Factor analysis provides linear factors that describe relationships between individual variables of a data set. We extend this classical formulation into linear factors that describe relationships between groups of variables, where each group represents either a set of related variables or a data set. The model also na…
We introduce a factor analysis model that summarizes the dependencies between observed variable groups, instead of dependencies between individual variables as standard factor analysis does. A group may correspond to one view of the same set of objects, one of many data sets tied by co-occurrence, or a set of alternati…
Efficient CVI for NGFA improves GFA inference for large-scale data.
problem Inference limitations in GFA models for large-scale data.
method Collapsed variational inference for nonparametric Bayesian GFA.
result CVI algorithm effectively approximates NGFA posterior in collapsed space.
Sparse GFA identifies disease factors in FTD subgroups.
problem Heterogeneity in neurological disorders hinders understanding and treatment.
method Sparse Group Factor Analysis (GFA) with regularised horseshoe priors.
result Identified latent disease factors differentially expressed in FTD subgroups.
New nonconvex regularizers improve low-rank matrix recovery efficiency and accuracy.
problem Efficiently recover low-rank matrices from incomplete data.
method Factor group-sparse regularization, related to Schatten-p norms.
result Improved generalization error bounds for Schatten-p norms as p decreases.
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.
New FGSPCA method captures grouping and sparse structures in PCA without prior info.
problem Capture grouping and sparse structures in PCA without prior info.
method Truncated regularization with alternating algorithm.
result FGSPCA method reduces model complexity and increases interpretability.
This paper compares two stock factor models in China's A-share market.
problem Contradicting results in existing research on stock factor models.
method Empirical analysis using China's A-share data from 2005-2020, orthogonalizing redundant factors, and 25-group portfolio returns calculation.
result The five-factor model outperforms the three-factor model in explaining excess return rates.
XCAN uses cross-product penalization for sparse matrix factorization.
problem Understanding complex data structures.
method Sparse matrix factorization with a loss function balancing variance and structural preservation.
result Flexible modeling approach for diverse applications.
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…
Method learns shared and specific factors in multi-study gene expression data.
problem Understanding shared and specific factors in high-dimensional multi-study data.
method Nonlinear multi-study factor model with sparse variational autoencoder.
result Method recovers meaningful shared and specific factors in platelet gene expression data.
Random forest identifies key features for diagnosing machine faults.
problem Identifying specific factors causing machine faults.
method Gaussian mixture model clustering, spectrum analysis, random forest classification.
result Identified significant features for different machine states.
Many data-driven approaches exist to extract neural representations of functional magnetic resonance imaging (fMRI) data, but most of them lack a proper probabilistic formulation. We propose a group level scalable probabilistic sparse factor analysis (psFA) allowing spatially sparse maps, component pruning using automa…
Study uses ML and causal analysis to predict student performance factors.
problem Understanding socio-academic and economic factors affecting student performance.
method Employed machine learning techniques and causal analysis on 1,050 student profiles.
result Ridge Regression achieved robust predictions with MAE of 0.12 and MSE of 0.024.
We propose a generative model of a group EEG analysis, based on appropriate kernel assumptions on EEG data. We derive the variational inference update rule using various approximation techniques. The proposed model outperforms the current state-of-the-art algorithms in terms of common pattern extraction. The validity o…
Latent factor models are the canonical statistical tool for exploratory analyses of low-dimensional linear structure for an observation matrix with p features across n samples. We develop a structured Bayesian group factor analysis model that extends the factor model to multiple coupled observation matrices; in the cas…
Deep generative models have recently yielded encouraging results in producing subjectively realistic samples of complex data. Far less attention has been paid to making these generative models interpretable. In many scenarios, ranging from scientific applications to finance, the observed variables have a natural groupi…
We propose a novel classification model for weak signal data, building upon a recent model for Bayesian multi-view learning, Group Factor Analysis (GFA). Instead of assuming all data to come from a single GFA model, we allow latent clusters, each having a different GFA model and producing a different class distribution…
Projections to a graph have bounded diameter for certain group structures.
problem Analyzing the diameter of projections to a specific graph for group structures.
method Analysis of the boundary of hyperbolic groups relative to subgroups and cyclic subgroups.
result The diameter of projections is bounded and depends only on the length bound.
Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) …
Effective rank rigidity proved for cubulated groups with factor systems.
problem Rank rigidity in cubulated groups with factor systems.
method Exhibiting special pairs of hyperplanes and curtains for skewering.
result Effective form of rank rigidity proved for cubulated groups.
Enhances FAVAR models with autoencoder for better economic forecasting and interpretability.
problem Limitations of linear FAVAR models in forecasting and structural analysis.
method Introduces Grouped Sparse autoencoder with time-varying parameters.
result The Grouped Sparse autoencoder produces more interpretable factors and superior forecasting performance.
New method detects intrinsic cross-correlations in non-stationary time series affected by common factors.
problem Bias in cross-correlation analysis due to common external factors.
method Multifractal temporally weighted detrended partial cross-correlation analysis (MF-TWDPCCA).
result MF-TWDPCCA accurately detects intrinsic cross-correlations between non-stationary time series.
Study finds significant but limited connections between cryptocurrencies and mainstream asset classes.
problem Investigating the relationship between cryptocurrencies and traditional asset classes.
method Granger-causality tests and forecast error variance decompositions to estimate connectedness.
result Less than 2.2% of cryptocurrency uncertainty is from non-crypto assets, and vice versa.
Group-invariant neural networks improve approximation accuracy for symmetric functions.
problem Improving approximation accuracy for symmetric functions using neural networks.
method Investigates the generalization error of group-invariant neural networks within the Barron framework.
result Group invariance introduces a factor δ that can significantly improve approximation accuracy when it is small.
Sharp inequalities on Siegel domains and complex hyperbolic spaces established.
problem Establishing inequalities on complex hyperbolic spaces and Siegel domains.
method Helgason-Fourier analysis, Kunze-Stein phenomenon, factorization theorem.
result Sharp Hardy-Adams and Adams type inequalities on Sobolev spaces of any positive fractional order on complex hyperbolic spaces.
New model learns content and transformation separately from data.
problem Learning disentangled representations from data without explicit labels.
method Group-based variational autoencoders, assuming content and transformation groups.
result Model learns generalizable content representations from unseen data.
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.
A new text clustering method using NMF and LSA improves stability and performance.
problem Text data's large, sparse term-document matrix makes clustering difficult.
method Proposes a new feature agglomeration method based on NMF and deterministic K-Means initialization.
result Significantly improves clustering performance and stability.
Interactive DR framework for comparing datasets.
problem Limited flexibility in existing DR methods for comparative analysis.
method Unified linear comparative analysis (ULCA) with interactive optimization and visualization.
result ULCA and optimization algorithm improve comparative analysis efficiency and flexibility.
Method estimates shared and study-specific factors for multi-study data.
problem Covariance estimation for multi-study data with shared and study-specific components.
method Spectral decomposition for latent factors, surrogate Bayesian regressions for loadings and variances.
result Strong frequentist guarantees and superior performance in simulations and real data.
Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation. Another practical challenge is that we may have data from multiple related classe…
Homotopy equivalent to spheres, free factor complex of a free group.
problem Understanding the homotopy type of free factor complexes.
method Proving homotopy equivalence and connectivity of relevant complexes.
result Homotopy equivalence of free factor complexes to spheres and other complexes.
GFA model uncovers brain-behavior associations in incomplete data sets.
problem Incomplete data sets and lack of robust statistical inferences.
method Hierarchical Bayesian model that handles missing data and models modality-specific associations.
result GFA identified four relevant shared factors and predicted non-imaging measures from brain connectivity.
Paper studies colored Alexander polynomials and their relation to KP soliton τ-functions.
problem Exploring group theoretic structures of colored HOMFLY polynomials in a specific limit.
method Perturbative analysis of SU(N) Chern-Simons Wilson loops and their relation to KP soliton τ-functions. result Colored Alexander polynomial is embedded in the action of KP generating function on soliton τ-function.
Motivation: Modelling methods that find structure in data are necessary with the current large volumes of genomic data, and there have been various efforts to find subsets of genes exhibiting consistent patterns over subsets of treatments. These biclustering techniques have focused on one data source, often gene expres…
We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country i took action a toward country j at time t"---known as dyadic events---in order to form an…
Corrects a 1998 proof about free factors of free groups.
problem Verifying the proof of free factors in free groups.
method Analyzes the geometric realization of free factors.
result Geometric realization is homotopy equivalent to a wedge of spheres.
Maps between automorphism groups are isomorphisms for free factor complexes.
problem Understanding the structure of automorphism groups of free factor complexes.
method Establishing isomorphisms between automorphism groups and automorphism groups of free factor complexes.
result Natural maps from mAut(Fn) to the automorphism group of the free-factor complex AFn are isomorphisms. Many tasks require finding groups of elements in a matrix of numbers, symbols or class likelihoods. One approach is to use efficient bi- or tri-linear factorization techniques including PCA, ICA, sparse matrix factorization and plaid analysis. These techniques are not appropriate when addition and multiplication of mat…
Paper extends quantile factor analysis with probabilistic methods for better economic policy and financial condition prediction.
problem Improving accuracy in economic and financial condition prediction.
method Probabilistic quantile factor analysis with regularization and variational approximations.
result The probabilistic estimator outperforms a recent loss-based estimator in many cases.
Factor Engine simplifies financial factor computation and analysis in Python.
problem Efficient computation and analysis of financial factors.
method Modular, extensible Python library with decorators, integrates with data science ecosystem.
result Mispricing factors computed by Factor Engine and Stata implementation are highly similar.
A new tensor decomposition method for fMRI data captures both spatial and temporal variability.
problem Challenges in modeling shared and subject-specific structure in multisubject spatiotemporal data, especially in neuroimaging.
method Introduces a spatiotemporal variational tensor decomposition (ST-VTD) framework combining tensor factorization with structured priors for flexible representation of spatial and temporal dynamics.
result Significantly improves latent factor recovery in fMRI data compared to classical and probabilistic decomposition benchmarks.
Proposes Robust Matrix Factorization with Grouping Effect (GRMF) for better performance and robustness.
problem Improves matrix factorization by incorporating grouping effect for better performance and robustness.
method Integrates grouping effect into matrix factorization, using an efficient alternating minimization framework with DC programming and ADMM.
result Demonstrates improved performance and robustness compared to five benchmark algorithms on real-world data sets with outliers and noise.
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.
NCFA uses deep learning and causal discovery to analyze complex data.
problem Analyzing complex, interdependent data with causal relationships.
method NCFA combines latent causal discovery and variational autoencoders.
result NCFA outperforms standard VAEs in sparsity, complexity, and causal interpretability.
We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We…
FedSplit improves federated learning for heterogeneous data.
problem Data heterogeneity in federated learning degrades convergence and performance.
method FedSplit splits data into shared and personalized groups, optimizing a novel objective function.
result FedSplit converges faster and performs better than standard federated learning.