Related papers: Statistical Modeling of Univariate Multimodal Data

Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised…

Multi-view learning often faces challenges in effectively leveraging images captured from different angles and locations. This challenge is particularly pronounced when addressing inconsistencies and uncertainties between views. In this…

Density-based clustering methods often surpass centroid-based counterparts, when addressing data with noise or arbitrary data distributions common in real-world problems. In this study, we reveal a key property intrinsic to density-based…

The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…

Clustering aims to group similar objects together while separating dissimilar ones apart. Thereafter, structures hidden in data can be identified to help understand data in an unsupervised manner. Traditional clustering methods such as…

The maximum mean discrepancy (MMD) is a kernel-based nonparametric statistic for two-sample testing, whose inferential accuracy depends critically on variance characterization. Existing work provides various finite-sample estimators of the…

A graphical tool for investigating unimodality of hyperspherical data is proposed. It is based on the notion of statistical data depth function for directional data which extends the univariate concept of rank. Firstly a local version of…

Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…

Traditional multimodal learners find unified representations for tasks like visual question answering, but rely heavily on paired datasets. However, an overlooked yet potentially powerful question is: can one leverage auxiliary unpaired…

With the powerful reasoning capabilities of large language models (LLMs) and vision-language models (VLMs), many recent works have explored using them for decision-making. However, most of these approaches rely solely on language-based…

Spectral clustering is an effective methodology for unsupervised learning. Most traditional spectral clustering algorithms involve a separate two-step procedure and apply the transformed new representations for the final clustering results.…

Unsupervised classification called clustering is a process of organizing objects into groups whose members are similar in some way. Clustering of uncertain data objects is a challenge in spatial data bases. In this paper we use Probability…

Until recently obtaining data on populations of networks was typically rare. However, with the advancement of automatic monitoring devices and the growing social and scientific interest in networks, such data has become more widely…

Unimodal univariate distributions can be characterized as piecewise convex-concave cumulative distribution functions. In this note we transfer this shape constraint characterization to the quantile function. We show that this…

The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical…

This paper introduces the Univariate Gaussian Mixture Model Neural Network (uGMM-NN), a novel neural architecture that embeds probabilistic reasoning directly into the computational units of deep networks. Unlike traditional neurons, which…

We introduce PMODE (Partitioned Mixture Of Density Estimators), a general and modular framework for mixture modeling with both parametric and nonparametric components. PMODE builds mixtures by partitioning the data and fitting separate…

The development of multi-modal learning for Unmanned Aerial Vehicles (UAVs) typically relies on a large amount of pixel-aligned multi-modal image data. However, existing datasets face challenges such as limited modalities, high construction…

Shape constraints enable us to reflect prior knowledge in regression settings. A unimodality constraint, for example, can describe the frequent case of a first increasing and then decreasing intensity. Yet, data shapes often exhibit…