We present a unifying framework which reduces the construction of probabilistic component analysis techniques to a mere selection of the latent neighbourhood, thus providing an elegant and principled framework for creating novel component analysis models as well as constructing probabilistic equivalents of deterministi…
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48 results for “Probabilistic Latent Component Analysis”
Proposes a deep probabilistic multi-view model for multi-view learning.
problem Learning from multiple related views with shared latent structure.
method Probabilistic Canonical Correlation Analysis (CCA) in latent space, deep generative networks, variational inference.
result Efficient variational inference approximates posterior distributions of latent multi-view layer.
Probabilistic Autoencoder learns latent space weights' distribution.
problem Nonlinear model reconstruction error and sample quality.
method Normalizing flow for latent space weights' probability distribution.
result PAE achieves small reconstruction errors, high sample quality, and good performance.
Survey of factor analysis, PCA, variational inference, and VAE.
problem Dimensionality reduction and generative modeling of data.
method Variational inference, factor analysis, probabilistic PCA, and VAE.
result Derivation and explanation of ELBO, EM, and closed-form solutions.
Generative model improves sound synthesis realism.
problem Synthesize natural sounds with realistic perception.
method Latent force modelling with physical knowledge incorporated.
result Generated sounds perceived as more realistic.
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.
Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. However, they are difficult to train efficiently, since backpropagation through discrete variables is generally not possible. We present a novel method to train a class of probabilistic models with discrete late…
nnLDA combines neural and probabilistic methods for better topic modeling with side information.
problem Lack of integration of auxiliary information in traditional topic models.
method nnLDA integrates side information through a neural prior mechanism, optimizing both neural and probabilistic components.
result nnLDA outperforms traditional models in topic coherence, perplexity, and classification.
This paper improves PPCA robustness using -distributions.
problem Improving robustness of probabilistic PCA.
method Using multivariate -distributions and a hierarchical model.
result Clarified the correct correspondence between the multivariate -PPCA framework and the hierarchical model.
Theoretical Connection between Locally Linear Embedding, Factor Analysis, and Probabilistic PCAstat.ML
This work connects LLE, factor analysis, and probabilistic PCA through a stochastic perspective.
problem Exploring the theoretical connection between LLE, factor analysis, and probabilistic PCA.
method Solving the stochastic linear reconstruction of LLE using expectation maximization.
result LLE, factor analysis, and probabilistic PCA are shown to be connected through a stochastic perspective.
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.
In this tutorial, I will discuss the details about how Probabilistic Latent Semantic Analysis (PLSA) is formalized and how different learning algorithms are proposed to learn the model.
Methods for analysis of principal components in discrete data have existed for some time under various names such as grade of membership modelling, probabilistic latent semantic analysis, and genotype inference with admixture. In this paper we explore a number of extensions to the common theory, and present some applic…
Bayesian nonparametric PCA infers the number of significant components.
problem Selecting the number of significant components in PCA is challenging.
method Introduces a Bayesian nonparametric approach using a Stiefel manifold prior and Indian buffet process for uncertainty modeling.
result Proposes a new estimator of the subspace dimension and a refined statistical significance test.
D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.
problem Analyzing nonlinear dynamical systems with probabilistic understanding.
method Combines deep learning and probabilistic modeling, using KL annealing and normalizing flows.
result Captures latent dynamics in sequential datasets with improved convergence and flexibility.
Scalable psFA for fMRI data extracts sparse components.
problem Extracting neural representations from fMRI data with probabilistic formulation.
method Group level scalable probabilistic sparse factor analysis (psFA) with spatial sparsity, component pruning, and heteroscedastic noise modeling.
result Sparse components similar to group ICA and reduced noise in activated areas.
HMMs improve music transcription accuracy.
problem Improving automatic transcription of music.
method Employed PLCA for multi-pitch estimation and integrated HMMs for note segmentation and post-processing.
result HMMs enhance transcription accuracy on different instruments.
Probabilistic Latent Semantic Analysis is a novel statistical technique for the analysis of two-mode and co-occurrence data, which has applications in information retrieval and filtering, natural language processing, machine learning from text, and in related areas. Compared to standard Latent Semantic Analysis which s…
Paper introduces MPPGA for integrating multiple PGA models on Riemannian manifolds.
problem Challenges in dimensionality reduction on Riemannian manifolds with multiple modalities.
method Develops a mixture probabilistic principal geodesic analysis (MPPGA) model.
result Demonstrates improved clustering and shape analysis using MPPGA.
Hybrid model combines continuous and tractable probabilistic models.
problem Intractable probabilistic inference in continuous latent-space models.
method Continuous mixtures of tractable probabilistic models with finite integration points.
result Hybrid models achieve state-of-the-art performance in density estimation.
Paper develops a dual formulation for PCA in Hilbert spaces.
problem Characterizing probabilistic PCA in Hilbert spaces.
method Dual formulation for probabilistic PCA in Hilbert spaces.
result Generative framework for kernel methods developed.
Exact solution for missing data in factor analysis using autoencoders.
problem Handling missing data in factor analysis models.
method Developed an exact solution for factor analysis with missing data using autoencoders.
result An exact latent posterior distribution for factor analysis with missing data.
A new method improves target selection for manipulating complex systems like the brain.
problem Improper incorporation of low-variance outcomes into latent space of predictive models.
method Developed a novel objective based on supervised variational autoencoders (SVAEs) for PPCA (Probabilistic Principal Component Analysis).
result gPCR (Generative Principal Component Regression) dramatically improves target selection in manipulation compared to standard PCR and SVAEs.
Proposes a flexible feature allocation model for sparse factor analysis.
problem Sparse data and rigid assumptions in traditional exploratory tools.
method Adaptive latent feature sharing with control over feature sparsity.
result Derives a novel adaptive Factor analysis (aFA) and aPPCA for flexible dimensionality reduction.
Linear VAEs explain posterior collapse in VAEs via local maxima in log marginal likelihood.
problem Posterior collapse in VAEs where variational posterior matches prior for some latent variables.
method Analysis of linear VAEs and their relation to pPCA, proving ELBO does not introduce spurious local maxima.
result Linear VAEs have identifiable global maxima corresponding to principal component directions, explaining posterior collapse.
Causal Component Analysisstat.ML
Causal Component Analysis aims to recover latent variables with causal relationships.
problem Recover latent variables with causal relationships from observed mixtures.
method Introduces a likelihood-based approach using normalizing flows to estimate unmixing function and causal mechanisms.
result Demonstrates effectiveness through synthetic experiments in CauCA and ICA settings.
A new probabilistic model for CCA reduces data complexity without vectorization.
problem Reducing data complexity for two-dimensional canonical correlation analysis.
method A latent variable model for matrix-variate data with two variational inference approaches.
result The proposed methods outperform existing probabilistic and non-probabilistic CCA approaches.
New method SP-PPCA reduces outlier impact in PCA.
problem Outliers make standard PCA and PPCA less robust.
method Integrates self-paced learning into PPCA, using iterative optimization.
result SP-PPCA effectively reduces or eliminates outlier impact.
A new approach to disentangled representations using structured latent priors.
problem Learning disentangled representations in unsupervised learning.
method Proposed a structured latent prior to encourage disentanglement and mitigate trade-offs.
result The structured latent prior significantly mitigates the trade-off between reconstruction loss and disentanglement.
ILDM combines diffusion and latent learning for generative modeling on unknown manifolds.
problem Diffusion models struggle with high-dimensional data and lack geometric structure.
method ILDM integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds.
result ILDM significantly improves generation quality compared to standard models.
This work closes the gap between theory and practice for nICA identifiability.
problem Identifying latent components in nonlinearly mixed data.
method Finite-sample analysis of GCL-based nICA, combining GCL properties, statistical generalization, and numerical differentiation.
result Establishes a trade-off between function learner complexity and expressiveness.
New model separates images into independent factors quickly and easily.
problem Separating high-dimensional data like images into independent latent factors.
method Combines bijective feature maps with linear ICA model on the Stiefel manifold.
result Models converge quickly and achieve better unsupervised latent factor discovery.
We propose a nonparametric Bayesian probabilistic latent variable model for multi-view anomaly detection, which is the task of finding instances that have inconsistent views. With the proposed model, all views of a non-anomalous instance are assumed to be generated from a single latent vector. On the other hand, an ano…
Bayesian neural networks decompose uncertainty into epistemic and aleatoric components.
problem Uncertainty in Bayesian neural networks with latent variables.
method Information theoretic approach and risk-sensitive objective for safe reinforcement learning.
result Natural decomposition of predictive uncertainty in Bayesian active learning and safe RL.
Paper forecasts dynamic transportation networks using probabilistic models.
problem Forecasting temporal evolution of transportation networks.
method Probabilistic latent network model with Bayesian inference.
result Models accurately predict future network states and community structures.
Deep equilibrium models estimate latent variables from data.
problem Estimating latent variables from data.
method Generalized exponential family models, deep equilibrium networks.
result Deep equilibrium models solve MAP estimates for latent and transformation parameters.
Bitcoin's Crypto Flow Networkq-fin.GN
Study reveals structure of Bitcoin's crypto flow network.
problem Understanding crypto flows among Bitcoin users.
method Blockchain data, user identification, network construction, bow-tie structure, Hodge decomposition, non-negative matrix factorization.
result Users are located in upstream, downstream, and core of the crypto flow network.
Hierarchical probabilistic models, such as mixture models, are used for cluster analysis. These models have two types of variables: observable and latent. In cluster analysis, the latent variable is estimated, and it is expected that additional information will improve the accuracy of the estimation of the latent varia…
A new approach to unsupervised learning using recognition-parametrised models.
problem Discovering meaningful latent structure in observational data.
method Recognition-Parametrised Model (RPM) combining parametric and non-parametric components.
result Effective learning of latent structure without explicit generative models.
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.
Survey of spectral, probabilistic, and deep metric learning methods.
problem Developing effective distance metrics for various machine learning tasks.
method Divided into spectral, probabilistic, and deep approaches, covering various techniques and their applications.
result Comprehensive overview of metric learning methods, including new developments and applications.
LSSDM improves imputation of multivariate time series data.
problem Imputation of multivariate time series data without labels.
method LSSDM projects observed data into latent space, reconstructs missing values without labels, and uses a conditional diffusion model for precise imputation.
result LSSDM achieves superior imputation performance and uncertainty analysis.
Proposes iVDFM for identifying latent factors in multivariate time series.
problem Identifying latent factors in multivariate time series with structural dynamics.
method Identifiable Variational Dynamic Factor Model (iVDFM) with iVAE-style conditioning.
result Identifiable latent factors up to permutation and component-wise affine transformations.
A combined model integrates latent factor and logistic regression for citation network analysis.
problem Insufficient representation by either latent factor or logistic regression alone.
method Proposes a combined model integrating latent factor and logistic regression, with parameter estimation through joint-likelihood and penalty terms.
result The proposed method captures both main technological trends and ad-hoc dependencies in citation networks.
Decomposition of Uncertainty in Bayesian Deep Learning for Efficient and Risk-sensitive Learningstat.ML
Bayesian neural networks decompose uncertainty into epistemic and aleatoric components for efficient and risk-sensitive learning.
problem Uncertainty in Bayesian neural networks estimation of weights and complex noise patterns in data.
method Decomposition of uncertainty into epistemic and aleatoric components, and definition of a risk-sensitive criterion for reinforcement learning.
result Identification of informative points for active learning and policies balancing expected cost, model-bias, and noise aversion.
Overview of latent variable models in probabilistic frameworks.
problem Understanding the interconnectedness of latent variable models.
method Conceptual overview emphasizing compositional nature.
result Emphasizes the interconnectedness of latent variable models.
LDF combines neural networks with probabilistic models for data fusion.
problem Combining limited primary data with readily available auxiliary data.
method Neural networks as conjugate mappings of auxiliary data for posterior analysis.
result Efficient inference and compact latent variable posterior distributions.
Machine learning improves financial stress testing in Indian markets.
problem Conventional stress testing limitations in Indian financial markets.
method Dimensionality reduction, latent factor modeling, Variational Autoencoders, Monte Carlo simulation.
result Improved flexibility, robustness, and realism in financial stress testing.