New approach predicts under latent shifts using high-dimensional images.
problem Prediction under latent subgroup shifts with high-dimensional observations.
method Recognition-parametrised model (RPM) for identifying causal latent structure.
result Successfully adapts predictions for high-dimensional image data.
Method determines latent dimensionality in international trade flows.
problem Finding meaningful low-dimensional latent features in high-dimensional international trade data.
method Proposes a latent dimension determination method based on clustering of nonnegative RESCAL decompositions.
result Validates the latent features against empirical economic facts.
Method learns latent SDEs from high-dimensional time series.
problem Learning latent stochastic differential equations from time series data.
method Self-supervised learning with variational autoencoders and Euler-Maruyama approximation.
result Can recover SDE coefficients and latent variables up to isometry with infinite data.
VAELLS learns latent manifold structure to improve VAE model accuracy.
problem VAEs struggle with mismatched latent structure and global structure.
method Integrates learnable manifold model into latent space of VAE.
result Improves model accuracy by matching prior to data manifold structure.
A new method for generative modeling of discrete data using geometric latent subspaces.
problem Learning generative models for discrete data with statistical dependencies.
method Geometric latent-subspace framework in exponential parameter space of product manifolds of categorical distributions.
result Low-dimensional latent space encodes statistical dependencies and accurately models high-dimensional discrete data.
Latent DiTs improve data distribution recovery and inference efficiency under low-dimensional latent space.
problem Improving data distribution recovery and inference efficiency in latent DiTs.
method Investigates statistical and computational limits of latent DiTs under low-dimensional latent space assumption, deriving approximation error bounds, sample complexity, and efficient inference and training algorithms.
result Latent DiTs can bypass high dimensionality challenges and achieve almost-linear time inference and training.
Moment Pooling reduces latent space dimensions in machine learning models.
problem High-dimensional latent spaces in machine learning models are hard to interpret.
method Moment Pooling extends Deep Sets networks to arbitrary multivariate moments.
result Latent dimensions as small as 1 can achieve similar performance to higher dimensions.
Proposes D-CDLF for multi-view data decomposition.
problem Uncorrelatedness between common and distinctive latent factors.
method Decomposes data into common, distinctive, and noise components.
result Effective uncorrelatedness between distinctive latent factors from different views.
Variational Auto-Encoder (VAE) has been widely applied as a fundamental generative model in machine learning. For complex samples like imagery objects or scenes, however, VAE suffers from the dimensional dilemma between reconstruction precision that needs high-dimensional latent codes and probabilistic inference that f…
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…
Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the Euclidean structure of the latent space may be a poor match for the underlying lat…
GCAE uses density estimation to achieve reliable disentanglement in latent space.
problem Disentangled learning representations suffer from reliability issues.
method GCAE uses Gaussian Channel Autoencoder with Dual Total Correlation (DTC) to avoid the curse of dimensionality.
result GCAE achieves highly competitive and reliable disentanglement scores.
Study improves interpretability in generative models by disentangling latent variables in scientific datasets.
problem Extracting generative factors from complex, high-dimensional datasets in unsupervised or semi-supervised settings.
method Introducing Aux-VAE, a novel architecture within the VAE framework, which disentangles latent variables by guiding them with auxiliary variables.
result Aux-VAE achieves disentanglement with minimal modifications to the standard VAE loss function, validated on multiple datasets.
VED framework learns low-dimensional latent representations of physical systems.
problem Learning latent representations of complex physical systems.
method Variational Encoder-Decoder (VED) framework with KL divergence and covariance regularization.
result VED achieves lower-dimensional latent representations with improved feature disentanglement.
Paper proposes a novel auto-encoder for latent density estimation.
problem Challenges of learning generative probabilistic models due to curse of dimensionality.
method Joint dimensionality reduction and non-parametric density estimation framework using a novel estimator.
result Proposed model achieves promising results on various datasets.
We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space that spans the conditional means, it is possible to consistently recover the struc…
LOL method simplifies forming linear combinations of latent variables.
problem Lack of general-purpose methods for manipulating latent variables.
method Latent Optimal Linear combinations (LOL) method.
result LOL simplifies creation of expressive low-dimensional representations.
Early stopping improves sample quality in latent diffusion models.
problem Latent diffusion models degrade sample quality with conventional early stopping.
method Analyzed the interaction between latent dimension and stopping time under Gaussian framework.
result Lower-dimensional representations benefit from earlier termination, higher-dimensional spaces require later stopping.
New methods improve sampling from complex dynamical models.
problem Sampling from high-dimensional, non-linear latent dynamical models is computationally challenging.
method Introduce auxiliary MCMC and Particle Gibbs samplers with improved performance and parallelisation.
result Enhanced samplers maintain performance in high-dimensional latent spaces and support parallelisation.
Proposes flexible auto-encoders for varying data dimensions.
problem Fixed latent dimensions limit data flexibility.
method Stochastic bottleneck with weighted dropouts.
result Seamless variable dimensionality reduction with high performance.
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.
Formalizes concepts as latent variables in hierarchical models for high-dimensional data.
problem Lack of formalization and theoretical insights for learning discrete concepts from high-dimensional data.
method Formalizes concepts as latent causal variables in a hierarchical model, formulates conditions for concept identification.
result Conditions for identifying latent hierarchical models in unsupervised data, handling complex structures and high-dimensional data.
Structured latent attribute models (SLAMs) are a special family of discrete latent variable models widely used in social and biological sciences. This paper considers the problem of learning significant attribute patterns from a SLAM with potentially high-dimensional configurations of the latent attributes. We address …
Estimates latent dimensionality for prediction tasks using mutual information.
problem Estimating the latent dimensionality needed for accurate prediction.
method Formulates the problem as an Information Bottleneck question and uses neural mutual information estimators with a hybrid critic to preserve latent geometry.
result The hybrid critic method provides a more accurate estimation of task-relevant dimensionality.
The paper develops a method to dynamically adjust VAE latent space dimensions during training.
problem Under- or overprovisioning of latent space dimensions in VAEs.
method GECO optimizer with L0-ARM gradient estimator to dynamically adjust latent space dimensions. result The latent space can be pruned effectively without violating reconstruction error constraints.
New method recovers latent confounders from high-dimensional proxy variables.
problem Detecting latent confounders from high-dimensional proxy variables.
method Proxy Confounder Factorization (PCF) framework using ICA-PCF and GD-PCF.
result ICA-PCF recovers confounders with high correlation and low error in synthetic and real-world data.
FSGD uses latent factors to scale SGD for high-dimensional learning.
problem Scalable optimization in high-dimensional machine learning.
method Factor-Augmented SGD (FSGD) that operates on streaming data.
result Established theoretical framework for latent factor estimation error in SGD.
A new model clusters networks with community-specific submanifold structures.
problem Clustering networks with community-specific submanifold structures.
method Latent Structure Block Models (LSBM) for Bayesian spectral graph clustering.
result LSBM correctly recovers underlying communities in one-dimensional manifold structures.
Bayesian neural networks improve uncertainty quantification in non-linear dimensionality reduction.
problem Current neural network models lack adequate uncertainty quantification.
method Deploy Markov chain Monte Carlo sampling algorithms for Bayesian inference in ANN models with latent variables.
result New research directions are needed due to fundamental challenges in neural networks with latent variables.
Gradient-based meta-learning techniques are both widely applicable and proficient at solving challenging few-shot learning and fast adaptation problems. However, they have practical difficulties when operating on high-dimensional parameter spaces in extreme low-data regimes. We show that it is possible to bypass these …
Model learns cancer tissue images onto a low-dimensional space revealing tissue characteristics.
problem Improving cancer diagnosis through high-fidelity digital pathology.
method Deep generative model using PathologyGAN to map real images onto a latent space.
result Latent space encodes morphological characteristics and reveals distinct tissue clusters.
LIT-LVM improves linear predictors by estimating interaction terms with latent vectors.
problem Accurately estimating coefficients for interaction terms in linear predictors.
method Structured regularization using latent vectors to represent features.
result LIT-LVM achieves superior prediction accuracy compared to other methods.
The paper optimizes hyperplanes for binary classification in high-dimensional data with latent Gaussian mixtures.
problem Binary classification in high-dimensional data with latent Gaussian mixtures.
method Generalized least squares estimator for estimating the direction of the optimal separating hyperplane. Simple correction for intercept estimation.
result The procedure is minimax optimal in many scenarios and can retain the interpolation property.
PLIs improve classifier performance by fine-tuning latent representations.
problem Difficult interpretation of high-dimensional latent representations in neural networks.
method Back-propagation of manual changes to low-dimensional embeddings using t-distributed stochastic neighbourhood embeddings.
result Manual separation of class clusters in latent space enhances classifier performance.
Novel approach detects early warning indicators in complex systems.
problem Detecting abrupt transitions in complex systems.
method Directed anisotropic diffusion map and latent stochastic dynamical systems.
result Early warning indicators can detect tipping points in state transitions.
The paper analyzes PLS-SVD in high-dimensional data integration, revealing its strengths and limitations.
problem Understanding the behavior of PLS-SVD in high-dimensional data integration.
method Analysis using random matrix theory and singular value decomposition.
result PLS-SVD exhibits counter-intuitive or limiting behavior in certain regimes and outperforms PCA when detecting common latent subspace.
Simple model explains manifold structure in high-dimensional data.
problem Understanding manifold structure in high-dimensional data.
method Latent Metric Model with latent variables, correlation, and stationarity.
result Establishes statistical explanation for manifold hypothesis.
Generative Topological Networks (GTNs) simplify latent space generation.
problem Complex latent space generation in generative models.
method GTNs use topology theory for a simple, supervised learning approach.
result GTNs improve upon VAEs and converge quickly, generating realistic samples.
Proposes PredVAR model for reduced-dimensional dynamics from noisy data.
problem Extracting low-dimensional dynamics from high-dimensional noisy data.
method Probabilistic reduced-dimensional vector autoregressive model with oblique projection.
result Iterative algorithm yields dynamic latent variables with rank-ordered predictability.
LOL-BO improves latent space Bayesian optimization over structured inputs.
problem Optimizing complex functions over high-dimensional, structured search spaces.
method Adapting trust regions from high-dimensional to structured settings, using a DAE to map inputs into a latent space.
result Achieves up to 20x improvement over state-of-the-art methods.
A new tree-Wasserstein distance for high-dimensional data with latent feature hierarchy.
problem Finding meaningful distances between high-dimensional data samples with latent feature hierarchy.
method Proposes a new tree-Wasserstein distance (TWD) for high-dimensional data with a latent feature hierarchy, using diffusion geometry and tree decoding.
result The proposed TWD effectively recovers the latent feature hierarchy and is efficient and scalable.
Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis, such as clustering or classification. Finding reduced-dimension representations tha…
New method for high-dimensional manifold-based inference tackles latent responses.
problem Inference on latent right factor vectors in multi-task learning with large numbers of responses and features.
method SOFARI-R method with two variants: one for strongly orthogonal factors and another for weakly orthogonal factors.
result Bias-corrected estimators for latent right factor vectors with asymptotically normal distributions and justified asymptotic variance estimates.
Study on reliability of latent reuse in diffusion models under distribution shift.
problem When can latent spaces from a source dataset be reused for a target dataset with different distributions?
method Considered a source-target setting with approximately low-dimensional datasets near different subspaces. Analyzed the target-domain score error due to principal-angle misalignment and target ambient noise.
result Latent reuse is reliable only if the source and target subspaces are close and the target ambient noise is not too amplified.
A new method maps high-dimensional Bayesian inverse problems to lower dimensions.
problem High-dimensional Bayesian inverse problems with complex prior information.
method Data-driven VAE prior and KRnet map for posterior approximation in latent space.
result Efficiently reduces computational cost and approximates posterior distributions.
In this paper we present a fully Bayesian latent variable model which exploits conditional nonlinear(in)-dependence structures to learn an efficient latent representation. The latent space is factorized to represent shared and private information from multiple views of the data. In contrast to previous approaches, we i…
Proposes LAE-EnKF for improved nonlinear data assimilation.
problem Performance of EnKF deteriorates for strongly nonlinear dynamics.
method Reformulates assimilation in a learned latent space with linear dynamics.
result LAE-EnKF yields more accurate and stable assimilation.
A model learns causal representations from high-dimensional data.
problem Challenges in learning causal representations from high-dimensional data.
method Formulated a latent variable decoder model, Decoder BCD, for Bayesian causal discovery.
result Shows that using known intervention targets as labels helps in unsupervised Bayesian inference over structure and parameters.