Hierarchical regularization networks for sparsification based learning
on noisy datasets
- URL: http://arxiv.org/abs/2006.05444v1
- Date: Tue, 9 Jun 2020 18:32:24 GMT
- Title: Hierarchical regularization networks for sparsification based learning
on noisy datasets
- Authors: Prashant Shekhar and Abani Patra
- Abstract summary: hierarchy follows from approximation spaces identified at successively finer scales.
For promoting model generalization at each scale, we also introduce a novel, projection based penalty operator across multiple dimension.
Results show the performance of the approach as a data reduction and modeling strategy on both synthetic and real datasets.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We propose a hierarchical learning strategy aimed at generating sparse
representations and associated models for large noisy datasets. The hierarchy
follows from approximation spaces identified at successively finer scales. For
promoting model generalization at each scale, we also introduce a novel,
projection based penalty operator across multiple dimension, using permutation
operators for incorporating proximity and ordering information. The paper
presents a detailed analysis of approximation properties in the reconstruction
Reproducing Kernel Hilbert Spaces (RKHS) with emphasis on optimality and
consistency of predictions and behavior of error functionals associated with
the produced sparse representations. Results show the performance of the
approach as a data reduction and modeling strategy on both synthetic
(univariate and multivariate) and real datasets (time series). The sparse model
for the test datasets, generated by the presented approach, is also shown to
efficiently reconstruct the underlying process and preserve generalizability.
Related papers
- Fast and Scalable Semi-Supervised Learning for Multi-View Subspace Clustering [13.638434337947302]
FSSMSC is a novel solution to the high computational complexity commonly found in existing approaches.
The method generates a consensus anchor graph across all views, representing each data point as a sparse linear combination of chosen landmarks.
The effectiveness and efficiency of FSSMSC are validated through extensive experiments on multiple benchmark datasets of varying scales.
arXiv Detail & Related papers (2024-08-11T06:54:00Z) - Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein [56.62376364594194]
Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets.
In this work, we revisit these approaches under the lens of optimal transport and exhibit relationships with the Gromov-Wasserstein problem.
This unveils a new general framework, called distributional reduction, that recovers DR and clustering as special cases and allows addressing them jointly within a single optimization problem.
arXiv Detail & Related papers (2024-02-03T19:00:19Z) - Joint Distributional Learning via Cramer-Wold Distance [0.7614628596146602]
We introduce the Cramer-Wold distance regularization, which can be computed in a closed-form, to facilitate joint distributional learning for high-dimensional datasets.
We also introduce a two-step learning method to enable flexible prior modeling and improve the alignment between the aggregated posterior and the prior distribution.
arXiv Detail & Related papers (2023-10-25T05:24:23Z) - RGM: A Robust Generalizable Matching Model [49.60975442871967]
We propose a deep model for sparse and dense matching, termed RGM (Robust Generalist Matching)
To narrow the gap between synthetic training samples and real-world scenarios, we build a new, large-scale dataset with sparse correspondence ground truth.
We are able to mix up various dense and sparse matching datasets, significantly improving the training diversity.
arXiv Detail & Related papers (2023-10-18T07:30:08Z) - Large-scale Fully-Unsupervised Re-Identification [78.47108158030213]
We propose two strategies to learn from large-scale unlabeled data.
The first strategy performs a local neighborhood sampling to reduce the dataset size in each without violating neighborhood relationships.
A second strategy leverages a novel Re-Ranking technique, which has a lower time upper bound complexity and reduces the memory complexity from O(n2) to O(kn) with k n.
arXiv Detail & Related papers (2023-07-26T16:19:19Z) - DDAC-SpAM: A Distributed Algorithm for Fitting High-dimensional Sparse
Additive Models with Feature Division and Decorrelation [16.232378903482143]
We propose a new distributed statistical learning algorithm, DDAC-SpAM, which divides the features under a high-dimensional sparse additive model.
The effectiveness and efficiency of the proposed algorithm are demonstrated through theoretical analysis and empirical results on both synthetic and real data.
Our approach provides a practical solution for fitting sparse additive models, with promising applications in a wide range of domains.
arXiv Detail & Related papers (2022-05-16T18:31:03Z) - Latent Space Model for Higher-order Networks and Generalized Tensor
Decomposition [18.07071669486882]
We introduce a unified framework, formulated as general latent space models, to study complex higher-order network interactions.
We formulate the relationship between the latent positions and the observed data via a generalized multilinear kernel as the link function.
We demonstrate the effectiveness of our method on synthetic data.
arXiv Detail & Related papers (2021-06-30T13:11:17Z) - A Forward Backward Greedy approach for Sparse Multiscale Learning [0.0]
We propose a feature driven Reproducing Kernel Hilbert space (RKHS) for which the associated kernel has a weighted multiscale structure.
For generating approximations in this space, we provide a practical forward-backward algorithm that is shown to greedily construct a set of basis functions having a multiscale structure.
We analyze the performance of the approach on a variety of simulation and real data sets.
arXiv Detail & Related papers (2021-02-14T04:22:52Z) - Out-of-distribution Generalization via Partial Feature Decorrelation [72.96261704851683]
We present a novel Partial Feature Decorrelation Learning (PFDL) algorithm, which jointly optimize a feature decomposition network and the target image classification model.
The experiments on real-world datasets demonstrate that our method can improve the backbone model's accuracy on OOD image classification datasets.
arXiv Detail & Related papers (2020-07-30T05:48:48Z) - Model Fusion with Kullback--Leibler Divergence [58.20269014662046]
We propose a method to fuse posterior distributions learned from heterogeneous datasets.
Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors.
arXiv Detail & Related papers (2020-07-13T03:27:45Z) - Asymptotic Analysis of an Ensemble of Randomly Projected Linear
Discriminants [94.46276668068327]
In [1], an ensemble of randomly projected linear discriminants is used to classify datasets.
We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator.
We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
arXiv Detail & Related papers (2020-04-17T12:47:04Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.