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.
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…
It was shown recently that the K L1-norm principal components (L1-PCs) of a real-valued data matrix X∈RD×N (N data samples of D dimensions) can be exactly calculated with cost O(2NK) or, when advantageous, O(NdK−K+1) where $d=\mathrm{rank}(\mathbf …
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.
Recently, the intervention calculus when the DAG is absent (IDA) method was developed to estimate lower bounds of causal effects from observational high-dimensional data. Originally it was introduced to assess the effect of baseline biomarkers which do not vary over time. However, in many clinical settings, measurement…
A recent trend of fair machine learning is to define fairness as causality-based notions which concern the causal connection between protected attributes and decisions. However, one common challenge of all causality-based fairness notions is identifiability, i.e., whether they can be uniquely measured from observationa…
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.
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.
A new algorithm infers causal networks from data using topological thresholds.
problem Inferring causal networks from data.
method Two methods for determining topological thresholds: one to leave no disconnected nodes, the other to find a causal large connected component.
result The novel algorithm is faster and more accurate than the PC algorithm.
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.
Building and expanding on principles of statistics, machine learning, and scientific inquiry, we propose the predictability, computability, and stability (PCS) framework for veridical data science. Our framework, comprised of both a workflow and documentation, aims to provide responsible, reliable, reproducible, and tr…
A method predicts posterior PCs for faster uncertainty quantification in imaging.
problem Uncertainty visualization in image restoration models is limited by per-pixel variances.
method Neural Posterior Principal Components (NPPC) method for predicting PCs in a single forward pass.
result Orders of magnitude faster uncertainty quantification compared to posterior samplers.
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.
A dynamical system can be regarded as an information processing apparatus that encodes input streams from the external environment to its state and processes them through state transitions. The information processing capacity (IPC) is an excellent tool that comprehensively evaluates these processed inputs, providing de…
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. 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.
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 …
In our previous study, we introduced stable specification search for cross-sectional data (S3C). It is an exploratory causal method that combines stability selection concept and multi-objective optimization to search for stable and parsimonious causal structures across the entire range of model complexities. In this st…
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.
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.
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). 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…
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.
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.
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.
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 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.
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.
The study learns causal graphs from time series data using entropy measures.
problem Learning causal graphs from time series data.
method Constraint-based framework, information-theoretic measures, generalized causation entropy, PC and FCI algorithms.
result The methods effectively construct causal graphs from time series data.
This paper deals with multivariate regression chain graphs (MVR CGs), which were introduced by Cox and Wermuth [3,4] to represent linear causal models with correlated errors. We consider the PC-like algorithm for structure learning of MVR CGs, which is a constraint-based method proposed by Sonntag and Peña in [18]. We …
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…
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.
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.
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.
Generative Adversarial Networks (GAN) can achieve promising performance on learning complex data distributions on different types of data. In this paper, we first show a straightforward extension of existing GAN algorithm is not applicable to point clouds, because the constraint required for discriminators is undefined…
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.
In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the average-case complexity of sparse PCA through reductions from the planted clique (PC) con…
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.
Exact inference in the linear regression model with spike and slab priors is often intractable. Expectation propagation (EP) can be used for approximate inference. However, the regular sequential form of EP (R-EP) may fail to converge in this model when the size of the training set is very small. As an alternative, we …
We take steps towards understanding the "posterior collapse (PC)" difficulty in variational autoencoders (VAEs),~i.e. a degenerate optimum in which the latent codes become independent of their corresponding inputs. We rely on calculus of variations and theoretically explore a few popular VAE models, showing that PC alw…
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…
Bio-inspired neural networks use predictive coding for efficient weight updates.
problem Training artificial neural networks efficiently and biologically plausibly.
method Predictive Coding (PC) updates weights locally using only local information.
result PC provides theoretical advantages like automatic gradient scaling.
Asymptotic factorizations for the small-ball probability (SmBP) of a Hilbert valued random element X are rigorously established and discussed. In particular, given the first d principal components (PCs) and as the radius ε of the ball tends to zero, the SmBP is asymptotically proportional to (a) the joi…
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.
CCs learn high-dimensional distributions from heterogeneous data.
problem Learning high-dimensional distributions from heterogeneous data.
method Introducing characteristic circuits (CCs) that learn from data and use spectral domain.
result CCs outperform state-of-the-art density estimators on common benchmark data sets.