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…
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48 results for “sparse spectrum”
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 frequently used. In this paper we introduce several new Deep recurrent Gaussian process (DRGP) models based on…
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.
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.
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…
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.
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…
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 …
Recent advances in the sparse neural network literature have made it possible to prune many large feed forward and convolutional networks with only a small quantity of data. Yet, these same techniques often falter when applied to the problem of recovering sparse recurrent networks. These failures are quantitative: when…
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.
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 …
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.
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…
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.
We empirically investigate the best trade-off between sparse and uniformly-weighted multiple kernel learning (MKL) using the elastic-net regularization on real and simulated datasets. We find that the best trade-off parameter depends not only on the sparsity of the true kernel-weight spectrum but also on the linear dep…
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.
This paper presents a Bayesian nonparametric latent feature model specially suitable for exploratory analysis of high-dimensional count data. We perform a non-negative doubly sparse matrix factorization that has two main advantages: not only we are able to better approximate the row input distributions, but the inferre…
New method for multiclass classification reduces error bounds.
problem High-dimensional multiclass classification with sparse coefficients.
method Sparse multinomial logistic regression with convex penalties.
result Plug-in classifiers achieve minimax generalization error bounds.
Spectral method detects communities in sparse hypergraphs, achieving detection threshold.
problem Community detection in sparse hypergraphs.
method Non-backtracking operator and spectral approach.
result Spectral method achieves detection threshold for sparse HSBMs.
Graph energy helps detect communities in networks better than traditional methods.
problem Detecting communities in sparse networks where traditional methods fail.
method Using graph energy based on the full spectrum of adjacency matrices.
result The difference in graph energy between a planted partition model and an Erdős--Rényi network has a distinct transition at the detectability threshold.
Sparse-mode DMD disambiguates local and global modes in spatiotemporal data.
problem Disambiguating local and global modes in spatiotemporal data.
method Sparse-mode DMD with sparsity-promoting regularization.
result Explicitly constructs discrete and continuous spectra.
Given two sets of variables, derived from a common set of samples, sparse Canonical Correlation Analysis (CCA) seeks linear combinations of a small number of variables in each set, such that the induced canonical variables are maximally correlated. Sparse CCA is NP-hard. We propose a novel combinatorial algorithm for s…
Sparse random features improve accuracy in data-scarce settings.
problem Limited accuracy of random feature methods in data-scarce applications.
method Sparse random feature expansion using compressive sensing.
result Improved generalization bounds for sparse random features.
We present an approach to model time series data from resting state fMRI for autism spectrum disorder (ASD) severity classification. We propose to adopt kernel machines and employ graph kernels that define a kernel dot product between two graphs. This enables us to take advantage of spatio-temporal information to captu…
Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity and low-rankness. It can handle both a non-symmetric and a symmetric tensor respo…
We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the target matrix by the scaled Lasso and then adjusts the matrix estimator to be symmet…
We analyze large, multi-dimensional, sparse counting data sets, finding unsupervised groups to provide unique insights into genetic data. We create gene and biological pathway groups based on patients' variants to find common risk factors for four common types of cancer (breast, lung, prostate, and colorectal) and auti…
The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that enables to build ultra-sparse NN (u-NN) graphs with guaranteed preservation of the or…
Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include previously unstudied graphs including kNN graphs. We also introduce a kernel-fr…
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…
Adaptive Bayesian model for covariate-dependent power spectra analysis.
problem Estimating complex relationships and interactions between covariates and power spectra.
method Bayesian sum of trees model with local power spectrum estimation and reversible-jump MCMC for tree modifications.
result The method can accurately recover both smooth and abrupt changes in power spectra across multiple covariates.
Bayesian method uses data spectra to estimate non-sparse high-dimensional models.
problem Handling many parameters in high-dimensional Bayesian statistics.
method Data-adaptive Gaussian prior aligned with leading eigenvectors of sample covariance.
result Posterior contraction rates reveal the effect of spectral mass on prediction error.
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.
The generalized partially linear additive model (GPLAM) is a flexible and interpretable approach to building predictive models. It combines features in an additive manner, allowing each to have either a linear or nonlinear effect on the response. However, the choice of which features to treat as linear or nonlinear is …
Conjugate gradient methods improve efficiency for high-dimensional GLMMs.
problem Efficiency bottleneck in computing high-dimensional GLMM precision matrices.
method Combining spectral analysis and random graph theory with conjugate gradient methods.
result CG-based methods achieve linear scaling in cost with model parameters and observations.
We define a new spectrum for compact length spaces and Riemannian manifolds called the "covering spectrum" which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers which identify the distinct covers of the space. We investigat…
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
This letter presents the sparse vector signal detection from one bit compressed sensing measurements, in contrast to the previous works which deal with scalar signal detection. In this letter, available results are extended to the vector case and the GLRT detector and the optimal quantizer design are obtained. Also, a …
Study the energy spectrum of metrics on surfaces and its relation to simple length spectrum.
problem Relate the energy spectrum to the simple length spectrum of metrics on surfaces.
method Analyze the energy spectrum of metrics on surfaces and their Teichmüller spaces, considering homotopy conditions.
result The energy spectrum determines the simple length spectrum under certain conditions.
We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, base…
We learn sparse precision matrices from compressed data sketches.
problem Learning a graph from high-dimensional data with limited storage.
method Estimate a sparse precision matrix from a sketch of the data using non-linear random features.
result It is possible to estimate a sparse precision matrix from a sketch of size $m=Ω\left((d+2k)\log(d)
ight)$.
Study shows spectrum properties for specific Hadamard manifolds.
problem Spectrum properties of Hadamard manifolds.
method Absolute continuity and spectrum determination for two classes of Hadamard manifolds.
result Spectrum properties determined for specific Hadamard manifolds.
Proofs high-dimensional spectrum convergence of weighted sample covariance.
problem High-dimensional spectrum convergence of weighted sample covariance.
method Proposes a new, concise proof with stronger assumptions.
result Spectrum convergence proven for different weight distributions.
Iterative method 'Concent' corrects spectrum bias in covariance matrices.
problem Consistent bias in the spectrum of covariance matrices.
method 'Concent' iterative algorithm.
result Corrects spectrum bias for small and moderate dimensions.