distributions without hyperparameter tuning.

In this article we use the mean curvature flow with surgery to derive regularity estimates for the level set flow going past Brakke regularity in certain special conditions allowing for 2-convex regions of high density. We also show a stability result for the plane under the level set flow.

Adversarial attacks on deep learning models have compromised their performance considerably. As remedies, a lot of defense methods were proposed, which however, have been circumvented by newer attacking strategies. In the midst of this ensuing arms race, the problem of robustness against adversarial attacks still remai…

Improves generation of minority samples using diffusion models.

Modern deep neural networks are well known to be brittle in the face of unknown data instances and recognition of the latter remains a challenge. Although it is inevitable for continual-learning systems to encounter such unseen concepts, the corresponding literature appears to nonetheless focus primarily on alleviating…

Flow-based generative models are a family of exact log-likelihood models with tractable sampling and latent-variable inference, hence conceptually attractive for modeling complex distributions. However, flow-based models are limited by density estimation performance issues as compared to state-of-the-art autoregressive…

Super-resolution fluorescence microscopy, with a resolution beyond the diffraction limit of light, has become an indispensable tool to directly visualize biological structures in living cells at a nanometer-scale resolution. Despite advances in high-density super-resolution fluorescent techniques, existing methods stil…

We introduce a novel Entropy-driven Monte Carlo (EdMC) strategy to efficiently sample solutions of random Constraint Satisfaction Problems (CSPs). First, we extend a recent result that, using a large-deviation analysis, shows that the geometry of the space of solutions of the Binary Perceptron Learning Problem (a proto…

RVGP learns vector fields over unknown manifolds, preserving singularities.

With the improvement of medical data capturing, vast amount of continuous patient monitoring data, e.g., electrocardiogram (ECG), real-time vital signs and medications, become available for clinical decision support at intensive care units (ICUs). However, it becomes increasingly challenging to model such data, due to …

In this paper, we propose a new fuzzy clustering algorithm based on the mode-seeking framework. Given a dataset in $\mathbb{R}^d$, we define regions of high density that we call cluster cores. We then consider a random walk on a neighborhood graph built on top of our data points which is designed to be attracted by hig…

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…

CoCP optimizes prediction intervals by jointly learning center and radius, improving efficiency and coverage.

Understanding how spatial configurations of economic activity emerge is important when formulating spatial planning and economic policy. A simple model was proposed by Simon, who assumed that firms grow at a rate proportional to their size, and that new divisions of firms with certain probabilities relocate to other fi…

The Machine Recognition of Crystallization Outcomes (MARCO) initiative has assembled roughly half a million annotated images of macromolecular crystallization experiments from various sources and setups. Here, state-of-the-art machine learning algorithms are trained and tested on different parts of this data set. We fi…

CPS solves inverse problems using forward passes and constrained particle seeking.

Single-molecule localization fluorescence microscopy constructs super-resolution images by sequential imaging and computational localization of sparsely activated fluorophores. Accurate and efficient fluorophore localization algorithms are key to the success of this computational microscopy method. We present a novel l…

Machine learning helps create accurate models of neutron star postmerger signals.

We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or $\textit{modal-sets}$, of any bounded shape or dimension, including usual point-modes. In practice, modal-…

Improved VAEs by training a contrastive prior to match posterior.

We present an algorithm to generate synthetic datasets of tunable difficulty on classification of Morse code symbols for supervised machine learning problems, in particular, neural networks. The datasets are spatially one-dimensional and have a small number of input features, leading to high density of input informatio…

Study finds a linear lower bound on conformal dimension for random hyperbolic groups.

We present a method for finding high density, low-dimensional structures in noisy point clouds. These structures are sets with zero Lebesgue measure with respect to the $D$-dimensional ambient space and belong to a $d<D$ dimensional space. We call them "singular features." Hunting for singular features corresponds to f…

A new method for estimating density ratios in high dimensions.

GBOC detects anomalies in time series data using granular-ball vectors.

High density clusters can be characterized by the connected components of a level set $L(λ) = \{x:\ p(x)>λ\}$ of the underlying probability density function $p$ generating the data, at some appropriate level $λ\geq 0$. The complete hierarchical clustering can be characterized by a cluster tree ${\cal T}= \bigcup_λ L(λ)…

A general approach for anomaly detection or novelty detection consists in estimating high density regions or Minimum Volume (MV) sets. The One-Class Support Vector Machine (OCSVM) is a state-of-the-art algorithm for estimating such regions from high dimensional data. Yet it suffers from practical limitations. When appl…

Random groups with high density have Property (T).