The study shows mean partitions are consistent and asymptotically normal.
problem Lack of knowledge about the consistency of mean partitions in consensus clustering.
method Represented partitions as points in orbit space, used Fréchet means and stochastic programming, and analyzed continuous extensions of cluster criteria.
result Mean partitions are consistent and asymptotically normal under normal assumptions.
Enhances consensus clustering with a stronger Mean Partition Theorem.
problem Improving consensus clustering solutions for mean partition.
method Presented a stronger Mean Partition Theorem and Expected Partition Theorem.
result Shows versatility of the Mean Partition Theorem in multiple applications.
initKmix generates better initial partitions for k-means clustering of mixed datasets.
problem Random initial partitions lead to inconsistent clustering results.
method initKmix runs k-means multiple times, using different attributes to create initial clusters, then combines results.
result initKmix produces more accurate and consistent clustering results.
Study on estimating Gaussian mean from coarse data, resolving identifiability and computational efficiency questions.
problem Estimating the mean of a Gaussian distribution from coarse data (sets containing true samples rather than exact values).
method Analyzes the conditions for mean identifiability and computable estimation under convex partitions.
result Resolves the identifiability and computational efficiency questions for Gaussian mean estimation from coarse data.
Theoretical extension of Condorcet's Jury Theorem for consensus clustering.
problem Quality of consensus clustering depends on the diversity of sample partitions.
method Extending Condorcet's Jury Theorem to mean partition approach under specific assumptions.
result Limiting the diversity of mean partitions is necessary for controlling the quality of consensus clustering.
Study identifies partitions of probability distributions using multi-armed bandits.
problem Identifying the correct partition of a vector of probability distributions.
method Developed sample complexity bounds and proposed algorithms for multi-armed bandit settings.
result Characterized lower bounds on mean number of samples and proposed algorithms matching these bounds.
Develops an MS-inspired algorithm for regression mode finding and space partitioning.
problem Finding local modes of regression functions and partitioning input space.
method Mean-shift-inspired algorithm for iterative gradient ascent.
result Proves convergence and rates of convergence for estimated local modes.
Mean-field theory improves understanding of GNN in graph partitioning.
problem Understanding the performance and flexibility of GNN in graph partitioning.
method Developed a mean-field theory for a minimal GNN architecture.
result Good agreement between theory and numerical experiments.
New method reduces Gibbs partition function estimation complexity.
problem Estimating partition functions of Gibbs distributions.
method Doubly-adaptive MCMC with adaptive cooling schedule and mean estimator.
result Outperforms state-of-the-art algorithms in computational complexity and robustness.
A new method detects concept drift in streaming data using k-means space partitioning.
problem Detecting distribution changes in streaming data.
method Equal intensity k-means space partitioning (EI-kMeans) and heuristic sensitivity improvement.
result EI-kMeans improves drift detection accuracy and sensitivity.
In this paper, we consider unsupervised partitioning problems, such as clustering, image segmentation, video segmentation and other change-point detection problems. We focus on partitioning problems based explicitly or implicitly on the minimization of Euclidean distortions, which include mean-based change-point detect…
Unsupervised space partitioning improves ANNS performance without pre-processing.
problem Efficient nearest neighbor search in high-dimensional spaces.
method Custom unsupervised learning framework for space partitioning and learning-to-search.
result Our method outperforms state-of-the-art approaches on ANNS benchmarks.
K-means fails catastrophically in high dimensions, Hartigan's avoids it.
problem K-means algorithm's failure in high-dimensional data.
method Proof of k-means failure and Hartigan's algorithm success.
result Hartigan's algorithm avoids the catastrophic failure of k-means in high dimensions.
Study on hypermaps and KP hierarchy, proving tau function and enumerative meaning.
problem Understanding the partition function of meromorphic functions on the Riemann sphere.
method Analysis of Hurwitz Dubrovin--Frobenius manifold structure and rational reductions of the KP hierarchy.
result The all genera partition function is a tau function of a rational reduction of the Kadomtsev--Petviashvili hierarchy.
An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the variational approximation. In this paper, we present a novel combination of graph part…
Quantum algorithm speeds up Gibbs partition function estimation.
problem Estimating partition functions in sublinear time.
method Sublinear-time quantum algorithm using quantum phase and amplitude estimation.
result First sublinear-time speed-up for partition function estimation.
We prove that the unique least-perimeter way of partitioning the unit 2-dimensional disk into three regions of prescribed areas is by means of the standard graph consisting in three balanced constant geodesic curvature curves meeting themselves at 120 degrees, and reaching orthogonally the boundary of the disk.
New algorithm improves partition function approximation for graphical models.
problem Computing partition function of graphical models is computationally hard.
method Spectral mean-field scheme using FPTAS for low-rank matrices, and approximation of high-rank matrices.
result The proposed algorithm is more robust and accurate than previous methods.
Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of regions and region-specific models. This paper proposes novel convex region-specific…
Paper certifies k-means clustering optimality efficiently.
problem Detecting k-means optimality in suboptimal partitions. method Sub-linear Monte Carlo algorithm based on semidefinite relaxation.
result 3-approximation certificate with 99% confidence for mixtures of Gaussians.
New variational methods improve inference in graphical models.
problem Computing partition function in graphical models is intractable.
method Proposed Gauged-MF and Gauged-BP methods using gauge transformation.
result Gauged-MF and Gauged-BP provide exact solutions for GMs with a single loop.
Hybrid clustering merges K-means and hierarchical methods for diverse group shapes.
problem Clustering homogeneous spherical groups in large datasets.
method First, K-means partitions the dataset into spherical groups. Then, hierarchical clustering merges these groups with a data-driven distance measure. result Hybrid approach reveals general-shaped groups in datasets.
A new method for multilevel clustering using Wasserstein means.
problem Simultaneously partitioning data in each group and discovering grouping patterns among groups.
method Joint optimization over spaces of discrete probability measures with Wasserstein distance metrics, including variants that admit fast optimization.
result Consistency properties for estimates of both local and global clusters are established.
New method detects changes without partitioning distributions.
problem Detects changes in unknown probability distributions without partitioning.
method Aggregates e-processes over possible changepoints and infimum over candidate no-change distributions.
result Achieves first-order asymptotically optimal detection delay.
Given iid observations from an unknown absolute continuous distribution defined on some domain Ω, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function. Our density estimate is a piecewise constant function defined on a binary partition o…
Paper proposes a new method to learn EBMs and their partition function.
problem Intractability of exact MLE for EBMs due to partition function computation.
method Jointly learns an energy model and its log-partition function using neural networks.
result First tractable method for optimizing sparsemax loss in large spaces.
In this paper we propose a novel Bayesian methodology for Value-at-Risk computation based on parametric Product Partition Models. Value-at-Risk is a standard tool to measure and control the market risk of an asset or a portfolio, and it is also required for regulatory purposes. Its popularity is partly due to the fact …
K-Means and RBF networks are shown to be equivalent under certain conditions.
problem Discrete clustering vs. continuous optimization in machine learning.
method Established variational and gradient-based equivalence between K-Means and RBF networks.
result Gradient-based updates of RBF centers recover K-Means centroid update rule.
MSTs provide a fast and meaningful clustering method in low-dimensional data.
problem Quantifying the effectiveness of MSTs in low-dimensional clustering tasks.
method Identifying upper bounds for MST performance, reviewing and extending existing MST-based partitioning schemes.
result MST methods can be very competitive, often outperforming traditional clustering algorithms.
WHOMP optimizes randomized controlled trials by minimizing subgroup bias.
problem Minimizing subgroup bias in randomized controlled trials.
method Wasserstein Homogeneity Partition (WHOMP) method.
result WHOMP optimally minimizes type I and type II errors in trials.
We examine the effect of clamping variables for approximate inference in undirected graphical models with pairwise relationships and discrete variables. For any number of variable labels, we demonstrate that clamping and summing approximate sub-partition functions can lead only to a decrease in the partition function e…
A new clustering method combines Kalman filtering with K-Means for better results.
problem Improving clustering efficiency and accuracy in data mining.
method Proposes a new clustering algorithm (HKA-K) that integrates Kalman filtering and K-Means.
result HKA-K outperforms other hybrid meta-heuristic clustering approaches on UCI datasets.
We develop efficient methods to approximate maximum entropy distributions for pairwise moments.
problem Intractability of calculating exact maximum entropy distributions.
method Design distributions that approximate maximum entropy distributions while maintaining comparable entropy.
result Approximation guarantees for log-partition functions comparable to low-temperature limits.
This paper analyzes MFVBI for GMM using statistical mechanics.
problem Approximate fast computation of Gaussian Mixture Model.
method Statistical mechanics and MFVBI applied to GMM.
result Rigorous analysis and mathematical foundation for MFVBI applied to GMM.
K-bMOM robustly clusters data with outliers, improving on Lloyd-type methods.
problem Outliers in datasets disrupt traditional clustering algorithms.
method Lloyd-type iterations with robust median-of-means estimates.
result K-bMOM outperforms existing robust K-means methods.
DTE uses tree leaf means to embed data, balancing accuracy and speed.
problem High variance in decision tree splits and computational inefficiency of ensembles.
method DTE constructs an interpretable feature representation using leaf means of a trained tree.
result DTE strikes a balance between accuracy and computational efficiency, outperforming ensembles.
Greedy training of recursive partitioning estimators faces a computational barrier when the true function doesn't satisfy a specific property.
problem Computational inefficiency of greedy training for recursive partitioning estimators.
method Analysis of greedy training for sparse regression functions over binary features.
result Greedy training requires exponential samples when the true function doesn't satisfy a specific property (MSP), but only logarithmic samples when it does.
New bounds for estimating partition functions under bounded f-divergence.
problem Estimating partition functions with limited sample access.
method Information-theoretic characterization using integrated coverage profile and f-divergences. result Sharp phase transitions in sample complexity under f-divergences. Novel PairNet speeds up ANN training with fast hyperparameter optimization.
problem Slow training of traditional ANNs with many hyperparameters.
method Partition inputs into subspaces, optimize hyperparameters via linear equations, train local PairNets in subspaces.
result PairNet achieves higher speeds and lower MSEs than traditional ANNs.
TiK-means extends K-means for skewed groups, revealing structured clusters.
problem Clustering skewed groups using traditional K-means.
method Introduces TiK-means, a modified K-means algorithm that estimates skewness-transformation parameters.
result Reveals structured clusters that explain the skewness of groups.
The classical k-means algorithm for partitioning n points in Rd into k clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been observed in many scientific and business applications. In this paper, we present an…
Ant colony optimization for clustering with improved K-means.
problem Clustering a set of objects to minimize intra-variance.
method Constructive approach using ant-like solutions with visibility and pheromone trails, improved with K-means.
result Encouraging results in nearly all benchmark real-data sets.
Estimates means in metric spaces using quantization.
problem No practical estimator for Fréchet means in all metric spaces.
method Introduced estimators based on random quantization and data-driven partitioning.
result Universal consistency of estimators across separable metric spaces and Banach spaces.
A new clustering method learns shared hidden space and fuzzy partition between multi-view data.
problem Effective exploitation of relationship between different views in multi-view data.
method Hidden space sharing multi-view fuzzy clustering (HSS-MVFC) method based on fuzzy c-means.
result The proposed method outperforms many related clustering methods in experiments.
Given a singular Riemannian foliation on a compact Riemannian manifold, we study the mean curvature flow equation with a regular leaf as initial datum. We prove that if the leaves are compact and the mean curvature vector field is basic, then any finite time singularity is a singular leaf, and the singularity is of typ…
Rule-based classifiers quantify uncertainty using Bernoulli random variables.
problem Quantifying the uncertainty of precision estimates for rule-based text classifiers.
method Treat partitions of sub-strings as Bernoulli random variables, compare means using statistical tests, and combine classifiers using Dempster-Shafer theory.
result The approach can be used to combine binary classifiers into a multi-label classifier.
We explore the performance of several automatic bandwidth selectors, originally designed for density gradient estimation, as data-based procedures for nonparametric, modal clustering. The key tool to obtain a clustering from density gradient estimators is the mean shift algorithm, which allows to obtain a partition not…
Algorithm learns diffusion processes with high-dimensional state spaces.
problem Stochastic control of unbounded diffusion processes with high-dimensional state spaces.
method Adaptive partitioning and learning algorithm that refines discretization based on estimation bias and statistical confidence.
result Established regret bounds that depend on problem parameters, extending to unbounded diffusion processes.