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Tag: density

  • Mass Distribution versus Density Distribution in the Context of Clustering

    Mass Distribution versus Density Distribution in the Context of Clustering arXiv:2601.10759v1 Announce Type: new Abstract: This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the introduction of statistics. We show that density distribution…

  • Constrained Density Estimation via Optimal Transport

    Constrained Density Estimation via Optimal Transport arXiv:2601.06830v1 Announce Type: new Abstract: A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of functions adopts or exceeds given values. The framework…

  • Deep learning estimation of the spectral density of functional time series on large domains

    Deep learning estimation of the spectral density of functional time series on large domains arXiv:2601.00284v1 Announce Type: cross Abstract: We derive an estimator of the spectral density of a functional time series that is the output of a multilayer perceptron neural network. The estimator is motivated by difficulties with the computation of existing spectral density…

  • Implicit geometric regularization in flow matching via density weighted Stein operators

    Implicit geometric regularization in flow matching via density weighted Stein operators arXiv:2512.23956v1 Announce Type: new Abstract: Flow Matching (FM) has emerged as a powerful paradigm for continuous normalizing flows, yet standard FM implicitly performs an unweighted $L^2$ regression over the entire ambient space. In high dimensions, this leads to a fundamental inefficiency: the vast majority…

  • Quasiprobabilistic Density Ratio Estimation with a Reverse Engineered Classification Loss Function

    Quasiprobabilistic Density Ratio Estimation with a Reverse Engineered Classification Loss Function arXiv:2512.19913v1 Announce Type: new Abstract: We consider a generalization of the classifier-based density-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. The problem with most loss functions used for this task is that they implicitly define a relationship between the…

  • Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination

    Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination arXiv:2512.09266v1 Announce Type: new Abstract: We examine the non-asymptotic properties of robust density ratio estimation (DRE) in contaminated settings. Weighted DRE is the most promising among existing methods, exhibiting doubly strong robustness from an asymptotic perspective. This study demonstrates that Weighted DRE achieves sparse…

  • Learning density ratios in causal inference using Bregman-Riesz regression

    Learning density ratios in causal inference using Bregman-Riesz regression arXiv:2510.16127v1 Announce Type: new Abstract: The ratio of two probability density functions is a fundamental quantity that appears in many areas of statistics and machine learning, including causal inference, reinforcement learning, covariate shift, outlier detection, independence testing, importance sampling, and diffusion modeling. Naively estimating the numerator…

  • CINDES: Classification induced neural density estimator and simulator

    CINDES: Classification induced neural density estimator and simulator arXiv:2510.00367v1 Announce Type: new Abstract: Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical successes, implementation can be challenging due to the need to ensure non-negativity and unit-mass constraints,…

  • Cracking the Density Code: Why MAF Flows Where KDE Stalls

    Cracking the Density Code: Why MAF Flows Where KDE Stalls Learn why autoregressive flows are the superior density estimation tool for high-dimensional data The post Cracking the Density Code: Why MAF Flows Where KDE Stalls appeared first on Towards Data Science. Zackary Nay Go to original source

  • Time-dependent density estimation using binary classifiers

    Time-dependent density estimation using binary classifiers arXiv:2506.15505v1 Announce Type: new Abstract: We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel time-dependent binary classifier trained using a contrastive estimation-based…

  • Applications of Density Estimation to Legal Theory

    Applications of Density Estimation to Legal Theory A brief analysis using density estimation to compare the two-verdict and three-verdict systems. The post Applications of Density Estimation to Legal Theory appeared first on Towards Data Science. Jimin Kang Go to original source

  • Non-Parametric Density Estimation: Theory and Applications

    Non-Parametric Density Estimation: Theory and Applications In this article, we’ll talk about what Density Estimation is and the role it plays in statistical analysis. We’ll analyze two popular density estimation methods, histograms and kernel density estimators, and analyze their theoretical properties as well as how they perform in practice. Finally, we’ll look at how density…

  • Kernel Density Machines

    Kernel Density Machines arXiv:2504.21419v1 Announce Type: new Abstract: We introduce kernel density machines (KDM), a novel density ratio estimator in a reproducing kernel Hilbert space setting. KDM applies to general probability measures on countably generated measurable spaces without restrictive assumptions on continuity, or the existence of a Lebesgue density. For computational efficiency, we incorporate a…

  • Estimating Unbounded Density Ratios: Applications in Error Control under Covariate Shift

    Estimating Unbounded Density Ratios: Applications in Error Control under Covariate Shift arXiv:2504.01031v1 Announce Type: new Abstract: The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often depend on stringent regularity conditions, mainly focusing…

  • Density estimation via mixture discrepancy and moments

    Density estimation via mixture discrepancy and moments arXiv:2504.01570v1 Announce Type: new Abstract: With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed [D. Li, K. Yang, W. Wong, Advances in Neural Information Processing Systems (2016) 1099-1107] to learn an adaptive piecewise constant approximation…

  • Hierarchical clustering with maximum density paths and mixture models

    Hierarchical clustering with maximum density paths and mixture models arXiv:2503.15582v1 Announce Type: new Abstract: Hierarchical clustering is an effective and interpretable technique for analyzing structure in data, offering a nuanced understanding by revealing insights at multiple scales and resolutions. It is particularly helpful in settings where the exact number of clusters is unknown, and provides…

  • Median of Forests for Robust Density Estimation

    Median of Forests for Robust Density Estimation arXiv:2501.15157v1 Announce Type: new Abstract: Robust density estimation refers to the consistent estimation of the density function even when the data is contaminated by outliers. We find that existing forest density estimation at a certain point is inherently resistant to the outliers outside the cells containing the point,…