DBSCAN estimates density level sets on manifolds with i.i.d. samples.
problem Estimating connected components of density level sets on manifolds.
method DBSCAN algorithm applied to i.i.d. samples.
result Rates of estimation error for different data settings.
Study connects spectral clustering to maximum margin and level set estimation.
problem Connecting spectral clustering to maximum margin and level set estimation.
method Obtained bounds on eigenvectors of graph Laplacian matrices in terms of cluster separation and connectivity. Showed sensitivity mitigation by removing outliers and estimating level sets.
result Spectral clustering converges to maximum margin clustering as scaling parameter approaches zero.
The level set tree approach of Hartigan (1975) provides a probabilistically based and highly interpretable encoding of the clustering behavior of a dataset. By representing the hierarchy of data modes as a dendrogram of the level sets of a density estimator, this approach offers many advantages for exploratory analysis…
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≥0. The complete hierarchical clustering can be characterized by a cluster tree ${\cal T}= \bigcup_λ L(λ)…
The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an almost arbitrary level set estimator to estimate the smallest level at which th…
BDMBC clusters data with varying densities using a new PLLS measure.
problem Finding clusters with varying densities in data.
method Bagged k-distance with PLLS for mode estimation. result BDMBC achieves optimal convergence rates for mode and level set estimation.
Following Hartigan, a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering algorithm which combines a density estimate with spectral clustering techniques is proposed. Our algorithm is composed of two step…
New scoring rules for multivariate distributions and level sets.
problem Evaluating forecast accuracy for multivariate distributions and level sets.
method Theoretical framework for scoring rules, decomposition of multivariate scoring functions, numerical algorithm for computation.
result New scoring functions for multivariate distributions and level sets, including density and cumulative distribution level sets.
Paper proves stronger Penrose inequality with matter density.
problem Proves Penrose inequality with nonnegative matter density.
method Uses conformal flow and harmonic level set techniques.
result Total mass is at least black hole mass plus matter density contribution.
The article uses surgery on mean curvature flow to study level set flow's regularity and stability.
problem Analyzing the regularity and stability of level set flow.
method Using mean curvature flow with surgery to derive estimates.
result Demonstrates stability of the plane under level set flow.
SLS optimizes minimum-volume regions for conditional quantiles, bypassing density estimation.
problem Constructing minimum-volume prediction regions that satisfy conditional coverage.
method Super-level-set regression (SLS) directly optimizes geometric boundaries of conditional level sets.
result SLS optimizes regions directly, capturing complex conditional structures end-to-end.
Eigenfunction value distribution shows unimodal density with maximum at zero.
problem Understanding the value distribution of Laplace eigenfunctions.
method Analyzing the measure μ whose density is ∣ablaf∣2 and proving a monotonicity formula. result Eigenfunction value distribution under μ is unimodal with maximum at zero. Proposes a new clustering algorithm using random forest.
problem Density-based clustering with optimal level determination.
method Best-scored random forest algorithm.
result Guaranteed consistency and fast convergence rates.
New model predicts grain boundary migration in metals.
problem Anisotropic grain boundary migration in polycrystals.
method Level set-finite element formulation based on thermodynamics and mechanics.
result First analytical solution for anisotropic grain boundary configurations.
This work explores efficient reinforcement learning with density features in low-rank MDPs.
problem Efficient reinforcement learning with density features in low-rank MDPs.
method Proposes algorithms for off-policy estimation and online construction of exploratory data distributions.
result Demonstrates sample-efficient learning with density features in low-rank MDPs, overcoming technical challenges.
Adaptive clustering uses kernel density estimates for split detection.
problem Cluster detection in non-parametric settings.
method Recursive algorithm using kernel density estimates for splitting and clustering.
result Finite sample guarantees, consistency, and adaptive bandwidth selection.
Paper uses machine learning to estimate IRI from pavement distress types, densities, and severities.
problem Costly IRI measurements exclude many road classes; estimating IRI from distress data is needed.
method Data from in-service pavements; machine learning methods used to predict IRI.
result Machine learning can reliably estimate IRI based on distress types, densities, and severities.
Machine learning predicts electronic density of states for condensed matter.
problem Predicting the electronic density of states (DOS) in complex condensed matter systems.
method Developed a machine learning framework to predict DOS from density functional theory data, considering geometric configurations of atoms.
result Demonstrated the model's effectiveness in predicting DOS and its components for various silicon configurations.
Study shows zero level sets of solutions to Allen-Cahn equation are minimal surfaces with zero mean curvature.
problem Understanding phase transitions through entire solutions of the Allen-Cahn equation.
method Proving minimality of the zero level set with respect to a perimeter functional with density and showing zero mean curvature.
result The zero level set of entire solutions of the Allen-Cahn equation has zero mean curvature and is minimal.
We compute, using a formula of Dittmann, the Bures metric tensor (g) for the eight-dimensional convex set of three-level quantum systems, employing a newly-developed Euler angle-based parameterization of the 3 x 3 density matrices. Most of the individual metric elements (g_{ij}) are found to be expressible in relativel…
Study area and coarea formulas for graphs and submanifolds in Carnot groups.
problem Understanding geometric properties of submanifolds in Carnot groups.
method Developed area and coarea formulas for CH1 intrinsic graphs and submanifolds. result Deduced density properties for Hausdorff measures and coarea formula for Carnot groups.
Hierarchical VAEs detect out-of-distribution data by identifying low-level in-distribution features.
problem Out-of-distribution data often has in-distribution low-level features, leading to misleading likelihood estimates in deep generative models.
method Developed a fast, scalable, unsupervised likelihood-ratio score for out-of-distribution detection based on hierarchical variational autoencoders.
result Achieved state-of-the-art results on out-of-distribution detection across various data and model combinations.
MRCNet tackles crowd counting and density mapping in aerial imagery.
problem Accurate crowd counting and density estimation in aerial imagery.
method MRCNet is a novel encoder-decoder CNN that combines VGG-16 with FPN-inspired lateral connections.
result MRCNet outperforms state-of-the-art methods in aerial and CCTV-based crowd counting.
New framework quantifies uncertainty in flexible density-based clustering.
problem Uncertainty quantification in clustering with non-parametric density estimation.
method Martingale posterior distributions and density-based clustering.
result Efficient GPU-compatible inference on clustering structures with uncertainty.
DBSCAN++ speeds up density clustering for large datasets.
problem Slow runtime of DBSCAN for large datasets.
method DBSCAN++ computes densities for a subset of points instead of all.
result DBSCAN++ provides competitive performance and robustness.
Machine learning predicts nuclear physics parameters with high accuracy.
problem Predicting nuclear physics parameters for superheavy elements.
method Gradient boosted trees algorithm trained on nuclear data.
result Predictions have standard deviation from 0.00035 to 0.73.
mLSTM improves sequence modeling with better autoregressive density estimation.
problem Improving autoregressive density estimation in sequence modeling.
method Introduces mLSTM, a recurrent neural network combining LSTM and multiplicative recurrent networks.
result mLSTM outperforms standard LSTM and its variants in character-level language modeling tasks.
Paper introduces exact credible sets for classification problems.
problem No general way to construct exact credible sets for classification.
method Generalized credible set with connection to Neyman--Pearson lemma and randomized decision rule.
result Achieves any preassigned credible level for classification problems.
New findings suggest deep generative models can misclassify outliers, requiring new evaluation methods.
problem Deep generative models often assign higher likelihood to outliers, challenging existing outlier detection methods.
method Analyzed the typical set and high-density region of DGMs, proposing a novel outlier test.
result Existing likelihood-based outlier tests may fail due to model calibration issues, not just misclassification.
Study recovers Riemannian quantities from noisy data densities.
problem Recovering geometric structure from noisy data on submanifolds.
method Derive uniform small-noise expansions of noisy density and its derivatives; construct estimators for tangent spaces, intrinsic dimension, and second fundamental form.
result Fundamental Riemannian quantities identifiable from density derivatives.
Multitask Gaussian process regression reduces data generation costs for molecular property prediction.
problem Data bottleneck in training surrogate models for molecular properties.
method Multitask Gaussian process regression over heterogeneous data sources (CC and DFT).
result Predicts at CC-level accuracy with over an order of magnitude reduction in data generation cost.
Paper proposes a shape-constrained approach to distributionally robust learning.
problem Challenges in statistical learning under distribution shift.
method Shape-constrained approach to distributionally robust learning (DRL). Assumes isotonic density ratio.
result Improved accuracy demonstrated in empirical studies.
New bounds on generalization error using information density moments.
problem Bounding the generalization error of randomized learning algorithms.
method Derives bounds on average and tail probabilities of generalization error using mth central moments of the information density.
result Explicit bounds on generalization error are derived, showing better dependence on confidence level with higher-order information density moments.
DDR estimates personalized treatment effects from clinical trials.
problem Estimating personalized treatment effects from clinical trials data.
method Transforms outcome into Dirac delta distributions and estimates density using non-linear regression.
result Identifies significant patient-specific outcomes even when no population-level effect exists.
New insights into binary perceptron reveal phase transitions and algorithmic thresholds.
problem Understanding the statistical-computational gap in binary perceptron models.
method Application of fully lifted random duality theory (fl RDT) to uncover structural changes.
result Numerical estimates of constraint density thresholds align with theoretical predictions.
Generative models improved with smoothed score functions for better sample quality.
problem Improving generative models for better sample quality.
method Smoothed score functions based on factorial Gaussian kernels.
result Single noise level achieved 14.15 Fréchet inception distance on CIFAR-10.
New method improves transductive learning predictions with multiplicative oracle inequalities.
problem Improving transductive learning predictions with known covariates.
method Median of Level-Set Aggregation (MLSA) for transductive LOO prediction.
result Proved multiplicative oracle inequality for LOO error.
Injective flows for star-like manifolds improve variational inference efficiency.
problem Efficiently modeling densities on star-like manifolds with exact Jacobian computation.
method Proposed injective flows for star-like manifolds with exact Jacobian computation.
result Exact Jacobian computation for star-like manifolds reduces computational cost to NFs.
Consider transportation of one distribution of mass onto another, chosen to optimize the total expected cost, where cost per unit mass transported from x to y is given by a smooth function c(x,y). If the source density f^+(x) is bounded away from zero and infinity in an open region U' \subset R^n, and the target densit…
LMC algorithm improved for nonsmooth distributions.
problem LMC's limitations in nonsmooth settings.
method Adding a small Gaussian perturbation to iterates, controlling bias and variance.
result Polynomial-time convergence guarantees for nonsmooth log-concave distributions.
Robustly infers manifold density and geometry under high-dimensional noise.
problem Inaccurate kernel density estimation under high-dimensional noise.
method Doubly stochastic normalization of Gaussian kernel.
result Robust tools for density estimation, noise magnitude estimation, and distance approximation.
New method protects group privacy in sampling, overcoming traditional privacy limits.
problem Protecting group privacy in statistical sampling with strong differential privacy guarantees.
method Integrates boosting theory for non-private density estimation and bypasses sensitivity analysis.
result Achieves strong privacy guarantees for sampling without scaling noise variance.
PFs and iPFs learn principal manifolds for efficient density estimation.
problem Understanding the geometric structure of normalizing flows.
method Characterize flows using principal manifolds and contours.
result PFs and iPFs can learn principal manifolds and perform density estimation.
LOO prediction method improves generalization guarantees for arbitrary datasets.
problem Understanding LOO error guarantees in fully transductive settings for arbitrary datasets.
method Median of Level-Set Aggregation (MLSA) for empirical-risk level sets.
result Multiplicative oracle inequality for LOO error with complexity scaling.
GCAO improves clustering of high-dimensional data by grouping low-density boundary points.
problem Stability and accuracy of clustering in high-dimensional, non-uniform data.
method Group-level optimization with gravitational attraction and optimization.
result GCAO outperforms 11 clustering methods on multiple datasets.
CTI produces efficient prediction intervals with guaranteed coverage.
problem Efficient and reliable uncertainty quantification in regression.
method CTI estimates conditional density for interval length, then thresholds intervals based on this density.
result CTI achieves smaller prediction sets with guaranteed coverage compared to existing methods.
Deep RL algorithm learns human-level policies on nearly all Atari games.
problem Consistent performance on diverse Atari games.
method Addressing three key challenges: diverse reward distributions, long-term reasoning, and efficient exploration.
result Exceeds human performance on 40 out of 42 Atari games.
A new method using normalizing flows speeds up Bayesian model comparison.
problem Computational challenges in calculating Bayesian evidence for complex models.
method Savage-Dickey density ratio with normalizing flows.
result The method scales to high-dimensional settings and provides consistent Bayes factors.