Proposes GPLFR for predicting high-dimensional outputs with few data.
problem Predicting high-dimensional outputs from limited data.
method GPLFR combines Gaussian process and linear-Gaussian decoding for high-dimensional prediction.
result GPLFR outperforms existing methods in predicting high-dimensional outputs.
Improves Gaussian process factor models for multi-population recordings.
problem Cubic runtime scaling with trial length and group number limits application to large-scale recordings.
method Two approximate approaches: inducing variables and frequency domain.
result Achieved orders of magnitude speed-up with minimal statistical performance impact.
New model extracts shared brain activity patterns from fMRI data.
problem Challenges in aggregating multi-subject fMRI data due to variability.
method Shared Gaussian Process Factor Analysis (S-GPFA) incorporating temporal information.
result Model reveals ground truth latent structures and replicates experimental performance.
We develop a fast inference method for non-conjugate Gaussian process models on spike count data.
problem Non-Gaussian spike count data complicates Gaussian Process Factor Analysis.
method We introduce Polynomial Approximate Log-Likelihood (PAL) estimators for non-conjugate GPFA models.
result PAL estimators achieve fast and accurate extraction of latent structure from spike train data.
It is now known that an extended Gaussian process model equipped with rescaling can adapt to different smoothness levels of a function valued parameter in many nonparametric Bayesian analyses, offering a posterior convergence rate that is optimal (up to logarithmic factors) for the smoothness class the true function be…
Framework for sensitivity analysis in biomanufacturing processes.
problem High complexity and uncertainty in biomanufacturing processes.
method Shapley value estimation for linear and nonlinear pKG models, using quasi-Monte Carlo and antithetic sampling.
result Improved efficiency and accuracy in sensitivity analysis for biomanufacturing processes.
A scalable factorized Gaussian process VAE for faster inference.
problem Inference bottlenecks in Gaussian process VAEs.
method Factorizes latent kernel across auxiliary features, leveraging independence.
result Significant speed-up in inference time (in theory and practice).
We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequentl…
We consider the problem of discriminative factor analysis for data that are in general non-Gaussian. A Bayesian model based on the ranks of the data is proposed. We first introduce a new {\em max-margin} version of the rank-likelihood. A discriminative factor model is then developed, integrating the max-margin rank-lik…
A new model detects anomalies in time series data efficiently.
problem Detect anomalies in high-dimensional time series data.
method r-ssGPFA, an unsupervised online anomaly detection model using state space Gaussian processes.
result The model detects anomalies efficiently and is computationally cheaper.
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian processes framework, the computational bottlenecks are the inversion of the (regulariz…
Paper improves efficiency in matrix computations for Gaussian processes.
problem Efficiency in matrix computations for Gaussian processes.
method Variance reduction via matrix factorization.
result Factorized estimator can be up to 1,000 times more efficient.
Method for factor analysis in short panels without assuming sphericity or Gaussianity.
problem Factor analysis in short panels without assuming sphericity or Gaussianity.
method Pseudo maximum likelihood method and asymptotically uniformly most powerful invariant test.
result Systematic risk explains a large part of cross-sectional total variance in bear markets but is not spanned by observed factors.
A new method speeds up factor analysis for high-dimensional data.
problem Estimating covariance parameters in high-dimensional Gaussian data with limited observations.
method Matrix-free likelihood method using implicitly restarted Lanczos and limited-memory quasi-Newton algorithms.
result Our method is faster than EM without sacrificing accuracy.
DF2M uses deep neural networks within a factor model for high-dimensional functional time series forecasting.
problem Forecasting high-dimensional functional time series with explainability and accuracy.
method Bayesian nonparametric model based on Indian Buffet Process and multi-task Gaussian Process, incorporating a deep kernel function.
result DF2M provides better explainability and superior predictive accuracy compared to conventional deep learning models.
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…
Gaussian processes struggle with compositional functions, but deep Gaussian processes can outperform.
problem Gaussian process regression struggles with compositional functions.
method We study information-theoretic lower bounds for posterior contraction rates in Gaussian process regression for a continuous regression model.
result Posterior based on any mean-zero Gaussian process can only recover the truth at a rate strictly slower than the minimax rate for generalized additive functions.
Jointly models cause-of-death mortality rates across multiple countries and genders.
problem Modeling cause-of-death mortality rates in a multinational setting.
method Multi-Output Gaussian Processes (MOGP) with Kronecker-structured kernels and latent factors.
result Efficiently captures heterogeneity and dependence across different factor inputs.
The paper reviews identifiability in linear and nonlinear models, from Gaussian to non-Gaussian.
problem Identifiability issues in latent-variable and structural-equation models, especially in nonlinear cases.
method Review of identifiability theory for linear and nonlinear models, including factor analysis and structural equation models.
result Even nonparametric nonlinear models can be estimated with additional assumptions.
The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In particular, we consider a Gaussian factor model where the short rate and the spreads are…
Optimal simple regret bound for Gaussian Process bandits.
problem Sequential optimization of expensive-to-evaluate functions.
method Proved a bound on simple regret for pure exploration algorithms.
result Order optimal bound on simple regret for Gaussian Process bandits.
GPLVMF improves CARS performance by addressing overfitting and context importance.
problem Overfitting and lack of automatic context importance determination in GP-based CARS.
method GPLVMF applies a non-zero mean function and real-valued latent space to improve GP model performance.
result Significant improvement in performance on real datasets and automatic context importance determination.
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to depend on a set of globally relevant inducing variables which factorize the model …
Probabilistic matrix factorization (PMF) is a powerful method for modeling data associated with pairwise relationships, finding use in collaborative filtering, computational biology, and document analysis, among other areas. In many domains, there is additional information that can assist in prediction. For example, wh…
A new factor analysis method using ICA reduces portfolio concentration and diversifies excess kurtosis.
problem Standard factor analysis suffers from issues with pairwise correlations of asset returns.
method Identifies factors based on non-Gaussianity instead of variance, using ICA.
result Fat-tailed portfolios significantly reduce portfolio concentration and winner-takes-all problem.
Modeling counterparty risk is computationally challenging because it requires the simultaneous evaluation of all the trades with each counterparty under both market and credit risk. We present a multi-Gaussian process regression approach, which is well suited for OTC derivative portfolio valuation involved in CVA compu…
Probabilistic matrix factorization (PMF) is a powerful method for modeling data associ- ated with pairwise relationships, Finding use in collaborative Filtering, computational bi- ology, and document analysis, among other areas. In many domains, there are additional covariates that can assist in prediction. For example…
HPPCA improves imputation of longitudinal data with missing values.
problem Handling incomplete, high-dimensional longitudinal data with nested sources of variation and temporal dependency.
method Hierarchical probabilistic principal component analysis (HPPCA) with a two-level latent factor model and Gaussian process.
result HPPCA outperforms standard PPCA and multivariate functional PCA in imputation accuracy, even under heavy missingness and model misspecification.
A new method speeds up Bayesian Optimization for hyperparameter tuning.
problem Efficient hyperparameter tuning for machine learning models.
method Lazy Gaussian Processes approximation to reduce cubic complexity to quadratic.
result Significant speedup in Bayesian Optimization, up to 162x in single node.
Proposes a nonparametric tensor factorization for sparse data.
problem Handling sparse tensor data with structural and interpretability benefits.
method Hierarchical Gamma processes and Poisson random measures for tensor-valued process, Dirichlet processes for sampling entry indices, Gaussian processes for values.
result Demonstrates superior performance on benchmark datasets.
A justification of the Basel liquidity formula for risk capital in the trading book is given under the assumption that market risk-factor changes form a Gaussian white noise process over 10-day time steps and changes to P&L are linear in the risk-factor changes. A generalization of the formula is derived under the more…
We analyze the structure of covariance matrices under graph constraints.
problem Analyzing the structure of covariance matrices under graph constraints.
method We explore the algebraic structure of the solution space of convex optimization problem Constrained Minimum Trace Factor Analysis (CMTFA) under a latent star topology.
result CMTFA can have either a rank 1 or a rank n-1 solution, with conditions for both.
IPGP framework improves psychological assessment by integrating shared and unique traits.
problem Tackles the debate on shared vs unique personality traits across individuals.
method Uses Gaussian process coregionalization model for non-Gaussian ordinal data, with stochastic variational inference for scalability.
result Improves prediction and estimation of individualized factor structures compared to existing methods.
Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model…
GP3 framework efficiently analyzes Gaussian processes on GPUs.
problem Certifiable safety in machine learning applications.
method GP3 framework using interval analysis and multi-resolution sampling on GPUs.
result Efficient analysis of Gaussian processes with certifiable safety.
Factor analysis has proven to be a relevant tool for extracting tissue time-activity curves (TACs) in dynamic PET images, since it allows for an unsupervised analysis of the data. Reliable and interpretable results are possible only if considered with respect to suitable noise statistics. However, the noise in reconstr…
Sentiment analysis consists of evaluating opinions or statements from the analysis of text. Among the methods used to estimate the degree in which a text expresses a given sentiment, are those based on Gaussian Processes. However, traditional Gaussian Processes methods use a predefined kernel with hyperparameters that …
A new model combines Gaussian processes with collaborative filtering for uncertainty-aware recommendations.
problem Uncertainty in recommendation systems.
method Combining Gaussian process multi-output models with collaborative filtering.
result Generates uncertainty estimates for predictions.
Paper proposes a new algorithm for graph learning with covariance constraints.
problem Graphical models and factor analysis not jointly leveraged in graph learning processes.
method Penalized maximum likelihood estimation of an elliptical distribution with Riemannian optimization.
result Effectiveness of the proposed approach demonstrated on real-world data sets.
Deep model learns complex latent codes without assuming factor structure.
problem Learning latent codes with complex, non-factorial distributions.
method Deep generative factor analysis with beta process prior and stochastic EM algorithm.
result Preliminary results show model can approximate complex distributions.
This paper improves credit risk analysis by incorporating state-dependent recovery rates into a factor model.
problem Accurate default forecasting in credit risk analysis.
method Extends a one-factor Gaussian copula model to include state-dependent recovery rates and a common factor.
result The proposed model outperforms other models in default prediction, especially during hectic periods.
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.
In this paper, we empirically study models for pricing Italian sovereign bonds under a reduced form framework, by assuming different dynamics for the short-rate process. We analyze classical Cox-Ingersoll-Ross and Vasicek multi-factor models, with a focus on optimization algorithms applied in the calibration exercise. …
Neural networks speed up covariance estimation in spatial Gaussian processes.
problem Efficiently estimating covariance parameters in spatial Gaussian processes.
method Training neural networks to approximate maximum likelihood estimates.
result Neural network estimates are as accurate as ML methods but much faster.
A scalable algorithm for GP regression selects relevant covariates efficiently.
problem Scalable variable selection in large GP regression models.
method VGPR algorithm using Vecchia approximation for sparse precision matrix, mini-batch subsampling.
result Improved scalability and accuracy in selecting relevant covariates.
In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously known bounds for algorithms like GP-UCB. We also introduce the novel Gaussian P…
This paper explores approximations for fully Bayesian Gaussian Process Regression.
problem Learning in Gaussian Process models through hyperparameter adaptation.
method Two approximation schemes: Hamiltonian Monte Carlo and Variational Inference.
result Predictive performance analysis on various benchmark datasets.
This study connects Gaussian processes and RKHS, bridging two machine learning communities.
problem Understanding the relationship between Gaussian processes and RKHS.
method Examining connections and equivalences in regression, interpolation, and other topics.
result Established the equivalence between Gaussian Hilbert space and RKHS.