New theory allows ICA without assuming non-Gaussian sources.
problem Traditional ICA struggles with Gaussian sources.
method Developed identifiability theory based on second-order statistics and sparsity.
result Identifiability theory and estimation methods validated experimentally.
A new method reduces energy consumption in machine learning by using multiple, less costly data sources.
problem High computational and energy costs in machine learning model training.
method Augmented Gaussian Process (AGP-MISO) with multi-source optimization.
result The AGP-MISO method reduces computational time and energy consumption compared to traditional approaches.
Study uses Wasserstein distance to identify causal orders and unmix sources.
problem Identifying causal relationships and separating sources in non-Gaussian data.
method Wasserstein distance for non-Gaussianity, linear ICA, causal inference.
result Exact identification of ICA unmixing matrix and causal orders.
Optimizes black-box functions with varying costs across multiple sources.
problem Optimizing black-box functions with varying costs across multiple sources.
method Uses Augmented Gaussian Process and Gaussian Process to model fidelity and location-dependent costs, respectively. Uses Confidence Bound acquisition function to select sources and locations.
result The approach significantly outperforms existing methods on Hyperparameters Optimization tasks.
Develops large-sample theory for non-stationary source separation.
problem Lack of large-sample results for non-stationary source separation methods.
method Large-sample theory for NSS-JD method under specific assumptions.
result Consistency of unmixing estimator and its convergence to Gaussian distribution.
PDGMM-VAE uses adaptive priors for better ICA recovery.
problem Nonlinear ICA recovery of latent source signals.
method Adaptive per-dimension Gaussian mixture model priors in a variational autoencoder.
result PDGMM-VAE effectively recovers source-specific non-Gaussian marginals.
Paper tackles online multi-source domain adaptation using Gaussian mixtures and dictionary learning.
problem Adapting multiple, heterogeneous source domains to a target domain in a streaming fashion.
method Introduces a novel approach for online fitting of Gaussian Mixture Models based on Wasserstein geometry, combined with dataset dictionary learning.
result Demonstrates ability to adapt 'on the fly' to target domain data streams.
HTFM improves mode coverage and tail-statistic recovery for heavy-tailed data.
problem Tackles heavy-tailed data in various domains with rare events.
method Proposes a framework using clock-conditioned Gaussian sources and truncated logsignature features.
result Improves mode coverage, sample quality, and tail-statistic recovery over Gaussian flow matching and baselines.
Proposes LVGP for multi-source data fusion in science and engineering.
problem Differences in quality and comprehensiveness of data sources.
method Latent Variable Gaussian Process (LVGP) framework.
result Improved predictions for sparse-data problems.
Plug-and-play L-GM-AMP improves CS recovery for any i.i.d. source prior.
problem Efficiently recovering signals from compressed measurements with unknown priors.
method Deep learning with Gaussian-mixture model to approximate source prior, combined with learned denoising.
result L-GM-AMP achieves state-of-the-art performance without prior knowledge of source distribution.
We extend the mixtures of Gaussians (MOG) model to the projected mixture of Gaussians (PMOG) model. In the PMOG model, we assume that q dimensional input data points z_i are projected by a q dimensional vector w into 1-D variables u_i. The projected variables u_i are assumed to follow a 1-D MOG model. In the PMOG model…
New Gaussian min-max theorem extends classical results to non-i.i.d. Gaussian matrices.
problem Extending classical Gaussian min-max theorems to non-i.i.d. Gaussian matrices.
method Identifying a new pair of Gaussian processes that satisfy comparison inequalities.
result New Gaussian min-max and convex Gaussian min-max theorems with applications in multi-source Gaussian regression and binary classification.
AR-Flow VAE improves blind source separation with flexible autoregressive priors.
problem Unsupervised blind source separation of latent signals from mixtures.
method AR-Flow VAE uses autoregressive flows to model latent sources, enhancing flexibility and capturing complex dependencies.
result AR-Flow VAE effectively separates latent sources, demonstrating improved performance over conventional methods.
StrEBM learns distinct latent components for better source separation.
problem Blind source separation with identifiable and decoupled latent components.
method Structured latent energy-based model with learnable structural biases.
result The model effectively recovers source components from mixed signals.
Proposes a framework to fuse heterogeneous data sources for better modeling.
problem Heterogeneous data sources with different input parameter spaces.
method Input mapping calibration (IMC) and latent variable Gaussian process (LVGP).
result Improved predictive accuracy over single source models.
Enhanced FastMNMF for better speech separation.
problem Improving blind source separation for speech.
method Gaussian scale mixture (GSM) for heavy-tailed distributions.
result GSM-FastMNMF outperforms existing methods in speech enhancement.
In this paper we address a classification problem where two sources of labels with different levels of fidelity are available. Our approach is to combine data from both sources by applying a co-kriging schema on latent functions, which allows the model to account item-dependent labeling discrepancy. We provide an exten…
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…
We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The proposed encoding algorithm sequentially chooses columns of the design matrix to suc…
StrADiff separates sources from mixtures without labels, using structured priors.
problem Blind source separation of linear and nonlinear mixtures without labeled data.
method Structured Source-Wise Adaptive Diffusion Framework with Gaussian process priors.
result StrADiff can recover latent source trajectories in an unsupervised manner, especially stable in linear mixtures.
We introduce a probabilistic generative model for disentangling spatio-temporal disease trajectories from series of high-dimensional brain images. The model is based on spatio-temporal matrix factorization, where inference on the sources is constrained by anatomically plausible statistical priors. To model realistic tr…
LMGPs enable efficient, accurate data fusion across multiple data sources.
problem Data fusion across multi-fidelity data sources in engineering design.
method Latent-map Gaussian processes (LMGPs) for efficient and accurate data fusion.
result LMGPs provide increased accuracy, reduced costs, and flexibility to fuse any number of data sources.
Gaussian processes are a class of flexible nonparametric Bayesian tools that are widely used across the sciences, and in industry, to model complex data sources. Key to applying Gaussian process models is the availability of well-developed open source software, which is available in many programming languages. In this …
CCVFM uses coreset to improve generative models by refining residual flows.
problem Generating multimodal distributions from scratch is challenging.
method Augments hierarchical rectified flow with a data-informed source distribution using a coreset.
result CCVFM achieves competitive few-step generation without a learned noise-to-data map.
Paper tackles MSDA with GMMs and OT, improving over prior art.
problem Adapting multiple heterogeneous source measures to a target measure.
method Optimal Transport between Gaussian Mixture Models, with novel barycenter calculation.
result Improves image classification and fault diagnosis benchmarks.
Method quantifies sensitivity of reliability analysis to uncertainty sources.
problem Computational expense in reliability analysis of complex models.
method Gaussian process surrogate model, active learning, sensitivity analysis.
result Reduces main source of error in estimating rare event probabilities.
SYNC generates synthetic data from aggregated sources using Gaussian copulas.
problem Creating synthetic datasets from aggregated sources.
method SYNC uses Gaussian copula models to infer high-resolution data from low-resolution sources.
result SYNC successfully merges sampled subsets into a single synthetic dataset.
In magnetoencephalography (MEG) the conventional approach to source reconstruction is to solve the underdetermined inverse problem independently over time and space. Here we present how the conventional approach can be extended by regularizing the solution in space and time by a Gaussian process (Gaussian random field)…
Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data widely used in observational sciences. In its classical form, ICA relies on modeling the data as a linear mixture of non-Gaussian independent sources. The problem can be seen as a likelihood maximization problem. We i…
This paper presents an unsupervised method that trains neural source separation by using only multichannel mixture signals. Conventional neural separation methods require a lot of supervised data to achieve excellent performance. Although multichannel methods based on spatial information can work without such training …
Study derives error decay rates for kernel classification under source and capacity conditions.
problem Understanding prediction error decay rates for real data sets.
method Derived decay rates for misclassification error under Gaussian design for SVM and ridge classification.
result Rates accurately describe learning curves for data sets satisfying source and capacity conditions.
In this work, we present an extension of Gaussian process (GP) models with sophisticated parallelization and GPU acceleration. The parallelization scheme arises naturally from the modular computational structure w.r.t. datapoints in the sparse Gaussian process formulation. Additionally, the computational bottleneck is …
We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a design matrix. Called a Sparse Superposition or Sparse Regression codebook, this s…
A novel Gaussian process approach for deconvolution of missing data signals.
problem Recovering a latent source from observations with missing parts and unknown filters.
method Gaussian process prior for Bayesian nonparametric deconvolution.
result The proposed Gaussian process deconvolution (GPDC) method is feasible and effective.
A new method for binary ICA using non-stationary sources.
problem Independent component analysis of binary data.
method Linear mixing model in latent space, followed by binary observation model with non-stationary sources.
result Proves non-identifiability with few observed variables but identifies with more variables.
This paper evaluates heterogeneous information fusion using multi-task Gaussian processes in the context of geological resource modeling. Specifically, it empirically demonstrates that information integration across heterogeneous information sources leads to superior estimates of all the quantities being modeled, compa…
This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a…
This article addresses the modeling of reverberant recording environments in the context of under-determined convolutive blind source separation. We model the contribution of each source to all mixture channels in the time-frequency domain as a zero-mean Gaussian random variable whose covariance encodes the spatial cha…
FlowMO uses Gaussian Processes for molecular property prediction with uncertainty.
problem Predicting molecular properties with uncertainty for small datasets.
method Gaussian Processes implemented in FlowMO, built on GPflow and RDKit.
result Comparable predictive performance to deep learning but superior uncertainty calibration.
New algorithm identifies causal effects in latent confounding models.
problem Identifying causal effects in linear non-Gaussian models with latent confounding.
method Recursive algorithm using rank conditions on higher-order cumulants.
result Algorithm achieves comparable performance to overcomplete ICA without knowing the number of latent variables.
Proposes a method to combine datasets with missing values using Gaussian process latent variables.
problem Combining datasets with missing values under non-Missing at Random (NMAR) missingness.
method Gaussian process latent variable model for non-MAR missing data.
result Valid estimates are obtained using the proposed method, while existing methods provide severely biased estimates.
We propose a new blind source separation algorithm based on mixtures of alpha-stable distributions. Complex symmetric alpha-stable distributions have been recently showed to better model audio signals in the time-frequency domain than classical Gaussian distributions thanks to their larger dynamic range. However, infer…
Gaussian Processes improve data interpolation from diverse experiments.
problem Interpolation of sparse and inconsistent datasets from various experiments.
method Used Gaussian Processes (GP) for data interpolation, including uncertainty quantification.
result GPs successfully interpolate data and quantify uncertainties, demonstrating consistency across different sources.
In this tutorial we explain the inference procedures developed for the sparse Gaussian process (GP) regression and Gaussian process latent variable model (GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias & Lawrence (2010) is brief, hence getting a full picture of it requires collecting resul…
Algorithm finds frequencies, amplitudes, and phases of sinusoids in noisy data.
problem Finding frequencies, amplitudes, and phases of sinusoids in noisy data.
method Maximum likelihood approach to estimate tone parameters from contaminated observations. Successively estimates frequencies and jointly optimizes amplitudes and phases.
result Near-linear computational complexity (O(N)) for estimating M number of sinusoidal sources. Meta-models predict model hyperparameters for NDT experiments.
problem Non-destructive testing experiments are isolated; this work connects them.
method Bayesian multilevel approach, capturing inter-task relationships.
result Meta-models encode knowledge between and within tasks for transfer learning.
Survey of Gaussian process constraints for modeling expensive data.
problem Modeling expensive data with physical constraints.
method Overview of various Gaussian process constraints and their implementation.
result Discussion of computational challenges introduced by constraints.
ESS-Flow guides flow models without retraining, using Bayesian inference in source space.
problem Training flow models on paired data for conditional generation or sample production.
method Gradient-free Bayesian inference in source space using Elliptical Slice Sampling.
result Effective in diverse tasks including material design and protein structure prediction.