The Gibbs-type Indian buffet process extends feature allocation models with power-law behaviors.
problem Feature allocation models with power-law behaviors.
method Gibbs-type random measures parameterization.
result Properties of Gibbs-type partitions allow for black-box posterior inference.
Within the description of stochastic differential equations it is argued that the existence of Boltzmann-Gibbs type distribution in economy is independent of the time reversal symmetry in econodynamics. Both power law and exponential distributions can be accommodated by it. The demonstration is based on a mathematical …
New model detects hidden group structures in criminal networks.
problem Challenges in identifying group structures in criminal networks with noisy data.
method Developed an extended stochastic block model (ESBM) to infer group structures.
result Unveiled complex block structures in an Italian mafia network.
Bayesian inference over admissible histories leads to irreversible kinetics.
problem Modeling irreversible processes in systems with uncertain histories.
method A Gibbs-type measure weighted by energy-dissipation action and observation constraints, interpreted as a Bayesian posterior.
result The measure concentrates on maximum-a-posteriori (MAP) histories, recovering classical deterministic evolution.
Adjoint sampler targets infinite-dimensional function spaces for efficient sampling.
problem Limited theory and algorithms for sampling infinite-dimensional function spaces.
method Adjoint Sampler for infinite-dimensional function spaces based on stochastic maximum principle.
result FAS achieves superior performance in synthetic and real systems.
In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities which become closer and closer to …
SRFE clarifies KL divergences without unifying learning frameworks.
problem Inductive biases of KL divergences and their limitations.
method Introducing SRFE, a log-moment-based functional of the likelihood ratio.
result SRFE recovers KL divergences as limits and reveals a mean-variance tradeoff.
Paper compares graph and set partition measures for graph clustering.
problem Comparing graph clustering methods using different similarity measures.
method Introduces graph-aware partition similarity measures and compares them with set partition measures.
result Graph-aware measures provide complementary information to set partition measures.
The study limits how many parts regular simplicial partitions can overlap.
problem Bounding the intersection number of regular simplicial partitions.
method Analyzing the properties of regular simplicial partitions.
result Established a maximum limit for the intersection number.
Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …
New method improves nearest neighbor search using neural networks and graph partitioning.
problem Efficient nearest neighbor search in high-dimensional spaces.
method Developed a new framework for space partitioning using neural networks and graph partitioning.
result Neural LSH partitions outperform existing methods on standard benchmarks.
Better spectral partitioning of signed graphs using standard Laplacian.
problem Meaningless partitioning using signed Laplacian eigenvectors.
method Use standard graph Laplacian for spectral partitioning.
result Fiedler vector of standard Laplacian is easier to compute and more beneficial.
Rectangular Bounding Process (RBP) improves partitioning efficiency in multi-dimensional spaces.
problem Creating many unnecessary divisions in sparse regions when describing dense regions.
method Introduces Rectangular Bounding Process (RBP) to efficiently partition multi-dimensional spaces using a bounding strategy.
result The RBP is self-consistent and can be extended to infinite space, offering rich yet parsimonious expressiveness.
GAP uses deep learning to efficiently partition graphs.
problem Graph partitioning to minimize edge cut.
method Deep learning approach with a differentiable loss function.
result GAP achieves competitive partitions and generalizes to unseen graphs.
The study examines the balancedness of random partition models and finds the rich-get-richer characteristic is a result of model assumptions.
problem The balancedness of random partition models is largely neglected in the literature.
method Formulated a framework to define and study the balancedness of exchangeable random partition models, analyzed using product-form exchangeability and projectivity assumptions.
result The 'rich-get-richer' characteristic is an inevitable consequence of the model assumptions.
The paper develops mixed-integer formulations for neural networks using partitioning.
problem Optimizing trained ReLU neural networks with balanced model size and tightness.
method Partitioning node inputs into groups, forming the convex hull via disjunctive programming.
result The proposed formulations outperform existing ones, especially with fewer partitions.
New partition designs reduce star discrepancy in high-dimensional sampling.
problem Improving the expected star discrepancy in high-dimensional sampling.
method Developed non-equal volume partitions to achieve lower expected star discrepancy.
result Explicit upper bounds for expected star discrepancy under non-equal volume partitions.
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.
The paper constructs Markov partitions for geodesic flow on hyperbolic surfaces.
problem Understanding Markov partitions for general hyperbolic flows.
method Rigorous construction of Markov partitions for geodesic flow on Riemann surfaces of constant negative curvature.
result Explicit forms of rectangles and local cross sections provided for the geodesic flow.
New method unifies and formalizes data partitioning using a single vector.
problem Data partitioning and clustering methods.
method Rank-one matrix factorization and denoising of piecewise constant signals.
result Demonstrates robustness of denoising step in partitioning.
Survey of mass partition problems in geometry and topology.
problem Inducing partitions on measures or sets by dividing space.
method Recent progress in topology, discrete geometry, and computer science.
result Connections between different fields.
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.
Locally isoperimetric partitions minimize perimeter in space.
problem Finding minimal perimeter partitions in space.
method Proving closure theorem to limit sequences of isoperimetric clusters.
result Examples of isoperimetric partitions in various dimensions.
Online BSP-Forest improves space partitioning for large-scale classification and regression.
problem Efficient space partitioning for large-scale classification and regression problems.
method Developed an online BSP-Forest framework that expands space coverage and refines partition structure in real-time.
result Guaranteed universal consistency for both classification and regression problems.
Study of Torelli groups of partitioned surfaces with bounds and asymptotic lengths.
problem Understanding Torelli groups of partitioned surfaces.
method Topological and dynamical analysis of Torelli groups of partitioned surfaces.
result Asymptotic translation lengths of Torelli groups of partitioned surfaces behave almost like the reciprocal of the Euler characteristic of the surface.
Efficiently calculates PL model likelihood for partitioned preference data.
problem Computational infeasibility of calculating PL model likelihood for partitioned preference data.
method Random utility model formulation and efficient numerical integration approach.
result Proposed method outperforms existing LTR baselines and scales to real-world tasks.
Paper recovers lattice signal partitions efficiently.
problem Estimating lattice partition from noisy data.
method Uses dyadic CART for computationally-efficient partition recovery.
result Consistently estimates partition with optimal error rate.
New proof of a unique 3-part partition in 8D space.
problem Existence of a non-standard isoperimetric partition in high dimensions.
method Analytical proof showing existence of a specific partition.
result Existence of a non-standard isoperimetric partition in 8D space.
We prove that the least-perimeter partition of the sphere into four regions of equal area is a tetrahedral partition.
Maps discrete manifolds to partitions to define new manifolds.
problem Creating manifolds from discrete structures.
method Mapping discrete d-manifolds onto (k+1)-partite complexes to define new manifolds.
result Defines a (d-k)-manifold from simplices in G mapped to P.
Proposes a new BSP-Tree process for flexible space partition modeling.
problem Limited modelling flexibility of axis-aligned partitions in Mondrian process.
method Introduces a self-consistent Binary Space Partitioning (BSP)-Tree process with oblique cuts.
result Clear inferential improvements over standard Mondrian process and related methods.
Standard bubbles and partitions are stable in various model spaces.
problem Stability of standard bubbles and partitions in different model spaces.
method New conjugated Brascamp-Lieb inequality and conformally flattening boundary potential.
result Stability of standard bubbles and partitions in Rn, Sn, and Hn. Algorithms learn and test variable partitions in various groups and error metrics.
problem Learning and testing variable partitions in different groups and error metrics.
method Algorithms for agnostically learning and testing k-partitionability over various groups and error metrics. result Learning algorithms for k-partitionability with polynomial time complexity and testing with adaptive queries. The paper extends cyclic cocycles and proves relative index theorems for partitioned manifolds.
problem Index theorems on partitioned manifolds.
method Extending Roe's cyclic 1-cocycle to relative settings and proving index theorems using the cyclic cocycle.
result Generalizations of index theorems on partitioned manifolds.
GRAF uses global partitioning to improve ensemble classifier performance.
problem Improving ensemble classifier performance.
method GRAF extends oblique decision trees to global partitioning.
result GRAF reduces generalization error and improves performance on benchmark datasets.
A new multilabel classification framework improves ANN search performance.
problem Efficiently finding approximate nearest neighbors in large datasets.
method Formulated ANN search as a multilabel classification problem, using partitioning classifiers.
result Natural classifier leads to strictly improved performance in ANN search.
Norm-range partition improves MIPS search efficiency by reducing query complexity.
problem Efficiently searching for maximum inner product in large datasets.
method Norm-range partition technique that divides datasets into sub-datasets with similar norms and builds independent hash indexes.
result Significantly reduces the number of probed buckets for LSH-based MIPS algorithms.
This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or tertiary predictors and allows the number of predictors to exceed the size of the sa…
The study explores continuous noncrossing partitions and their relation to weighted circular factorizations.
problem Understanding the structure of continuous noncrossing partitions on the unit circle.
method Analyzes degree-d continuous noncrossing partitions and their equivalence classes of weighted linear factorizations.
result Maximal elements in the poset of continuous noncrossing partitions form a subspace homeomorphic to the dual Garside classifying space for the d-strand braid group.
Proves an Euler-type formula for Möbius strip partitions.
problem No specific problem stated; focuses on a mathematical formula.
method Analyzes partitions of the Möbius strip.
result Proves an Euler-type formula for Möbius strip partitions.
Study on stable partitions in convex domains with three phases, finding disconnected phase stability.
problem Stability of partitions in convex domains with multiple phases.
method Careful derivation of the second variation of area, proving existence of stable partitions involving disconnected phases.
result Existence of stable partitions involving a disconnected phase in three phase problem.
Homology of partition algebras matches symmetric group homology under certain conditions.
problem Understanding homology of partition algebras and comparing it to symmetric groups.
method Inductive resolution and high acyclicity arguments, parallel to earlier work on Brauer algebras.
result Homology of partition algebras is isomorphic to symmetric group homology under specific conditions.
New hypergraph clustering method assigns different costs to hyperedge cuts.
problem Hypergraph partitioning assumes uniform costs for different hyperedge cuts.
method Inhomogeneous hypergraph partitioning assigns different costs to different hyperedge cuts.
result Inhomogeneous partitioning offers significant performance improvements in various applications.
New algorithms for efficient hypergraph partitioning in computer vision.
problem Efficiently partitioning weighted uniform hypergraphs for computer vision tasks.
method Provable tensor methods and sampling techniques.
result Rigorous analysis justifies practical sampling techniques.
Topological recursion recovers a specific partition function for colored knots.
problem Recovering the extended Ooguri-Vafa partition function for colored HOMFLY-PT polynomials of torus knots.
method Applying topological recursion to the spectral curve of colored HOMFLY-PT polynomials of torus knots.
result Topological recursion reproduces the n-point functions of the extended Ooguri-Vafa partition function.
This thesis classifies pseudo-Anosov homeomorphisms using geometric Markov partitions.
problem Classifying pseudo-Anosov homeomorphisms up to topological conjugacy.
method Algorithmic approach using geometric Markov partitions.
result Geometric type is a complete invariant of conjugation.
A new approach to Kernel Ridge Regression using partitioning.
problem Efficiently estimating KRR for large datasets.
method Divide and conquer approach via partitioning of input space.
result Achieves optimal minimax rates and reduces approximation error.
New model of vague knowledge without strict partitions or transitivity.
problem Standard economic models of information fail to capture real-world vague knowledge.
method Relaxing assumptions of transitivity and partition structure to formalize vague knowledge.
result Vague knowledge can distinguish some states but not partition the state space.