BP pretreatment reduces multi-label classification time.
problem Efficiently annotate large label sets for extreme multi-label classification.
method Divide instances into clusters, attach most relevant labels, train on pairs of clusters.
result BP reduces prediction time significantly without sacrificing accuracy.
BlockEcho method improves imputation of block-wise missing data.
problem Block-wise missing data reduces interpolation capability and predictive power.
method Integrates Matrix Factorization (MF) within Generative Adversarial Networks (GAN) to retain long-distance inter-element relationships.
result Superior performance on public datasets across three domains, especially at higher missing rates.
DiffusionBlocks trains neural networks by breaking them into independent blocks, reducing memory usage.
problem Memory bottlenecks in end-to-end neural network training.
method Transforming transformer-based networks into independent trainable blocks via a denoising process.
result Independent block-wise training matches end-to-end training performance while reducing memory requirements.
The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection methods to update the entire coefficient vector simultaneously at e…
New algorithms solve complex minimax problems without needing derivatives.
problem Solving nonconvex-concave minimax problems efficiently.
method Zeroth-order alternating and proximal gradient algorithms.
result Iteration complexity and function value estimation bounds established.
Paper proposes an algorithm for robust estimation using Huber's criterion.
problem Non-convexity and non-robustness of joint maximum likelihood estimation.
method Block-wise minimization majorization framework with data-adaptive step sizes.
result Improved convergence and robustness in sparse learning.
Existing MAP inference algorithms for determinantal point processes (DPPs) need to calculate determinants or conduct eigenvalue decomposition generally at the scale of the full kernel, which presents a great challenge for real-world applications. In this paper, we introduce a class of DPPs, called BwDPPs, that are char…
FunCLBM clusters time series data for autonomous driving validation.
problem Validation of autonomous driving systems using large amounts of data.
method FunCLBM model for co-clustering high-dimensional time series data.
result FunCLBM provides structured partition and clustering views of datasets.
Improved EXACT strategy reduces GNN memory consumption and runtime.
problem Efficiently training large-scale GNNs with reduced memory usage.
method Block-wise quantization of intermediate activation maps with improved variance minimization.
result Further reduction in memory consumption (>15%) and runtime speedup (5%) with similar performance trade-offs.
We propose a penalized likelihood method to jointly estimate multiple precision matrices for use in quadratic discriminant analysis and model based clustering. A ridge penalty and a ridge fusion penalty are used to introduce shrinkage and promote similarity between precision matrix estimates. Block-wise coordinate desc…
Dynamic sparseness reduces neural network computation by selectively omitting parts of computations.
problem Reducing the computational and memory footprint of neural networks.
method Combining dynamic sparseness with block-wise matrix-vector multiplications to selectively omit parts of computations.
result The proposed method outperforms static sparseness and achieves similar perplexities at half the computational cost.
Model compression is essential for serving large deep neural nets on devices with limited resources or applications that require real-time responses. As a case study, a state-of-the-art neural language model usually consists of one or more recurrent layers sandwiched between an embedding layer used for representing inp…
AdapDISCOM tackles high-dimensional multimodal data with missingness and errors, improving prediction and biomarker selection.
problem High-dimensional multimodal data with block-wise missingness and measurement errors.
method AdapDISCOM introduces modality-specific weighting schemes to address heterogeneity and error magnitudes.
result AdapDISCOM consistently outperforms existing methods under heterogeneous contamination and heavy-tailed distributions.
We propose an approach to reduce the bias of ridge regression and regularization kernel network. When applied to a single data set the new algorithms have comparable learning performance with the original ones. When applied to incremental learning with block wise streaming data the new algorithms are more efficient due…
Proposes BONMI for integrating noisy matrices from multi-source data.
problem Integrating noisy matrices from multi-source data with block-wise missingness.
method Exploits orthogonal Procrustes problem to align eigenspaces and completes missing blocks.
result Statistical rate for eigenspace of underlying matrix comparable to independently missing assumption.
Develops a multichannel deep network for faster, artifact-free image CS.
problem Block-wise sampling artifacts in image CS with multiple sampling rates.
method Multichannel deep network for block-based image CS, removing blocking artifacts.
result Significantly outperforms state-of-the-art CS methods in objective and subjective metrics.
Latent Block-Diffusion Temporal Point Processes (LBDTPP) is a semi-autoregressive framework for generating asynchronous event sequences.
problem Generating asynchronous event sequences
method Latent Block-Diffusion Temporal Point Processes
result Outperforms state-of-the-art TPP baselines in both unconditional and conditional generation tasks
Knowledge distillation (KD) is a popular method for reducing the computational overhead of deep network inference, in which the output of a teacher model is used to train a smaller, faster student model. Hint training (i.e., FitNets) extends KD by regressing a student model's intermediate representation to a teacher mo…
This paper revisits the classic iterative proportional scaling (IPS) from a modern optimization perspective. In contrast to the criticisms made in the literature, we show that based on a coordinate descent characterization, IPS can be slightly modified to deliver coefficient estimates, and from a majorization-minimizat…
Paper proposes efficient methods for clustering and signal recovery in high-dimensional data with block structures.
problem High-dimensional clustering and signal recovery under block signal structures.
method CFA-PCA and MA-PCA methods for sparse and dense block signals.
result Proposed methods achieve computational minimax optimality for clustering and signal recovery.
Sequential coordinate ascent is more robust in high-dimensional linear regression.
problem Behavior difference between sequential and parallel coordinate ascent in variational inference.
method Comparison of sequential and parallel coordinate ascent algorithms in high-dimensional linear regression.
result Sequential algorithm converges under more relaxed conditions than parallel algorithm.
Paper proposes a new method for estimating conditional densities using logistic regressions.
problem Estimating conditional densities for complex distributions.
method Parametric conditional density estimation via weighted logistic regressions.
result Maximum likelihood estimates can be obtained efficiently via a block-wise alternating maximization scheme and local case-control sampling.
We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We formulate two convex optimization problems to jointly learn the metric and the clas…
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.
Paper proposes protecting DNN models with secret key preprocessing.
problem Protecting deep learning models from unauthorized access.
method Block-wise pixel shuffling with secret key for preprocessing.
result Protected models maintain close performance to non-protected models with correct key, but accuracy drops significantly with incorrect key.
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.
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.
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…
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.
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.
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.
We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of the signed Laplacian may be meaningless, in contrast to partitioning based on th…
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.
Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different p…
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.