Topics

A Double-Variational Bayesian Framework in Random Fourier Features for Indefinite Kernels.

08:00 EDT 10th September 2019 | BioPortfolio

Summary of "A Double-Variational Bayesian Framework in Random Fourier Features for Indefinite Kernels."

Random Fourier features (RFFs) have been successfully employed to kernel approximation in large-scale situations. The rationale behind RFF relies on Bochner's theorem, but the condition is too strict and excludes many widely used kernels, e.g., dot-product kernels (violates the shift-invariant condition) and indefinite kernels [violates the positive definite (PD) condition]. In this article, we present a unified RFF framework for indefinite kernel approximation in the reproducing kernel Kreĭn spaces (RKKSs). Besides, our model is also suited to approximate a dot-product kernel on the unit sphere, as it can be transformed into a shift-invariant but indefinite kernel. By the Kolmogorov decomposition scheme, an indefinite kernel in RKKS can be decomposed into the difference of two unknown PD kernels. The spectral distribution of each underlying PD kernel can be formulated as a nonparametric Bayesian Gaussian mixtures model. Based on this, we propose a double-infinite Gaussian mixture model in RFF by placing the Dirichlet process prior. It takes full advantage of high flexibility on the number of components and has the capability of approximating indefinite kernels on a wide scale. In model inference, we develop a non-conjugate variational algorithm with a sub-sampling scheme for the posterior inference. It allows for the non-conjugate case in our model and is quite efficient due to the sub-sampling strategy. Experimental results on several large classification data sets demonstrate the effectiveness of our nonparametric Bayesian model for indefinite kernel approximation when compared to other representative random feature-based methods.

Affiliation

Journal Details

This article was published in the following journal.

Name: IEEE transactions on neural networks and learning systems
ISSN: 2162-2388
Pages:

Links

DeepDyve research library

PubMed Articles [13028 Associated PubMed Articles listed on BioPortfolio]

Variational representational similarity analysis.

This technical note describes a variational or Bayesian implementation of representational similarity analysis (RSA) and pattern component modelling (PCM). It considers RSA and PCM as Bayesian model c...

Bayesian Low-Tubal-Rank Robust Tensor Factorization with Multi-Rank Determination.

Robust tensor factorization is a fundamental problem in machine learning and computer vision, which aims at recovering tensors corrupted with outliers as a sum of the low-rank and sparse components. H...

Endoscopic submucosal dissection for gastric indefinite for neoplasia: which lesions should be resected?

The management plan for gastric indefinite for neoplasia is undetermined, and endoscopic forceps biopsy might be inconclusive in ascertaining whether a resection is required. This study aimed to evalu...

A stochastic variational framework for Recurrent Gaussian Processes models.

Gaussian Processes (GPs) models have been successfully applied to the problem of learning from sequential observations. In such context, the family of Recurrent Gaussian Processes (RGPs) have been rec...

The Optimally Designed Variational Autoencoder Networks for Clustering and Recovery of Incomplete Multimedia Data.

Clustering analysis of massive data in wireless multimedia sensor networks (WMSN) has become a hot topic. However, most data clustering algorithms have difficulty in obtaining latent nonlinear correla...

Clinical Trials [3951 Associated Clinical Trials listed on BioPortfolio]

Modeling Clinical Failure in Prostate Cancer Patients Based on a Two-stage Statistical Model

Biomarker series can indicate disease progression and predict clinical endpoints. When a treatment is prescribed depending on the biomarker, confounding by indication might be introduced i...

Comparison Between Injection Molded PEEK Framework and Cobalt Chromium Framework in Removable Partial Denture Regarding Retention

This study is aiming to evaluate the retentive forces in PEEK framework RPD compared to Cobalt-Chrome framework RPD during attachment/detachment cycles in mandibular kennedy class I edentu...

Fourier Transformed Infrared Spectroscopy in Macular Surgery

Epiretinal membranes (ERM) are disorders leading to vision loss and metamorphopsia. Vitrectomy with membrane peeling has developed to be the gold-standard in treatment of ERM. ERM can be w...

Reproducibility of Dual Beam Doppler Fourier-domain Optical Coherence Tomography in Healthy Subjects

Dual beam Doppler Fourier-domain Optical coherence tomography (DOCT) is a noninvasive technique to quantify total retinal blood flow. To enable further development of this technique it is...

Bayesian Hemodynamics Model for Personalized Monitoring of Congestive Heart Failure Patients

Heart failure (HF) is a serious and challenging syndrome. Globally 26 million people are living with this chronic disease and the prevalence is still increasing. Besides this growing numbe...

Medical and Biotech [MESH] Definitions

Analysis based on the mathematical function first formulated by Jean-Baptiste-Joseph Fourier in 1807. The function, known as the Fourier transform, describes the sinusoidal pattern of any fluctuating pattern in the physical world in terms of its amplitude and its phase. It has broad applications in biomedicine, e.g., analysis of the x-ray crystallography data pivotal in identifying the double helical nature of DNA and in analysis of other molecules, including viruses, and the modified back-projection algorithm universally used in computerized tomography imaging, etc. (From Segen, The Dictionary of Modern Medicine, 1992)

A genus of PROCHLOROPHYTES occurring in unbranched chains of indefinite length and containing both chlorophylls a and b.

The residual framework structure of the CELL NUCLEUS that maintains many of the overall architectural features of the cell nucleus including the nuclear lamina with NUCLEAR PORE complex structures, residual CELL NUCLEOLI and an extensive fibrogranular structure in the nuclear interior. (Advan. Enzyme Regul. 2002; 42:39-52)

A spectroscopic technique in which a range of wavelengths is presented simultaneously with an interferometer and the spectrum is mathematically derived from the pattern thus obtained.

Devices capable of receiving data, retaining data for an indefinite or finite period of time, and supplying data upon demand.

Quick Search


DeepDyve research library

Searches Linking to this Article