Divide-and-conquer method splits large data sets for efficient analysis.
problem Handling large data sets that exceed computational limits.
method Split data into smaller sets, analyze each separately, then combine results.
result Combined results provide statistical inference similar to analyzing entire data set.
This paper analyzes divide-and-conquer estimators for functional linear regression without assuming target function in the RKHS.
problem Functional linear regression without target function in RKHS.
method Integral operator approach to establish upper bounds and prove asymptotic optimality.
result Sharp finite sample upper bounds and asymptotic optimality of divide-and-conquer estimators.
In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks. We propose two algorithms which perform clustering on a number of small subgraphs and finally patches the results into a single clustering. The main advantage of these algorithms is that they bring down si…
We propose a novel class of Sequential Monte Carlo (SMC) algorithms, appropriate for inference in probabilistic graphical models. This class of algorithms adopts a divide-and-conquer approach based upon an auxiliary tree-structured decomposition of the model of interest, turning the overall inferential task into a coll…
DiCoLa recursively decomposes causal structure learning for latent variables.
problem Learning causal structures in high-dimensional settings with latent variables.
method Recursive decomposition framework for divide-and-conquer causal discovery.
result Theoretical soundness and completeness of DiCoLa framework.
SwISS improves scalability of Bayesian inference for large datasets.
problem Scalability issues in Bayesian inference for large datasets.
method Divide-and-conquer approach with SwISS for recombining sub-posterior samples.
result SwISS accurately approximates the original posterior distribution.
Tuning parameter selection is of critical importance for kernel ridge regression. To this date, data driven tuning method for divide-and-conquer kernel ridge regression (d-KRR) has been lacking in the literature, which limits the applicability of d-KRR for large data sets. In this paper, by modifying the Generalized Cr…
Study risk bounds for distributed ERM with general loss functions and hypothesis spaces.
problem Limited theoretical analysis for distributed ERM with general loss functions and hypothesis spaces.
method Derive tight risk bounds under assumptions on hypothesis space and loss function.
result Developed more general risk bound for distributed ERM without strong convexity restriction.
Paper connects two portfolio methods, HRP and Minimum Variance, revealing their underlying similarity.
problem Inability to universally adopt optimization-based portfolio construction methods.
method Unifies Hierarchical Risk Parity and Minimum Variance approaches.
result Schur complementary allocation reveals the connection between HRP and Minimum Variance.
We improve kernel ridge regression for skewed responses using oversampling and adaptive partitioning.
problem Kernel ridge regression struggles with skewed response variables, leading to poor estimates.
method Combines adaptive partitioning with oversampling to address skewed responses in kernel ridge regression.
result The proposed method yields estimates with smaller risk compared to classical methods under mild conditions.
We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures. We justify our approach by proving that modestly correlated, large stochastic blo…
New method for efficient inference in large datasets.
problem Statistical inference in massive datasets.
method Combines divide-and-conquer method and empirical likelihood.
result Reduces computation burden and demonstrates effectiveness.
Twinning splits data into fast, statistically similar sets.
problem Creating statistically similar data splits for Big Data.
method Twinning is a method based on SPlit for fast, model-independent dataset splitting.
result Twinning is orders of magnitude faster than SPlit.
Divide-and-conquer framework speeds up black-box inference for large data.
problem Computational intractability of uncertainty quantification for expensive data simulation.
method Divide data into partitions, train on a subset, bootstrap on partitions, combine results.
result Feasibility of estimating max-stable process parameters with tens of thousands of locations.
New method merges MCMC samples without distributional assumptions.
problem Efficiently merging MCMC samples from disjoint subsets.
method Diffusion generative modelling for density approximation.
result Outperforms existing methods on high-dimensional problems.
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important characteristic for large distributed systems. We establish connections between performance of…
Divide-and-conquer method speeds sparse factorization for large matrices.
problem Sparse factorization of large matrices for statistical learning.
method Statistical problem formulation, divide-and-conquer approach, stagewise learning.
result Efficient algorithm with lower complexity than existing methods.
A new Fusion method combines multiple distributions efficiently.
problem Combining multiple distributions for big data or privacy.
method Recursive divide-and-conquer Monte Carlo approach.
result A robust Fusion method for many sub-posteriors.
We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks that are amenable to the principle of divide and conquer, and study what are it…
Study analyzes crypto asset risk exposures using a divide-and-conquer approach.
problem Lack of high-frequency macro-financial proxies for estimating risk.
method Two-stage divide-and-conquer approach: first stage estimates idiosyncratic and market risk, second stage identifies latent economy-wide factors.
result Heterogeneous exposures to idiosyncratic and systematic risk across crypto assets.
For Bayesian computation in big data contexts, the divide-and-conquer MCMC concept splits the whole data set into batches, runs MCMC algorithms separately over each batch to produce samples of parameters, and combines them to produce an approximation of the target distribution. In this article, we embed random forests …
New algorithm groups variables by ancestral relationships to improve causal graph estimation accuracy.
problem Difficulty in estimating causal graphs with small sample sizes relative to variables.
method CAG algorithm groups variables based on ancestral relationships, reducing complexity and improving accuracy.
result CAG outperforms existing methods in estimation accuracy and computation time.
DC-NAS improves neural architecture search by clustering and evaluating sub-networks.
problem Inaccurate evaluation of neural architectures in large search spaces.
method Divide-and-Conquer approach: feature representation, clustering, and evaluation of clusters.
result Achieved 75.1% top-1 accuracy on ImageNet, surpassing state-of-the-art methods.
Develops a new method to recover large latent tree models efficiently.
problem Inference of large latent tree structures from terminal node observations.
method Spectral Top-Down Recovery (STDR) using Fiedler vector partitioning.
result Proves statistical consistency and sample complexity for accurate tree recovery.
SDSR reconstructs species trees from genetic markers efficiently.
problem Challenges in reconstructing species trees from genetic data.
method Spectral divide-and-conquer approach based on graph theory.
result SDSR achieves up to 10-fold faster runtime with comparable accuracy.
Active learning (AL) repeatedly trains the classifier with the minimum labeling budget to improve the current classification model. The training process is usually supervised by an uncertainty evaluation strategy. However, the uncertainty evaluation always suffers from performance degeneration when the initial labeled …
The deep layers of modern neural networks extract a rather rich set of features as an input propagates through the network. This paper sets out to harvest these rich intermediate representations for quantization with minimal accuracy loss while significantly reducing the memory footprint and compute intensity of the DN…
Paper speeds up Gaussian process inference using Matérn kernels.
problem Efficiently performing Gaussian process inference for large datasets.
method Exact Matérn kernel decomposition into empirical cumulative distribution functions, combined with divide-and-conquer approach.
result The proposed algorithm significantly speeds up Gaussian process inference for low-dimensional problems with hundreds of thousands of data points.
New method quantifies uncertainty in distributed regression.
problem Large datasets make traditional regression techniques ineffective.
method Data-driven approach to uncertainty quantification for averaged estimator.
result Rigorous theoretical guarantees for sup-norm consistency.
In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form solution. By recursively solving these sub-problems in an analytical way, an ef…
We show how to use Bar-Natan's `divide and conquer' approach to computations to efficiently compute the universal sl(2) dotted foam cohomology groups, even for big knots and links. We also describe a purely topological version of the sl(2) foam theory, in the sense that no dots are needed on foams.
A new method for sampling complex posterior distributions in DDMs.
problem Challenging posterior distributions in DDMs.
method Divide-and-Conquer Posterior Sampling (DCPS)
result Significantly reduces approximation error without retraining.
Two new scalable K-means initialization methods proposed for large-scale clustering.
problem Efficient initialization for large-scale clustering problems.
method Divide-and-conquer approach and random projection method for multiple lower-dimensional subspaces.
result The proposed methods outperform state-of-the-art in large-scale clustering tasks.
This paper introduces a divide-and-conquer inspired adversarial learning (DACAL) approach for photo enhancement. The key idea is to decompose the photo enhancement process into hierarchically multiple sub-problems, which can be better conquered from bottom to up. On the top level, we propose a perception-based division…
A new predictive coding algorithm improves machine learning performance.
problem Improving performance of variational inference algorithms in high-dimensional, structured problems.
method Divide-and-Conquer Predictive Coding (DCPC) that respects generative model correlation structure and performs maximum-likelihood updates.
result DCPC achieves better numerical performance and accurate inference in structured generative models.
New algorithm ranks players from partial comparisons with optimal rate.
problem Ranking players from partial pairwise comparisons.
method Divide-and-conquer approach, local MLE within groups.
result Optimal ranking algorithm with minimax rate.
Dual-T method improves transition matrix estimation in noisy label learning.
problem Large estimation error in noisy class posterior leads to poor transition matrix estimation.
method Introducing an intermediate class to avoid direct estimation of noisy class posterior, factorizing the transition matrix into two easier-to-estimate matrices.
result The dual-T estimator leads to better classification performances.
We reduce a broad class of machine learning problems, usually addressed by EM or sampling, to the problem of finding the k extremal rays spanning the conical hull of a data point set. These k "anchors" lead to a global solution and a more interpretable model that can even outperform EM and sampling on generalizatio…
SURF simplifies distribution estimation with simple, robust, and fast algorithms.
problem Efficient and accurate distribution estimation in statistics and machine learning.
method Piecewise polynomial approximation using empirical probability interpolation and divide-and-conquer merging.
result Surpassing state-of-the-art algorithms in efficiency and accuracy, SURF estimates distributions robustly and quickly.
Novel hybrid method for Bayesian network structure learning reduces computational time without sacrificing accuracy.
problem Bayesian network structure learning efficiency and accuracy trade-off.
method Partitioned PC (pPC), p-value adjacency thresholding (PATH), hybrid greedy initialization (HGI). result pHGS achieves significant computational reductions compared to the PC algorithm without sacrificing structure learning accuracy.
uMoE trains NNs with uncertain data by embedding uncertainty into training.
problem Managing aleatoric uncertainty in NN-based predictive models.
method Divide and Conquer strategy, Expert components, Gating Unit.
result uMoE outperforms baseline methods in uncertainty management.
We present a novel cross-view classification algorithm where the gallery and probe data come from different views. A popular approach to tackle this problem is the multi-view subspace learning (MvSL) that aims to learn a latent subspace shared by multi-view data. Despite promising results obtained on some applications,…
Paper introduces PTL-SI for statistical inference in TL-HDR, controlling FPR.
problem Quantifying statistical significance in TL-HDR with limited data.
method PTL-SI framework for valid p-values in TL-HDR feature selection. result Valid p-values and controlled FPR in TL-HDR feature selection. We use the divide-and-conquer and scanning algorithms for calculating Khovanov cohomology directly on the Lee- or Bar-Natan deformations of the Khovanov complex to give an alternative way to compute Rasmussen s-invariants of knots. By disregarding generators away from homological degree 0 we can considerably improve …
Efficient algorithm for Bayesian networks reduces marginal probability distribution computation.
problem Exact computation of marginal probability distribution is NP-hard for categorical variables in Bayesian networks.
method Divide-and-conquer approach exploiting graphical properties of Bayesian networks.
result Novel algorithm outperforms state-of-the-art methods in classification and cancer subtype identification.
Study metric learning from limited preference comparisons, showing how low-dimensional structure can still reveal metric information.
problem Learning metric from limited pairwise preference comparisons.
method Ideal point model, divide-and-conquer approach for low-dimensional structure.
result Metric can be jointly identified even with limited comparisons when items exhibit low-dimensional structure.
The paper develops efficient estimators for semi-parametric binary models in distributed computing.
problem Estimation and inference challenges in large-scale data under non-smooth objective functions.
method Proposes one-shot and multi-round divide-and-conquer estimators with adaptive kernel smoothing to relax constraints and achieve superlinear optimization error.
result Establishes quadratic convergence up to optimal statistical error rate and handles dataset heterogeneity and high-dimensional sparse parameters.
Divide-and-conquer is a general strategy to deal with large scale problems. It is typically applied to generate ensemble instances, which potentially limits the problem size it can handle. Additionally, the data are often divided by random sampling which may be suboptimal. To address these concerns, we propose the $DC^…