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 …
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48 results for “partition models”
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.
Rectangular Bounding Processstat.ML
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.
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.
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.
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.
Partition-wise Linear Modelsstat.ML
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…
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 , , and .
Algorithm for exact partitioning of high-order models using convex tensor relaxation.
problem Exact partitioning of high-order models.
method Defining a general class of -degree Homogeneous Polynomial Models, relaxing the high-order combinatorial problem to a convex conic form problem, defining the Carathéodory symmetric tensor cone, and constructing a primal-dual certificate.
result The solution of the convex relaxation is correct and provides a statistical upper bound for exact partitioning.
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.
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.
Survey of Bayesian nonparametric space partition models and their applications.
problem Partitioning high-dimensional spaces into homogeneous regions.
method Various strategies for generating partitions in a D-dimensional space.
result Review of current progress in BNSP research.
Bayesian nonparametric method partitions shapes using curves.
problem Capturing complex shapes in multi-dimensional data.
method Proposes a novel spline partitioning approach using curves.
result Demonstrates improved shape modeling compared to existing methods.
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…
We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for approximating the partition function are Markov Chain Monte Carlo and Variational Method…
Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (i…
We prove that the model-free typical (in the sense of Vovk) càdlàg price paths with mildly restricted downward jumps possess quadratic variation which does not depend on the specific sequence of partitions as long as these partitions are obtained from stopping times such that the oscillations of a path on the consecuti…
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 relate the partition function to the max-statistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As a result, we can use efficient MAP solvers such as graph-cuts to evaluate the c…
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 …
New methods reveal consensus and dissensus in network partitions.
problem Degenerate community detection methods often yield multiple competing answers.
method Comprehensive set of methods to characterize and summarize complex populations of partitions.
result It is not possible to obtain a consistent answer from point estimates when the distribution is heterogeneous.
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.
FairGP uses graph partitioning to make Graph Transformers fair and scalable.
problem Fairness issues in Graph Transformers, especially against sensitive features.
method Graph partitioning to minimize the influence of higher-order nodes and optimize attention mechanisms.
result FairGP improves fairness in Graph Transformers while reducing computational complexity.
Graph-partitioning-based DCRNN improves traffic forecasting for large highways.
problem Challenges in accurately forecasting traffic on large highway networks.
method Graph-partitioning method to decompose large networks into smaller, independent networks.
result Demonstrated improved traffic forecasting on a large California highway network.
A dependent partition-valued process for multitask clustering and time evolving network modellingstat.ML
The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation processes, but these, being Markov processes, are restricted to linear or tree s…
Exact partitioning of high-order planted models achieved through convex optimization.
problem Efficiently partitioning hypergraphs generated by high-order planted models.
method Solving a computationally efficient convex optimization problem with a tensor nuclear norm constraint.
result Exact recovery of true underlying cluster structures with high probability.
Partition Tree estimates conditional densities for mixed continuous and categorical variables.
problem Estimating conditional densities for mixed data types.
method Tree-based framework modeling conditional distributions as piecewise-constant densities on adaptive partitions, minimizing conditional negative log-likelihood.
result Improved probabilistic prediction compared to CART-style trees and state-of-the-art methods.
Enhances robustness of multi-view clustering via partition fusion.
problem Dealing with noises and inconsistency in multi-view data.
method Generates multiple partitions, integrates them, and co-evolves graph learning, partition generation, and view weight learning.
result Empirical results verify the effectiveness and robustness of the proposed approach.
Beta-Negative Binomial Process and Exchangeable Random Partitions for Mixed-Membership Modelingstat.ME
The beta-negative binomial process (BNBP), an integer-valued stochastic process, is employed to partition a count vector into a latent random count matrix. As the marginal probability distribution of the BNBP that governs the exchangeable random partitions of grouped data has not yet been developed, current inference f…
Differentially private method for synthetic data generation from vertically partitioned data.
problem Generating synthetic data from vertically partitioned data while preserving privacy.
method Differentially private stochastic gradient descent (DP-SGD) algorithm combined with secure multiparty computation (MPC).
result Comparable accuracy to non-partitioned data, demonstrating privacy-preserving synthetic data generation.
Proposes SPFB method for optimizing partition functions in stochastic learning.
problem Optimizing partition functions in stochastic learning settings.
method Stochastic Gradient Bound (SPFB) method based on upper-bounding the partition function with a quadratic surrogate.
result Sub-linear convergence rate of SPFB method and efficient training of deep learning models.
Efficiently resolves entities via scaled Ewens--Pitman model.
problem Entity resolution in large datasets.
method Microclustering Ewens--Pitman model with variational inference.
result Significant speed-up in entity resolution with competitive performance.
This study proposes a graph partitioning method to improve spatial prediction models.
problem Improving interpretability of spatial prediction models in industries.
method Graph partitioning problem to minimize within-segment variances, formulated as mixed-integer quadratic programming.
result Approximation scheme efficiently identifies spatial segments, improving computational efficiency.
SplitNN-driven Vertical Partitioning enables distributed learning from diverse data sources.
problem Learning from vertically distributed features across institutions.
method A configuration of SplitNN that does not share raw data or model details.
result Flexibility in merging split model outputs and resource efficiency.
Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population genetics, ecology or network analysis. While the exchangeability assumption is sensib…
Asynchronous federated learning for vertically partitioned data improves efficiency and privacy.
problem Efficiently train models on vertically partitioned data without a trusted third party.
method Proposed AFSGD-VP and its SVRG and SAGA variants for asynchronous federated learning.
result AFSGD-VP and its variants achieve higher efficiency than synchronous algorithms.
LA-MCTS learns search space partition for black-box optimization using Monte Carlo Tree Search.
problem High-dimensional black-box optimization challenges.
method LA-MCTS recursively splits search space into regions with high/low function values, learns nonlinear partition and local models online.
result LA-MCTS achieves strong performance in black-box optimization and reinforcement learning benchmarks, especially for high-dimensional problems.
Improved supervised EM learning for shared kernel models with feature space partitioning.
problem Lack of rigour in EM derivation and high computational complexity.
method Detailed derivation of EM for Gaussian shared kernel model, feature space partitioning to reduce complexity.
result Improved performance at reduced complexity achieved.
Paper proposes a method to predict optimal data partitioning based on query execution costs.
problem Finding optimal data partitioning for improved system performance and scalability.
method Formal model abstraction of workload queries, genetic algorithm for optimization, evaluation using PostgreSQL's query optimizer.
result The approach effectively reduces workload execution cost and improves system performance.
In this paper, we propose a family of graph partition similarity measures that take the topology of the graph into account. These graph-aware measures are alternatives to using set partition similarity measures that are not specifically designed for graph partitions. The two types of measures, graph-aware and set parti…
This paper tackles multi-modal label disentanglement in partition-based XMC.
problem Existing partition-based XMC methods create mutually exclusive clusters, which is sub-optimal for multi-modal labels.
method Formulates label assignment as an optimization problem to maximize precision rates, creating flexible and overlapped label clusters.
result Successfully disentangles multi-modal labels, leading to state-of-the-art results on XMC benchmarks.
This work proposes a method to optimize hyperparameters without validation data.
problem Optimizing hyperparameters for neural networks with limited data.
method Neural network partitioning and subnetwork optimization.
result The method optimizes hyperparameters efficiently and without validation data.
ALMA improves clustering of multilayer networks.
problem Clustering multilayer networks with distinct layers and communities.
method Alternating minimization algorithm (ALMA) for simultaneous layer partition and community estimation.
result ALMA achieves higher accuracy than TWIST in clustering multilayer networks.
A post-hoc framework improves model performance by calibrating different feature spaces.
problem Improving AUC performance on binary classification tasks for overconfident models.
method Identifies heterogeneous partitions of the feature space and applies post-hoc calibration techniques to each partition.
result Theoretical optimality of the framework for any model, demonstrated on deep neural networks.
Proposes a partitioned least squares model for feature grouping.
problem Modeling with feature groups to assess variable importance.
method Two methods: alternating least squares and exact reformulation.
result Exact method provides better results in less time.
Paper corrects GIRP algorithm to ensure isotonic models.
problem GIRP algorithm fails to produce isotonic models.
method Modified GIRP algorithm with binary partitioning.
result Correct solution exists and can be found.
We introduce a novel approach to feed-forward neural network interpretation based on partitioning the space of sequences of neuron activations. In line with this approach, we propose a model-specific interpretation method, called YASENN. Our method inherits many advantages of model-agnostic distillation, such as an abi…