Dual PC algorithm improves structure learning of Bayesian networks.
problem Learning the structure of Bayesian networks from observational data.
method Dual PC algorithm, leveraging covariance and precision matrices, and partial correlations.
result The dual PC algorithm outperforms the classic PC algorithm in structure recovery, even with non-Gaussian data.
Parabolic almost conformally symplectic structures were introduced in the first part of this series of articles as a class of geometric structures which have an underlying almost conformally symplectic structure. If this underlying structure is conformally symplectic, then one obtains a PCS-structure. In the current ar…
New algorithm learns causal structures by intersecting Markov blankets.
problem Learning causal relationships from data.
method Endogenous and Exogenous Markov Blankets Intersection (EEMBI) algorithm.
result EEMBI-PC integrates PC algorithm steps for improved accuracy.
Study of differential operators in PCS structures using contactifications.
problem Understanding differential operators in PCS structures.
method Use of parabolic contactifications and BGG sequences.
result Construction of families of differential operator complexes.
Bayesian scores improve structure learning in probabilistic circuits.
problem Improper structure learning in probabilistic circuits based on heuristics.
method Developed Bayesian structure scores for deterministic PCs, using them in a greedy cutset algorithm.
result Effective protection against overfitting and fast, almost hyper-parameter-free structure learner.
Paper tackles order-dependence in structure learning of multivariate regression chain graphs.
problem Order-dependence in structure learning of multivariate regression chain graphs.
method Proposes modifications to the PC-like algorithm to remove order-dependence.
result Improved performance in high-dimensional settings with modifications to the PC-like algorithm.
Quasi-conformal (QC) theory is an important topic in complex analysis, which studies geometric patterns of deformations between shapes. Recently, computational QC geometry has been developed and has made significant contributions to medical imaging, computer graphics and computer vision. Existing computational QC theor…
Paper introduces md-vtrees for efficient probabilistic and causal inference.
problem Efficient inference in complex probabilistic models.
method Introduces md-vtrees to generalize tractability conditions for advanced inference queries.
result Derives first polytime algorithms for causal inference queries.
We solve minimal separator problems in AMP chain graphs and improve structure learning algorithms.
problem Finding minimal separators in AMP chain graphs and learning their structure from data.
method We analyze and solve several versions of the minimal separator problem. We propose modifications to the PC-like algorithm and extend a decomposition-based method for AMP CGs.
result Our modifications of the PC-like algorithm and the LCD-AMP method improve structure learning and are more accurate and stable, especially in high-dimensional settings.
Improved algorithm for causal structure learning in large networks.
problem Estimating high-dimensional directed acyclic graphs from noisy data.
method A modified PC-Algorithm that uses small sets of variables for conditioning.
result Significant gains in computational complexity and estimation accuracy, especially in large networks with hub nodes.
SymCircuit learns PC structure via entropy-regularized RL, improving inference efficiency and accuracy.
problem Greedy algorithms in PC structure learning lead to suboptimal solutions.
method Entropy-regularized reinforcement learning to train a learned generative policy for PC structure inference.
result SymCircuit learns the optimal policy as a tempered Bayesian posterior, improving inference efficiency and accuracy.
We study the dynamic interactions and structural changes in global financial indices in the years 1998-2012. We apply a principal component analysis (PCA) to cross-correlation coefficients of the stock indices. We calculate the correlations between principal components (PCs) and each asset, known as PC coefficients. A …
Predictive coding networks are shown to be stable, robust, and converge faster than backpropagation.
problem Stability, robustness, and convergence of predictive coding networks.
method Dynamical systems theory and Lyapunov stability analysis.
result Predictive coding networks are Lyapunov stable and converge faster than backpropagation.
New PCstar algorithm discovers causal structure of max-linear Bayesian networks.
problem Discovering causal structure in max-linear Bayesian networks due to non-faithfulness.
method PC algorithm modified with C∗-separation assumptions. result PCstar algorithm can orient additional edges not possible with standard PC algorithm.
Study embeds PC matrices into Grassmannian manifold for geometric interpretation.
problem Understanding algebraic consistency of pairwise comparisons matrices.
method Leverages Plücker coordinates and geometric interpretation of Grassmannian manifold.
result Algebraic consistency condition is equivalent to geometric consistency in G(2,n). The study analyzes and mitigates errors in PC-based causal discovery methods.
problem Errors in PC-based causal discovery methods can lead to incorrect graphs.
method The study introduces coherency scores to detect assumption violations and small sample errors in PC-based methods.
result The coherency scores can detect errors that other methods cannot, bridging between global and local error detection.
We consider constraint-based methods for causal structure learning, such as the PC-, FCI-, RFCI- and CCD- algorithms (Spirtes et al. (2000, 1993), Richardson (1996), Colombo et al. (2012), Claassen et al. (2013)). The first step of all these algorithms consists of the PC-algorithm. This algorithm is known to be order-d…
The PC algorithm allows investigators to estimate a complete partially directed acyclic graph (CPDAG) from a finite dataset, but few groups have investigated strategies for estimating and controlling the false discovery rate (FDR) of the edges in the CPDAG. In this paper, we introduce PC with p-values (PC-p), a fast al…
AutoPC optimizes hyperparameters for the PC algorithm to improve its performance.
problem The unsupervised nature of the PC algorithm makes it difficult to tune the Type I α level. method AutoPC optimizes α directly for a chosen metric and ensures stability through a second run. result AutoPC consistently outperforms state-of-the-art methods across multiple metrics.
Proposes PCS framework for veridical data science results.
problem Ensuring reliable, reproducible, and transparent data science results.
method PCS workflow with predictability, computability, and stability principles.
result PCS inference procedures demonstrate favorable performance in high-dimensional simulations.
PCS-UQ framework improves uncertainty quantification for machine learning models.
problem Ensuring trustworthy uncertainty quantification for machine learning models in high-stakes domains.
method PCS-UQ framework based on Predictability, Computability, and Stability principles, integrating prediction-checking, bootstrap samples, and multiplicative calibration.
result PCS-UQ maintains target coverage while outperforming or matching conformal methods in interval width and subgroup coverage.
The paper improves PCS approximation for ranking and selection under limited simulation budgets.
problem Improving finite sample performance in Ranking and Selection.
method Develops a Bahadur-Rao type expansion for PCS, proposes a novel FCBA policy.
result FCBA policy achieves superior PCS performance compared to traditional methods.
Paper proposes Monarch matrices for scalable probabilistic circuits.
problem Improving scalability of probabilistic circuits.
method Sparse Monarch matrices for sum blocks in PCs.
result Significantly reduces memory and computation costs, enabling unprecedented scaling.
Unified framework for structure learning via conditional independence testing.
problem Optimal structure learning and conditional independence testing.
method Established a fundamental connection and reduction between structure learning and conditional independence testing.
result Optimal rates for structure learning are determined by conditional independence testing rates.
Enhanced PC2 improves surrogate modeling for high-dimensional problems.
problem Degrading performance and efficiency of PC2 in high-dimensional parameter spaces. method Integrates SULM solver and D-optimal sampling strategy into PC2 framework. result Enhanced PC2 demonstrates better comprehensive capability and efficiency. Bayesian optimization improves PC algorithm for learning Gaussian Bayesian networks.
problem Suboptimal reconstruction results due to human bias in parameter selection.
method Optimizes parameters using Bayesian optimization to find best reconstruction score.
result BO method finds better parameters than random search and expert recommendation.
A new algorithm calculates L1-norm principal components efficiently for large datasets.
problem Efficiently calculating L1-norm principal components for large datasets.
method Suboptimal algorithm with cost comparable to standard PCA, using bit flipping.
result Achieves higher L1-PC optimization metric than alternatives.
A new measure PC allows fair comparison of AIWP and NWP models.
problem Fair comparison of AIWP and NWP model outputs.
method Postprocessing deterministic model outputs with isotonic distributional regression (IDR) and calculating PC as mean CRPS of postprocessed forecasts.
result The GraphCast model outperforms the ECMWF HRES model in WeatherBench 2 data.
Study characterizes cryospheric spectral feature space using joint PC+t-SNE approach.
problem Characterize cryospheric spectral feature space for remote sensing applications.
method Compare and contrast two approaches for identifying feature space basis vectors via dimensionality reduction (PCA and t-SNE).
result Joint characterization reveals distinct continua and clusters of ice reflectance properties.
Optimal algorithms learn Gaussian trees and polytrees from data.
problem Learning undirected Gaussian trees and polytrees from data.
method Two approaches: Chow-Liu algorithm for tree structure and modified PC algorithm for polytree structure.
result Explicit finite-sample guarantees and matching lower bounds for both approaches.
New theory shows predictive coding makes learning landscape easier to navigate.
problem Understanding the impact of predictive coding's inference procedure on learning efficiency.
method Analyzed the geometry of the energy landscape of deep linear networks, proving many non-strict saddles become strict in the equilibrated energy.
result All highly degenerate (non-strict) saddles of the loss become strict in the equilibrated energy, suggesting a more robust learning landscape.
EiNets improve PCs for scalable probabilistic modeling.
problem Scalability issues in training PCs on real-world data.
method Combining einsum operations for speedups and memory savings; simplifying EM for PCs.
result EiNets can scale to large datasets like SVHN and CelebA.
Stable specification search now handles latent variables.
problem Discovering causal relationships between latent variables.
method Extended S3C to S3C-Latent, combining stability selection and multi-objective optimization.
result S3C-Latent outperformed PC-MIMBuild on simulated and real-world data.
Novel hybrid method for Bayesian network structure learning reduces computational time without sacrificing accuracy.
problem Bayesian network structure learning efficiency and accuracy trade-off.
method Partitioned PC (pPC), p-value adjacency thresholding (PATH), hybrid greedy initialization (HGI). result pHGS achieves significant computational reductions compared to the PC algorithm without sacrificing structure learning accuracy.
Bayesian Predictive Coding improves deep learning uncertainty quantification.
problem Limitations of maximum a posteriori and maximum likelihood estimates in predictive coding.
method Developed Bayesian Predictive Coding (BPC) that estimates a posterior distribution over network parameters.
result BPC offers comparable uncertainty quantification to existing methods in Bayesian deep learning and improves convergence properties.
MRPC improves causal graph inference in R with better accuracy.
problem Accurate inference of causal graphs from data.
method Improves the PC algorithm with online FDR control, v-structure identification, and robust correlation estimation.
result Significantly reduces false positive edges and accurately identifies v-structures.
Regularized MFPCA smooths multivariate functional data for clearer patterns.
problem Challenges in controlling roughness of multivariate functional PCs.
method ReMFPCA incorporates a roughness penalty in a penalized framework to smooth PCs.
result Smoothed multivariate functional PCs reveal clearer patterns.
New latent variable model improves inflation forecasting accuracy.
problem Improving medium-term inflation forecasting accuracy.
method Formulated and tested a latent variable Phillips curve hypothesis using 3,968 factor combinations.
result Latent variable PC models outperform traditional models by 6-8 quarters.
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components (PCs) are usually linear combinations of all the original variables, and it is thus…
PNCs balance tractability and expressiveness in probabilistic modeling.
problem Balancing tractability and expressiveness in probabilistic models.
method Introduce probabilistic neural circuits (PNCs) as a mix of Bayesian networks and neural networks.
result PNCs are powerful function approximators.
A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a hyperquadric of neutral signature if and only if the pc conformal curvature vanishes. I…
Reduces average-case complexity of sparse PCA from weak PC conjectures.
problem Characterizing the average-case complexity of sparse PCA.
method Reduction from planted clique conjecture to spiked covariance model.
result First full characterization of computational barrier in spiked covariance model, providing tight lower bounds at all sparsities.
PC-PG balances exploration and exploitation in reinforcement learning.
problem Local policy gradient methods struggle with exploration.
method PC-PG uses an ensemble of learned policies (policy cover) to balance exploration and exploitation.
result PC-PG provides strong theoretical guarantees and empirical validation.
New method solves sparse PCA for multiple components efficiently.
problem Sparse PCA for multiple orthogonal components.
method Reformulates orthogonality as rank constraints, uses semidefinite relaxations and bounds.
result Exact solutions with near-optimal variance explained and orthogonality.
New method estimates causal effects of time-varying biomarkers on patient outcomes.
problem Estimating causal effects of time-dependent exposures in high-dimensional settings.
method Chronologically ordered PC-algorithm (COPC-algorithm) to extend IDA method.
result CPDAGs obtained using COPC-algorithm provide more accurate causal effect estimates and preserve chronological structure.
Two samplers show similar performance on CIFAR-10, despite theoretical differences.
problem Comparing Predictor-Corrector (PC) and SGLD samplers on a canonical JEM model.
method Reproduced canonical JEM on CIFAR-10 using both PC and SGLD, tested across three protocols.
result No method-level advantage of PC over SGLD was observed; both methods perform similarly.
The paper develops a method for optimal projection selection in high-dimensional classification.
problem High-dimensional classification with latent variable structure.
method Formulates a latent-variable model and proposes a computationally efficient classifier.
result Explicit rates of convergence for excess risk of the proposed classifier are derived and shown to be optimal.
A new neural network model predicts inflation and output gap more accurately.
problem Traditional Phillips curves struggle with unobserved inflation expectations and output gaps.
method Hemisphere Neural Network (HNN) that estimates latent states for inflation and output gap.
result HNN accurately forecasts inflation and identifies a large positive output gap starting from late 2020.