New DRGP models improve prediction accuracy for sequential data.
problem Modeling sequential data for applications like autonomous driving.
method Introduces Deep recurrent Gaussian process (DRGP) models based on Sparse Spectrum Gaussian process (SSGP) and variational Sparse Spectrum Gaussian process (VSSGP).
result Improves prediction accuracy compared to current state of the art methods.
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for the sparse spectrum approximation to avoid both issues. We model the covariance fu…
Modeling sequential data has become more and more important in practice. Some applications are autonomous driving, virtual sensors and weather forecasting. To model such systems so called recurrent models are used. In this article we introduce two new Deep Recurrent Gaussian Process (DRGP) models based on the Sparse Sp…
While much research effort has been dedicated to scaling up sparse Gaussian process (GP) models based on inducing variables for big data, little attention is afforded to the other less explored class of low-rank GP approximations that exploit the sparse spectral representation of a GP kernel. This paper presents such a…
Two new methods improve block-sparse signal recovery from noisy data.
problem Recovering block-sparse signals with unknown partitions.
method LogLOP-l2/l1 and AdaLOP-l2/l1 methods using log-sum penalty and MCP.
result Our methods outperform existing techniques in estimation accuracy.
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this particular form of sparse approximations generates an overconfident GP, i.e. it produc…
New outlier detection method using graph Laplacian spectrum boosts performance.
problem Detecting outliers in large datasets efficiently.
method Boosted outlier detection based on graph Laplacian spectrum.
result Outperforms existing methods on synthetic datasets.
GEMSS discovers multiple sparse solutions in high-dimensional data.
problem Identifying multiple sparse feature combinations in high-dimensional, underdetermined systems.
method GEMSS (Gaussian Ensemble for Multiple Sparse Solutions) uses a structured spike-and-slab prior, mixture of Gaussians, and Jaccard-based penalty to optimize a single objective function via stochastic gradient descent.
result GEMSS consistently outperforms five feature selection methods on 128 experiments and real-world datasets.
Improved sample complexity for Gaussian process approximations.
problem Efficiently approximating Gaussian processes with sparse spectrum.
method Improved sample complexity analysis and auto-encoding algorithm.
result Gaussian process predictions and model evidence can be well-approximated with low sample complexity.
The paper confirms a Weyl law for the p-Laplacian on closed Riemannian manifolds.
problem The variational spectrum of the p-Laplacian on closed Riemannian manifolds.
method Based on ideas of Gromov and Liokumovich, Marques, Neves.
result A Weyl law holds for the variational spectrum of the p-Laplacian.
Gaussian process (GP) audio source separation is a time-domain approach that circumvents the inherent phase approximation issue of spectrogram based methods. Furthermore, through its kernel, GPs elegantly incorporate prior knowledge about the sources into the separation model. Despite these compelling advantages, the c…
New method prunes recurrent networks efficiently, improving performance.
problem Pruning recurrent neural networks (RNNs) is challenging and often leads to poor performance.
method Data-efficient pruning objective derived from the spectrum of the recurrent Jacobian.
result 95% sparse GRUs significantly improve on existing baselines.
A new method warps inputs to learn nonstationary kernels efficiently.
problem Learning nonstationary patterns in data with varying smoothness.
method Sparse spectrum Gaussian processes with input warping as conditional Gaussian measures.
result Efficient learning of nonstationary patterns with fewer parameters.
Paper develops efficient variational inference for sparse deep learning with theoretical guarantees.
problem Sparse deep learning's challenge of huge storage consumption and sparse structure recovery.
method Bayesian treatment with spike-and-slab priors and continuous relaxation of Bernoulli distribution for computationally efficient variational inferences.
result Provides variational posterior contraction rate, justifying consistency of the proposed method.
Mass spectrometry (MS) is an important technique for chemical profiling which calculates for a sample a high dimensional histogram-like spectrum. A crucial step of MS data processing is the peak picking which selects peaks containing information about molecules with high concentrations which are of interest in an MS in…
Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here we introduce a…
New method learns sparse distributions by thresholding samples, improving performance and efficiency.
problem Sparse coding optimization in high-dimensional problems is computationally expensive and inefficient.
method Proposes a new variational sparse coding approach that learns sparse distributions by thresholding samples.
result Shows superior performance, statistical efficiency, and gradient estimation compared to other sparse distributions.
While the harmonic function solution performs well in many semi-supervised learning (SSL) tasks, it is known to scale poorly with the number of samples. Recent successful and scalable methods, such as the eigenfunction method focus on efficiently approximating the whole spectrum of the graph Laplacian constructed from …
In this article we prove a generalization of Weyl's criterion for the spectrum of a self-adjoint nonnegative operator on a Hilbert space. We will apply this new criterion in combination with Cheeger-Fukaya-Gromov and Cheeger-Colding theory to study the k-form essential spectrum over a complete manifold with vanishing…
Multi-parameter cognition in a cognitive radio network (CRN) provides a more thorough understanding of the radio environments, and could potentially lead to far more intelligent and efficient spectrum usage for a secondary user. In this paper, we investigate the multi-parameter cognition problem for a CRN where the pri…
The paper analyzes uncertainty quantification in sparse Gaussian process regression with a Brownian motion prior.
problem Analyzing uncertainty in sparse Gaussian process regression with a Brownian motion prior.
method Theoretical guarantees and limitations for pointwise credible sets are derived for a rescaled Brownian motion prior with a sparse variational Gaussian process method.
result Theoretical characterization of asymptotic frequentist coverage for credible sets, distinguishing conservative and overconfident cases.
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the positive orthant of the unit sphere. This measure gathers information on the localizat…
VASE uses Bayesian neural networks to improve exploration in sparse reward environments.
problem Exploration in environments with continuous control and sparse rewards.
method VASE uses a Bayesian neural network model of the environment dynamics and variational inference to alternately update the model's accuracy and policy.
result VASE outperforms other surprise-based exploration techniques in continuous control sparse reward environments.
Develops SGP-VAE for efficient sparse GP inference in multi-dimensional datasets.
problem Sparse GP approximations and missing data in multi-dimensional spatio-temporal datasets.
method Leverages partial inference networks for sparse GP approximations and amortized variational inference.
result Outperforms multi-output GPs and structured VAEs in various experiments.
New method for hyperparameter tuning in sparse matrix factorization.
problem Hyperparameter tuning in sparse matrix factorization.
method Numerical method based on evaluating the zero point of normalization factor in sparse matrix prior.
result Our method outperforms existing algorithms in ground-truth sparse matrix reconstruction.
The angular power spectrum characterizes neural network complexity.
problem Characterizing the complexity of deep neural networks.
method Using the angular power spectrum of the limiting field to characterize network complexity.
result Classified neural networks as low-disorder, sparse, or high-disorder.
We propose a method for solving statistical mechanics problems defined on sparse graphs. It extracts a small Feedback Vertex Set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense interactions with an effective energy on every configuration of the FVS, then learn…
Introduces tunable basis functions for Gaussian processes.
problem Reduces computational complexity in Gaussian process approximations.
method Introduces tunable, local, and bounded basis functions for kernel approximation.
result Demonstrates superior performance compared to state-of-the-art methods, especially with poorly chosen kernel functions.
SVGP KAN integrates sparse variational GP with KANs for scalable probabilistic inference.
problem Lack of probabilistic outputs in standard KANs and cubic scaling of Gaussian Process methods.
method Sparse Variational GP-KAN combines KAN topology with sparse variational inference and permutation-based importance analysis.
result Enables probabilistic KANs to handle larger datasets with linear computational complexity.
Paper proposes a method to improve variational inference for sparse networks.
problem Variational inference struggles with sparse networks, leading to inaccurate community detection.
method The method involves hard thresholding the posterior of community assignment after each iteration.
result The proposed method accurately recovers true community labels in sparse networks.
Radio emitter recognition in dense multi-user environments is an important tool for optimizing spectrum utilization, identifying and minimizing interference, and enforcing spectrum policy. Radio data is readily available and easy to obtain from an antenna, but labeled and curated data is often scarce making supervised …
Paper tightens variational GP approximations for large datasets.
problem Scaling Gaussian processes to large datasets.
method Relaxing the standard assumption about inducing points' posterior matching the prior, leading to a tighter variational approximation.
result The proposed approximation consistently matches or outperforms standard sparse variational GPs while maintaining computational cost.
Improved sparse Gaussian processes using structured scaling matrices and Power-EP framework.
problem Scaling Gaussian processes for large datasets.
method Structured diagonal scaling matrix and Power-EP framework.
result Structured approximations improve performance without increasing computational cost.
A new method for efficient Gaussian process inference using sparse approximations.
problem Scalable and accurate inference for latent Gaussian processes.
method Variational approximation with sparse inverse Cholesky factors and double Kullback-Leibler minimization.
result The proposed method can achieve highly accurate approximations with polylogarithmic time complexity.
Recently, a number of mostly ℓ1-norm regularized least squares type deterministic algorithms have been proposed to address the problem of \emph{sparse} adaptive signal estimation and system identification. From a Bayesian perspective, this task is equivalent to maximum a posteriori probability estimation under a …
Improved model for non-smooth signals with complex spectra.
problem Current models struggle with non-smooth signals and complex spectral structures.
method CGPCM and RGPCM models with causality and Bayesian nonparametric interpretations, improved variational inference.
result Proposed models show better performance on synthetic and real-world data.
Study compares L1 and VG sparsity priors in inverse problems.
problem Sparse regularization in inverse problems with incomplete or corrupted measurements.
method Compared L1 regularization with Variational Garrote (VG), a probabilistic method approximating L0 sparsity.
result VG often achieves lower minimum generalization error and improved stability in strongly underdetermined regimes.
The study finds sparse sets that uniquely determine metrics on negatively curved manifolds.
problem Determining metrics on negatively curved manifolds using spectral data.
method Analyzing conjugacy classes and marked length spectra.
result Sparse sets exist that uniquely determine metrics on negatively curved manifolds.
New findings show sparse signals in MRA model require fewer measurements than previously thought.
problem Learning an unknown signal from repeated noisy images under group actions.
method Enhanced probabilistic method and analysis of uniform uncertainty principles.
result Sparse signals exhibit intermediate σ4 sample complexity, improving over traditional σ2. Adaptive variational Bayes framework improves inference adaptively.
problem Lack of general and computationally tractable variational Bayes method for adaptive inference.
method Proposes a novel adaptive variational Bayes framework combining variational posteriors over individual models.
result Adaptive variational Bayes achieves optimal contraction rates adaptively under general conditions.
New method improves GP regression by relaxing variational assumption.
problem Improving variational Gaussian processes for better predictive performance.
method Relaxing the variational assumption to a more general distribution for optimization.
result New tighter evidence lower bound for GP regression.
Improved VB algorithm for high-dimensional logistic regression with theoretical guarantees.
problem Sparse high-dimensional logistic regression model selection.
method Spike and slab variational Bayes approximation.
result Optimal convergence rates in ℓ2 and prediction loss for sparse truths. New interpretation of sparse Gaussian process approximations for scalability.
problem Scalability issues in Gaussian process models.
method Decomposes Gaussian process into two independent components: inducing points and remaining variation, leading to tighter bounds and new algorithms.
result Demonstrates efficiency in various Gaussian process models, including deep convolutional ones, achieving state-of-the-art results.
New method combines spectral and sparse methods for Gaussian processes.
problem Efficiently fitting Gaussian processes to large datasets.
method Orthogonally decoupled variational Fourier features.
result Competitive performance on synthetic and real-world data.
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods…
Sparse Polynomial Chaos expansions improve accuracy and efficiency in simulations.
problem Challenges in computational efficiency and accuracy for Polynomial Chaos modeling.
method Sparse Bayesian learning using Variational Relevance Vector Machines.
result Sparse Polynomial Chaos expansions achieve comparable performance to compressive sensing with fewer data points.
Post-process Bayesian inference speeds up posterior approximation.
problem Leveraging pre-existing model evaluations for quick posterior approximation.
method Variational Sparse Bayesian Quadrature (VSBQ) using sparse Gaussian process (GP) surrogate model.
result VSBQ builds high-quality posterior approximations from existing optimization traces.
We develop a sparse representation method for neural network uncertainty.
problem Estimating model uncertainty in neural networks.
method Sparse representation of model uncertainty using inverse Multivariate Normal Distribution (MND), with a novel sparsification algorithm and analytical sampler.
result The information form of neural networks can be effectively applied for model uncertainty representation, showing competitive performance.