We study graph matching with correlated Gaussian features and find thresholds for exact recovery.
problem Graph matching with correlated Gaussian features.
method Information-theoretic thresholds and conditions for exact and almost exact recovery.
result Contextual information introduces a richer structure, with thresholds for exact and almost exact recovery no longer coinciding.
Paper studies vertex correspondence recovery in correlated graphs with node features.
problem Recovering hidden vertex correspondence between two correlated graphs with observed edge weights and node features.
method Introduced featured correlated Gaussian Wigner model and proposed QPAlign algorithm for quadratic programming relaxation.
result Characterized optimal information-theoretic thresholds for exact and partial recovery of latent mapping.
Study connects database alignment and planted matching using Gaussian features.
problem Identify matching between correlated user features in anonymized databases.
method Derived results for database alignment and planted matching, showing connections and thresholds.
result Performance thresholds for database alignment converge to planted matching when feature dimensionality is sufficiently high.
A new method for approximating softmax and Gaussian kernels with reduced error.
problem Approximating softmax and Gaussian kernels with low error.
method Simplex Random Features (SimRFs) and SimRFs+.
result SimRFs provide the smallest MSE among weight-independent geometrically-coupled PRF mechanisms.
Unsupervised anomaly detection aims to identify anomalous samples from highly complex and unstructured data, which is pervasive in both fundamental research and industrial applications. However, most existing methods neglect the complex correlation among data samples, which is important for capturing normal patterns fr…
CatNet controls FDR in LSTM models using SHAP feature importance and Gaussian mirrors.
problem Controlling False Discovery Rate (FDR) in LSTM models with feature selection.
method CatNet uses SHAP values for feature importance and Gaussian Mirror algorithm for FDR control. It introduces a kernel-based independence measure to handle feature correlations.
result CatNet reduces overfitting and improves model interpretability on simulated and real-world data.
The paper models financial correlation matrices using permutation invariant Gaussian models and predicts market anomalies.
problem Modeling and predicting financial correlation matrices from high-frequency data.
method Constructing permutation invariant Gaussian matrix models with 4 parameters, using graph theory and polynomial functions.
result The permutation invariant Gaussian matrix model predicts the expectation values of cubic and quartic polynomials with strong evidence of fit.
New insights on how weight structure affects generalization in deep Gaussian feature models.
problem Understanding how weight structure impacts generalization in deep learning models.
method Using the replica trick from statistical physics to derive learning curves for models with structured Gaussian features.
result Allowing correlations between the rows of the first layer of features can aid generalization, while structure in later layers is generally detrimental.
The paper provides exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations.
problem Capturing the statistical properties of fluctuating correlations in non-stationary systems.
method Developed a random matrix model to average multivariate amplitude distributions from short time scales to large time scales.
result Explicit multivariate distributions for non-stationary correlation systems are provided, capturing the degree of non-stationarity.
The study identifies spurious correlations in high-dimensional regression and quantifies their impact.
problem Spurious correlations in high-dimensional regression models.
method Statistical characterization of spurious correlations, quantifying their amount via ridge regularization.
result The value of regularization strength that minimizes test loss is in an interval where spurious correlations increase.
The paper develops a Gaussian process model for predicting chemical efficacy.
problem Statistical methodologies for analyzing chemical databases are limited.
method Conditional Gaussian process models with Tanimoto distance and a scaling parameter.
result Predictive performance improves when accounting for chemical space correlation.
This study uses local Gaussian correlation to analyze stock return tails, revealing more sensitive network properties.
problem Misleading results from Pearson correlation in financial networks.
method Local Gaussian correlation coefficient for capturing nonlinear dependence and heavy-tailed distributions.
result Local Gaussian correlation network among negative tails is more sensitive to stock market risks.
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric models are usually built from completely random measures, a Poisson-process based c…
NGMs create mirrored features to assess neural network feature importance.
problem Lack of feature relevance information in DNNs limits their applicability.
method Structured perturbation and kernel-based conditional dependence measure for feature importance evaluation.
result Controls feature selection error rate and maintains high selection power with correlated features.
Polynomial time algorithm matches correlated Gaussian matrices without vanishing correlation.
problem Matching vertices in two correlated Erdős-Rényi graphs.
method Iterative matching algorithm for correlated Gaussian Wigner matrices.
result First polynomial time algorithm for graph matching with arbitrarily small constant correlation.
Study of deep linear neural networks with proportional width and depth.
problem Lack of descriptive power in Gaussian limit of deep linear neural networks.
method Proportional infinite-width infinite-depth limit for deep linear neural networks.
result Characterization of limiting distribution as a nontrivial mixture of Gaussians.
Optimal Bayesian feature filtering (OBF) is a supervised screening method designed for biomarker discovery. In this article, we prove two major theoretical properties of OBF. First, optimal Bayesian feature selection under a general family of Bayesian models reduces to filtering if and only if the underlying Bayesian m…
A new method for nonstationary Gaussian processes using Fourier features.
problem Efficient simulation of nonstationary Gaussian processes with high-dimensional distributions.
method Discretizes the spectral representation of nonstationary processes, avoiding probability measure assumptions.
result An efficient low-rank approximation of nonstationary spectral densities, consistent and positive semi-definite.
We consider analysis of relational data (a matrix), in which the rows correspond to subjects (e.g., people) and the columns correspond to attributes. The elements of the matrix may be a mix of real and categorical. Each subject and attribute is characterized by a latent binary feature vector, and an inferred matrix map…
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian distribution, both uncorrelated and correlated in time, are used. For the uncorrelated …
FABLE incorporates instance features into PWS label models for improved performance.
problem Lack of instance features in existing label models limits their performance.
method FABLE uses a mixture of Bayesian label models and a Gaussian Process classifier to incorporate instance features.
result FABLE achieves the highest averaged performance across nine baselines on benchmark datasets.
We analyze learning curves of RF models with convex regularization and derive precise asymptotic expressions.
problem Understanding the learning curves of RF models with general convex regularization.
method Novel multi-level application of the convex Gaussian min max theorem (CGMT) to compute precise asymptotic expressions.
result Precise asymptotic expressions for learning curves of RF models with separable strongly convex regularization or ℓ1 regularization. A new method identifies sub-populations in unlabelled heterogeneous data by accounting for co-features.
problem Estimating sub-populations in unlabelled heterogeneous data with co-features.
method Mixture of Conditional Gaussian Graphical Models (CGGM) with penalized EM algorithm.
result The method successfully identifies sub-populations disrupted by co-features.
Enhances robustness of MOGP regression for multiple correlated outputs.
problem Model misspecification and outliers in MOGP regression.
method Extends RCGP framework to multi-output setting.
result Provable robust MOGP with joint correlation capture.
We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long ho…
Optimal Bayesian feature selection (OBFS) is a multivariate supervised screening method designed from the ground up for biomarker discovery. In this work, we prove that Gaussian OBFS is strongly consistent under mild conditions, and provide rates of convergence for key posteriors in the framework. These results are of …
The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…
tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.
problem Agnostic latent variables in VAEs ignore data structure correlations.
method Proposes tensor-variate Gaussian process prior for variational autoencoder.
result Explicitly modeling correlation structures improves model performance in reconstruction.
Study predicts SGD test loss for structured features.
problem Understanding test loss dynamics in SGD for structured data.
method Solveable model of SGD on mean square loss for arbitrary covariance structure.
result Simpler Gaussian model accurately predicts test loss of nonlinear models.
New method improves portfolio allocation using local Gaussian correlation.
problem Asymmetric dependence in asset returns.
method Local Gaussian correlation to extend mean-variance framework.
result New method outperforms existing portfolios for monthly asset returns.
New inflation model captures correlations and skew in interest rates.
problem Modeling inflation with market correlations and skew.
method Multi-factor volatility structure with parametric correlation calibration, leveraging single-factor Gaussian model.
result Captures market volatility skew with a single process, simplifying model calibration.
The paper examines non-Gaussian models for financial data.
problem Modeling financial data with non-Gaussian distributions.
method Analysis of multivariate non-Gaussian models focusing on parsimony, dependence structure, and computational aspects.
result Characterization and calibration of models for financial log-returns.
A new method for Gaussian Processes handles mixed continuous and categorical inputs.
problem Modeling cross-correlations between continuous and categorical data.
method Low-Rank Correlation (LRC) method for Gaussian Processes with flexible rank approximation.
result LRC outperforms existing methods in estimating cross-correlations and predicting response surfaces.
Study on feature learning dynamics in infinite-depth neural networks, focusing on ResNets.
problem Understanding how features evolve during training in deep neural networks, especially in the large-depth limit.
method Conditional Gaussian representations and SDE system with decoupled backward weights.
result Depth-induced suppression of forward-backward coupling in infinite-depth networks, leading to a decoupled forward-backward SDE system.
Improved sample complexity for Gaussian Mixture Models using Pair Correlation Factor.
problem Understanding the sample complexity of Gaussian Mixture Models.
method Introducing Pair Correlation Factor (PCF) to measure clustering of component means and improving sample complexity bounds.
result The Pair Correlation Factor (PCF) more accurately determines the difficulty of parameter recovery in Gaussian Mixture Models.
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary non-Gaussian process which captures many features observed in time series of real stock r…
Paper relaxes differential privacy for correlated features, improving privacy-utility trade-off.
problem Standard differential privacy ignores feature correlation, leading to suboptimal privacy-utility balance.
method Introduces CorrDP framework that accounts for feature correlation, using total variation distance for quantification.
result CorrDP algorithms outperform standard DP in synthetic and real-world datasets with insensitive features.
This work explores variably scaled kernels to improve non-stationary Gaussian processes.
problem Limited ability of stationary kernels to represent heterogeneous correlation structures.
method Introduces variably scaled kernels to modify correlation structures explicitly.
result Improved reconstruction accuracy and better uncertainty estimates for non-stationary data.
Approach for selecting features by discarding nuisance and correlated ones.
problem Large datasets with correlated and nuisance features.
method Laplacian score criterion, autoencoder architecture, concrete layer.
result Outperforms similar approaches in clustering performance.
Kernel methods linked to feature subspaces and maximal correlation kernels.
problem Understanding kernel methods and their relationship to feature extraction.
method Established a correspondence between feature subspaces and kernels, introduced maximal correlation kernels, and demonstrated their optimality.
result Kernel SVM on maximal correlation kernel achieves minimum prediction error.
Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on Gaussian graphical models and covariance selection algorithms can not handle such d…
Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical model for such data, by combining assumptions from phylogenetics with Gaussian pro…
GNP models predictive correlations and outperforms NPs.
problem Training and understanding of Neural Processes.
method Proposed a new model, Gaussian Neural Process (GNP), which incorporates translation equivariance and provides universal approximation guarantees.
result Demonstrates encouraging performance and provides universal approximation guarantees.
Study reveals supply chain correlations in firm growth rates.
problem Understanding correlations in firm growth rates and their supply chain relationships.
method Investigated correlation structure of firm growth rates and used Gaussian Markov Models to reconstruct supply chain networks.
result Supply chain-linked firms exhibit stronger correlation in growth rates than non-linked firms.
DFI maps covariates to latent representations for feature importance.
problem Feature importance when predictors are statistically dependent.
method Disentangled Feature Importance (DFI) using entropic optimal transport.
result DFI yields stable, interpretable, uncertainty-quantified attributions of shared predictive signal.
A graph neural network transforms features in each vertex's neighborhood into a vector representation of the vertex. Afterward, each vertex's representation is used independently for predicting its label. This standard pipeline implicitly assumes that vertex labels are conditionally independent given their neighborhood…
Exact and scalable algorithm for Gaussian process regression with Matérn correlations.
problem Efficient Gaussian process regression with Matérn correlations.
method Novel kernel packet theory and sparse representation of covariance matrix.
result Significantly superior to existing alternatives in computational time and predictive accuracy.
Study examines challenges in variable importance ranking due to feature correlation.
problem Challenges in variable importance ranking under correlation.
method Simulation study and theoretical analysis of feature knockoffs and conditional predictive impact (CPI).
result Highly correlated features increase the correlation of knockoff variables, posing a limitation for CPI.