TPLVM models portfolio construction for non-Gaussian financial data.
problem Optimal asset allocation in finance with non-Gaussian fluctuations.
method Student's t-process latent variable model (TPLVM) for portfolio optimization.
result TPLVM outperforms Gaussian process latent variable model in minimum-variance portfolio construction.
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of graphical models known as the structural equation model with latent variables. While …
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of graphical models known as the structural equation model with latent variables. While …
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete variables or a combination of both continuous and discrete variables poses new cha…
tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.
problem Agnostic latent variables in VAEs ignore data structure correlations.
method Proposes tensor-variate Gaussian process prior for variational autoencoder.
result Explicitly modeling correlation structures improves model performance in reconstruction.
Bayesian non-linear latent variable modeling for complex data.
problem Inference for GPLVMs is computationally limited and often leads to overfitting or underestimates uncertainty.
method Approximate Gaussian process mappings with random Fourier features for MCMC inference.
result Generalized RFLVMs perform well on various data types and applications.
Study improves Gaussian Process Latent Variable Model for noisy longitudinal data.
problem Noisy and incomplete longitudinal data makes learning representations difficult.
method Augment variational approximation with systematic samples of unseen observations.
result Demonstrates improved learning of Gaussian Process Dynamical Systems in noisy data.
Method identifies latent variables from high-dimensional data with piecewise affine mixing.
problem Identifying latent variables from high-dimensional observations with dependencies and piecewise affine transformations.
method Proposes a two-stage method with sparsity and Gaussianity regularization.
result Effectively recovers ground-truth latent variables from synthetic and image data.
Develops a new method for nonlinear dimension reduction using random features.
problem Statistical challenges in generalizing Gaussian process-based latent variable models to non-Gaussian data.
method Random feature latent variable models (RFLVMs) that approximate nonlinear relationships with linear functions of random features.
result RFLVMs produce comparable results to state-of-the-art methods on various data types.
Paper extends FOFC algorithm to work with mixed data types.
problem Designing causal discovery algorithms for mixed data types.
method Proves tetrad constraint can be entailed for mixed data types and applies FOFC algorithm.
result FOFC algorithm can work on mixed data types.
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 introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo estimate for the marginal likelihood that approximately integrates over the late…
LVM-GP solves PDEs with uncertainty using latent variables and Gaussian processes.
problem Uncertainty quantification in PDE solutions with noisy data.
method Combines latent variable model and Gaussian process for uncertainty-aware prediction.
result Efficiently captures functional dependencies and robust uncertainty quantification.
Method identifies causal relationships in data with latent variables.
problem Learning causal models from observational data with latent variables.
method Proposes a method to check causal paths and identify causal effects.
result Causal effects can be identified uniquely under certain conditions.
Combines boosting and latent Gaussian models for better predictions.
problem Boosting's assumptions and latent Gaussian models' limitations.
method Integrates tree-boosting and latent Gaussian models.
result Increased prediction accuracy in simulations and real-world data.
Improves Bayesian optimisation for engineering design problems with many variables.
problem Efficiently searching for global minima in high-dimensional design spaces.
method Integrates input and output data to identify a reduced latent subspace using probabilistic partial least squares.
result Significant improvements in convergence to the global minimum compared to existing methods.
New neural network approach for optimizing latent variable models.
problem Stability issues in marginalizing Gaussian Bayesian networks.
method Developed a new graphical structure and a neural network algorithm.
result Established a duality between parameter optimization and neural network training.
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the interacting variables. However, in the presence of latent variables, the convention…
Study identifies parameters in causal models with latent confounding.
problem Parameter identification in linear non-Gaussian causal models with latent confounding.
method Graphical criterion for necessary and sufficient identifiability of direct causal effects, with polynomial-time algorithm.
result Developed a graphical criterion for identifying direct causal effects in latent variable models with arbitrary non-linear confounding.
Adaptive probabilistic PCA adapts complexity with varying subspaces.
problem Adaptive probabilistic PCA models varying complexity in data.
method Relaxed linear Gaussian model with discrete latent variables, Bayesian nonparametric approach.
result Proposes locally adaptive probabilistic PCA (A-PPCA) for varying subspaces.
Paper proposes RCD method to discover causal structure with latent confounders.
problem Causal discovery from data with latent confounders.
method Repetitive causal discovery (RCD) method to infer causal directions between observed variables.
result RCD effectively identifies latent confounders and causal directions between observed variables.
A new framework estimates causal effects for ordinal variables.
problem Existing causal inference methods fail for ordinal data.
method Presumes a latent Gaussian DAG model with constrained covariance matrix.
result Closed-form function for ordinal causal effects in latent space.
In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related to causal discovery in the presence of nonlinear confounders, which is a challeng…
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.
Regularizes sparse Gaussian processes for better model performance.
problem Efficient learning of inducing inputs in latent variable models.
method Proposes a regularization approach to balance reconstruction and approximation performance.
result Improves both inference and prediction performance in latent variable models.
Paper presents a reparameterized DP-DLGMM for clustering.
problem Non-parametric DP priors in DLGMM are hard to couple with variational inference.
method Closed-form updates for DP-DLGMM's variational posterior.
result Model generates realistic samples and performs competitively in semi-supervised settings.
New method identifies latent causal variables from observed data, overcoming indeterminacies.
problem Identifying latent causal variables from observed data, especially when latent variables are weight-variant.
method Introduces a novel identifiability condition for latent causal models, proposing SuaVE method.
result Identifies latent causal variables up to trivial permutation and scaling, demonstrating consistency and efficacy.
The Gaussian process latent variable model (GP-LVM) is a popular approach to non-linear probabilistic dimensionality reduction. One design choice for the model is the number of latent variables. We present a spike and slab prior for the GP-LVM and propose an efficient variational inference procedure that gives a lower …
We characterize distributional equivalence in latent-variable models with cycles.
problem Lack of an equivalence characterization for latent-variable causal models with cycles.
method Established graphical criterion for distributional equivalence and developed edge rank constraints.
result First equivalence characterization without structural assumptions for latent-variable models with cycles.
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a latent variable that is used to modulate the covariance function over the training …
A scalable GPLVM model using stochastic variational inference.
problem Scalable inference for Gaussian process latent variable models.
method Doubly stochastic formulation of Bayesian GPLVM with minibatch training.
result High-fidelity reconstructions in the presence of missing data.
A new estimator improves training of probabilistic models with latent Gaussian variables.
problem Improving gradient estimation for models with latent Gaussian variables.
method Rao-Blackwellised Reparameterisation Gradients (R2-G2)
result R2-G2 consistently yields better performance in models with multiple applications of the reparameterisation trick.
We present the Mixed Likelihood Gaussian process latent variable model (GP-LVM), capable of modeling data with attributes of different types. The standard formulation of GP-LVM assumes that each observation is drawn from a Gaussian distribution, which makes the model unsuited for data with e.g. categorical or nominal a…
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.
LeJEPA learns latent variables from nonlinear observations.
problem Learning latent variables from nonlinear observations.
method Proves linear identifiability of Gaussian latent distributions.
result Gaussian distribution uniquely guarantees linear identifiability.
Proposes a new VAE model to avoid posterior collapse by modeling latent variable dependencies.
problem Posterior collapse in variational autoencoders due to assumption of factorized variational posterior.
method Introduces Gaussian Copula Variational Autoencoder (GCVAE) to model latent variable dependencies explicitly.
result Empirical results show GCVAE can avoid posterior collapse while maintaining competitive performance.
Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller manifold. Additionally, in these applications the Euclidean geometry might induc…
This paper improves GP for learning complex data distributions.
problem Vanilla Gaussian processes struggle with complex data distributions.
method Introduces scalable GP paradigms with latent variables and variational inference.
result Scalable modulated GPs, especially latent GPs, learn diverse data distributions better.
We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for computational tractability. Inference is made tractable through a collapsed variation…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve Markov chain Monte Carlo sampling with limited applicability to large data sets. W…
The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP) estimation of the latent variables and hyperparameters can be used for model selection…
Enhances topology optimization with multiclass microstructures using latent variable Gaussian process.
problem Lack of an inherent ordering or distance measure between different classes of microstructures.
method Extended latent-variable Gaussian process (LVGP) models to multi-response LVGP (MR-LVGP) models for metamaterials.
result Improved performance through consistent load-transfer paths for micro- and macro-structures.
New method for mixed data types in graphical models.
problem Challenges in analyzing data with mixed variable types.
method Latent Gaussian copula models with leveraged polychoric and polyserial correlations.
result Flexible and scalable methodology for mixed data types.
The standard margin-based structured prediction commonly uses a maximum loss over all possible structured outputs. The large-margin formulation including latent variables not only results in a non-convex formulation but also increases the search space by a factor of the size of the latent space. Recent work has propose…
Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally. Unfortunately, real-world data often does not fit well to sparse graphical models. I…
Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length, but dataset diversity might be poor in comparison. Recent models have gained sig…
Paper proposes a new method to identify causal graphs with latent variables using higher-order cumulants.
problem Estimating causal directed acyclic graphs with latent confounders.
method Uses higher-order cumulants to identify causal structures among observed and latent variables.
result Validates the proposed algorithm through simulations and real-world data.
The paper identifies causal effects in latent variable models using higher-order cumulants.
problem Challenges in identifying causal effects in latent variable models with latent confounders.
method Using higher-order cumulants, the paper addresses two challenging setups: a single proxy variable and underspecified instrumental variables.
result Causal effects are identifiable with a single proxy or instrument.