arXiv research

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

Study identifies high-density anomalies in normal data regions.

Local Clustering improves semi-supervised learning models.

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

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…

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…

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…

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

A new method detects small holes in noisy data.

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.

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…

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…

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 …

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

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…

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…

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-…

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.

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…

New DL approach reveals feature construction in dense samples.

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…

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…

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)…

Random groups with high density have Property (T).

In many applications that involve processing high-dimensional data, it is important to identify a small set of entities that account for a significant fraction of detections. Rather than formalize this as a clustering problem, in which all detections must be grouped into hard or soft categories, we formalize it as an i…

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…

A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found using mean-shift algorithms. We describe the theory and practice behind clustering…

Traditional methods outperform LLMs in forecasting corporate credit ratings.

In the face of growing needs for water and energy, a fundamental understanding of the environmental impacts of human activities becomes critical for managing water and energy resources, remedying water pollution, and making regulatory policy wisely. Among activities that impact the environment, oil and gas production, …

Semisupervised methods are techniques for using labeled data $(X_1,Y_1),\ldots,(X_n,Y_n)$ together with unlabeled data $X_{n+1},\ldots,X_N$ to make predictions. These methods invoke some assumptions that link the marginal distribution $P_X$ of X to the regression function f(x). For example, it is common to assume that …

The problem of finding groups in data (cluster analysis) has been extensively studied by researchers from the fields of Statistics and Computer Science, among others. However, despite its popularity it is widely recognized that the investigation of some theoretical aspects of clustering has been relatively sparse. One …

Our recent study of a nation-wide production network uncovered a community structure, namely how firms are connected by supplier-customer links into tightly-knit groups with high density in intra-groups and with lower connectivity in inter-groups. Here we propose a method to visualize the community structure by a graph…

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…

Context. Generative models open up the possibility to interrogate scientific data in a more data-driven way. Aims: We propose a method that uses generative models to explore hypotheses in astrophysics and other areas. We use a neural network to show how we can independently manipulate physical attributes by encoding ob…

Research shows bias in machine learning can be due to algorithmic flaws, not just data.

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…

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…

Financial LLMs need explicit bias consideration to avoid invalid results.

A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density estimator. This paper addresses the basic question of quantifying our uncertainty by ass…

We study the phenomenon of bias amplification in classifiers, wherein a machine learning model learns to predict classes with a greater disparity than the underlying ground truth. We demonstrate that bias amplification can arise via an inductive bias in gradient descent methods that results in the overestimation of the…

It has been noticed that some external CVIs exhibit a preferential bias towards a larger or smaller number of clusters which is monotonic (directly or inversely) in the number of clusters in candidate partitions. This type of bias is caused by the functional form of the CVI model. For example, the popular Rand index (R…

We define and compute plausible counterfactual explanations using density constraints.