Two neural samplers improve high-quality sample generation from un-normalized densities.
problem Generating high-quality samples from un-normalized probability densities.
method Developed two neural samplers using deep neural networks to transform a reference distribution to a target distribution. Training schemes minimize Stein discrepancy variations.
result The proposed samplers generate samples instantaneously and perform better than traditional methods.
New method uses hypergraphs to improve semi-supervised learning accuracy.
problem Lack of pairwise relationships between samples in network-based learning.
method Un-normalized hypergraph p-Laplacian semi-supervised learning.
result Significantly improved accuracy compared to existing methods.
In this paper, we study the class of Finsler metrics, namely (α, β)- metrics, which satisfies the un-normal or normal Ricci flow equation.
BlackJAX simplifies Bayesian inference with modular, fast implementations.
problem Efficient and modular Bayesian inference methods for complex models.
method Functional approach to implementing sampling and variational inference algorithms in JAX.
result Ease of use, speed, and modularity in implementing Bayesian inference.
New method samples from multi-modal distributions on Riemannian manifolds without training.
problem Sampling from multi-modal distributions on Riemannian manifolds is challenging.
method Simulation of a non-equilibrium deterministic dynamics to transport noise toward target distributions.
result Method is entirely training-free and effective on various multi-modal problems.
This paper analyzes how normalization layers improve neural network training.
problem Improving generalization performance and training speed of neural networks.
method Global convergence analysis of two-layer neural networks with ReLU activations and Weight Normalization.
result Introduction of normalization layers changes the optimization landscape, enabling faster convergence.
The paper examines Finsler metrics under Ricci flow and finds they are Einstein.
problem Understanding Finsler metrics under Ricci flow.
method Investigated C3-like Finsler metrics and proved they are Einstein.
result C3-like Finsler metrics are Einstein under Ricci flow.
Protein function prediction is the important problem in modern biology. In this paper, the un-normalized, symmetric normalized, and random walk graph Laplacian based semi-supervised learning methods will be applied to the integrated network combined from multiple networks to predict the functions of all yeast proteins …
The paper proves spectral convergence rates for graph Laplacian to manifold Laplace-Beltrami operator.
problem Spectral convergence of graph Laplacian to manifold Laplace-Beltrami operator.
method Analysis of Dirichlet form convergence and construction of approximate eigenfunctions via manifold heat kernel.
result Proves spectral convergence rates for Gaussian kernelized graph Laplacian.
Most network-based protein (or gene) function prediction methods are based on the assumption that the labels of two adjacent proteins in the network are likely to be the same. However, assuming the pairwise relationship between proteins or genes is not complete, the information a group of genes that show very similar p…
New method for initializing networks robustly, improving performance across various settings.
problem Insufficient initialization strategies for weight-normalized networks and ResNets.
method Proposes a novel initialization strategy based on mean field approximation.
result Improves generalization performance and robustness to hyper-parameters.
Proposes a new method for probabilistic regression in computer vision.
problem Lack of natural probabilistic meaning in confidence-based regression.
method Energy-based model of conditional target density using deep neural network.
result 2.2% AP improvement over Faster-RCNN for object detection on COCO dataset.
We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution equations. Several novelties appear in the context of scale factor evolution, fix…
Detects illegal stock market trading behaviors using graph ranking methods.
problem Detecting irregular trade behaviors in the stock market.
method Three graph Laplacian based semi-supervised ranking methods.
result Un-normalized and symmetric normalized graph Laplacian based methods outperform the random walk Laplacian method.
New method improves sample diversity and efficiency from complex distributions.
problem Sampling from intractable un-normalized distributions with high auto-correlation.
method Stein self-repulsive dynamics using a repulsive force to push samples away from past trajectories.
result Significantly decreases auto-correlation and increases effective sample size.
We present the first provably sublinear time algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Our proposal is also the first hashing algorithm for searching with (un-normalized) inner product as the underlying similarity measure. Finding hashing schemes for MIPS was considered hard. We formally sho…
Extended Siegel-Jacobi upper half-plane geometry studied with invariant metrics.
problem Characterizing the geometry of the extended Siegel-Jacobi upper half-plane.
method Parameterized using S-coordinates and expressed in terms of invariant metrics.
result Extended Siegel-Jacobi upper half-plane is a reductive, non-symmetric manifold.
EBMs improve text discrimination by generating negatives from auto-regressive models.
problem Discriminating machine-generated text from human-generated text.
method Use energy-based models to discriminate text, generating negatives using pre-trained auto-regressive language models.
result EBMs can generalize well to changes in generator architectures but are sensitive to training set.
This paper introduces a neural sampler for scalable sampling from complex distributions.
problem Efficiently sampling from high-dimensional un-normalized distributions.
method Neural implicit sampler trained with KL and Fisher divergence methods.
result The neural sampler generates large batches of samples with low computational costs.
New speech recognition method uses hypergraphs for better label prediction.
problem Missed information in pairwise relationships between speech samples.
method Hypergraph Laplacian based semi-supervised learning methods applied to speech recognition.
result Sensitivity performance measures of hypergraph methods are better than state-of-the-art methods.
This research improves neural likelihood approximation for Bayesian inverse problems.
problem Challenges in modeling and inference for high-dimensional Bayesian inverse problems.
method Develops a strictly convex approximation framework for neural likelihood.
result Empirical minimizers converge to the true likelihood as sample size increases.
MCD reformulates conditional density estimation into binary classification.
problem Conditional density estimation in statistical and machine learning.
method Marginal Contrastive Discrimination, reformulating into marginal and ratio density functions for binary classification.
result Significantly outperforms existing methods on most density models and regression datasets.
A new model for estimating multivariate densities efficiently.
problem Estimating complex multivariate densities efficiently.
method CDO model based on kernel mean embeddings and RKHS.
result Competitive performance with neural models and Gaussian processes.
Paper proposes MMC to avoid high-density bias in clustering.
problem High-density bias in density-based clustering.
method Introduces mass distribution as a better foundation for clustering, proposing mass-maximization clustering (MMC).
result MMC avoids high-density bias and discovers clusters of arbitrary shapes, sizes, and densities.
New method minimizes robust density power-based divergences for general parametric densities.
problem Computational complexity of minimizing DPD for general parametric densities.
method Stochastic approach to minimize DPD for general parametric density models.
result Proposed method can be applied to minimize other density power-based γ-divergences.
Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges enables us to find lower-dimensional structures hidden in data. A key technical cha…
Normalizing flows improve density estimation from noisy data.
problem Estimating underlying density from noisy samples.
method Use normalizing flows for density estimation with arbitrary noise distributions, using amortized variational inference.
result Normalizing flows can outperform Gaussian mixtures for density deconvolution.
Study exact minimax rates for density estimation over convex classes, extending previous work.
problem Deriving minimax rates for density estimation over convex density classes.
method Building on Le Cam's work, determine exact minimax rates using local metric entropy.
result Exact minimax rates derived for any convex density class, including nonparametric and parametric cases.
New method uses SoS densities and α-divergences for efficient sequential transport maps.
problem Efficiently generating samples from approximated densities.
method Sequential transport maps using Sum-of-Squares (SoS) densities and α-divergences.
result Convex optimization problems with efficient semidefinite programming solutions.
The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determinant density. It is known that the sets of volume densities and determinant densities of links are dense in the interval [0,v_{oct}]. We cons…
TAKDE optimizes kernel density estimation for real-time dynamic processes.
problem Real-time density estimation in applications like computer vision and signal processing.
method Derives asymptotic mean integrated squared error (AMISE) upper bound for 'sliding window' kernel density estimator and proposes TAKDE as a novel, theoretically optimal estimator.
result TAKDE outperforms other dynamic density estimators in terms of test log-likelihood and runtime.
Most density-based clustering methods largely rely on how well the underlying density is estimated. However, density estimation itself is also a challenging problem, especially the determination of the kernel bandwidth. A large bandwidth could lead to the over-smoothed density estimation in which the number of density …
Optimizes kernel density ratios for better predictions and information measures.
problem Improving accuracy of kernel density estimates for density ratios.
method Derives an optimal weight function using calculus of variations.
result Reduces bias in kernel density estimates, leading to improved prediction posteriors and information-theoretic measures.
Study finds a linear lower bound on conformal dimension for random hyperbolic groups.
problem Understanding conformal dimension in random hyperbolic groups.
method Building undistorted round trees from lower density groups.
result Achieves a linear lower bound in l at all densities 0<d<1/2. Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are M-undecomposable. We also derive an inequality to show that it is better to represent an M-de…
Quantum method improves neural density estimation in high dimensions.
problem High-dimensional density estimation with poor performance and high computational complexity.
method Adaptive Fourier features based on quantum density matrices, integrated with neural networks.
result Competitive performance compared to state-of-the-art methods in various datasets.
Roundtrip uses deep generative models for flexible density estimation.
problem Density estimation in statistics and machine learning.
method Roundtrip is a deep generative neural density estimator that uses flexible mappings.
result Roundtrip achieves state-of-the-art performance in density estimation tasks.
Study on flow-based methods for capturing tail properties in densities.
problem Flow-based methods struggle with capturing non-Gaussian tails.
method Characterize and adapt triangular maps to capture tail properties.
result Flow models lack the ability to capture non-Gaussian tails.
Log-density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring non-Gaussianity. A naive two-step approach of first estimating the density and then taking its log-gradient is unreliable because an accurate density estimate does not neces…
The study proves optimal isoperimetric regions in manifolds with density.
problem Finding optimal regions with minimal boundary area in manifolds with density.
method Proving existence of isoperimetric regions and using subgroup actions.
result Isoperimetric regions in product manifolds are slabs.
Fully augmented links have dense volume densities but discrete in certain ranges.
problem Characterizing the volume density spectrum of fully augmented links.
method Analyzing the ratio of volume to the number of augmentations.
result The set of FAL volume densities is dense in $[2\voct, 10\vtet)$ but discrete in $[\voct,2\voct)$.
Explains BV Laplacian on half-densities in simple terms.
problem None explicitly stated; focuses on explanation.
method Didactical review of BV Laplacian on half-densities.
result Explains BV Laplacian concept in plain language.
Defines hierarchical clustering axioms for various densities.
problem Defining hierarchical clustering for different types of densities.
method An axiomatic approach to piecewise constant densities, then extending to general densities.
result Our axiomatic definition results in Hartigan's cluster tree under certain conditions.
The paper analyzes kNN density estimation's convergence rates under different conditions.
problem Analyzing convergence rates of kNN density estimation under bounded and unbounded support conditions.
method Examined two cases: bounded support with known and unknown support sets, and unbounded support with smooth density function.
result kNN density estimation is minimax optimal under certain conditions and better than kernel density estimation in some cases.
Estimation of density derivatives is a versatile tool in statistical data analysis. A naive approach is to first estimate the density and then compute its derivative. However, such a two-step approach does not work well because a good density estimator does not necessarily mean a good density-derivative estimator. In t…
Develops spherical density-equalizing maps for closed surfaces.
problem Lack of methods for genus-0 closed surfaces.
method Conformal parameterization onto unit sphere, density equalization, quasi-conformal theory, harmonic energy, landmark constraints.
result Landmark-aligned spherical density-equalizing maps balancing different distortion measures.
New clustering algorithm uses reverse nearest neighbour for better density-based clustering.
problem Density-based clustering of separated high-density regions.
method Uses reverse nearest neighbour (RNN) queries to estimate densities and recover clusters.
result Outperforms DBSCAN and ISDBSCAN on synthetic and real-world data.
Adapts RKHS methods to estimate density ratios with optimal error.
problem Estimating density ratios from limited data.
method Minimizes regularized Bregman divergence in RKHS, with Lepskii type parameter choice.
result Adaptive minimax optimal error rate for quadratic loss.