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.
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.
Local Gaussian correlation struggles in tails but a new method improves it.
problem Local Gaussian correlation's limitations in tail dependence.
method A new adaptive bandwidth method for LGC, optimizing for local effective sample size.
result Adaptive bandwidths outperform global ones in moderate dependence, but not in strong or weak dependence.
Central to robot exploration and mapping is the task of persistent localization in environmental fields characterized by spatially correlated measurements. This paper presents a Gaussian process localization (GP-Localize) algorithm that, in contrast to existing works, can exploit the spatially correlated field measurem…
In this paper we provide evidence that financial option markets for equity indices give rise to non-trivial dependency structures between its constituents. Thus, if the individual constituent distributions of an equity index are inferred from the single-stock option markets and combined via a Gaussian copula, for examp…
Real-world measurement noise in applications like robotics is often correlated in time, but we typically assume i.i.d. Gaussian noise for filtering. We propose general Gaussian Processes as a non-parametric model for correlated measurement noise that is flexible enough to accurately reflect correlation in time, yet sim…
Empirical Bayes method improves Gaussian sequence model inference.
problem Estimating parameters in correlated Gaussian sequence models.
method Maximum Composite Marginal Likelihood (CML) estimator, leveraging geometric Brascamp-Lieb inequality.
result CML estimator converges at rate \( n_*^{-1/2} \) in weighted Hellinger distance.
Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both random variables into the co-dependence structure. The analytical expression of…
We study a distributed estimation problem in which two remotely located parties, Alice and Bob, observe an unlimited number of i.i.d. samples corresponding to two different parts of a random vector. Alice can send k bits on average to Bob, who in turn wants to estimate the cross-correlation matrix between the two par…
A new method for sparse Gaussian process regression using correlated experts.
problem Sparse Gaussian process regression for large datasets with cubic computational complexity.
method Aggregating predictions from correlated experts to improve scalability and accuracy.
result Superior performance compared to state-of-the-art methods for synthetic and real-world datasets.
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.
We define a random-matrix ensemble given by the infinite-time covariance matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a Gaussian symmetric matrix. The spectral properties of this ensemble are shown to be in qualitative agreement with some stylized facts of financial markets. Through the…
A new TwinGP framework for efficient large-scale GP modeling.
problem Efficiently modeling large-scale Gaussian processes with computational constraints.
method Combines global and local approximations using a subset-of-data approach.
result TwinGP framework performs on par or better than state-of-the-art methods at a fraction of the computational cost.
We investigate 17 digital currencies making an analogy with quantum systems and develop the concept of eigenportfolios. We show that the density of states of the correlation matrix of these assets shows a behavior between that of the Wishart ensemble and one whose elements are Cauchy distributed. A metric for the parti…
Study uses Shapley value for sensor anomaly detection, proving its superiority in certain cases.
problem Anomaly detection in sensor networks using the Shapley value.
method Optimized binary classifiers, mathematical proofs for different scenarios.
result Shapley value test can be superior or inferior to single-term tests, depending on sensor correlation and attack type.
A scalable GPVAE method using local adjacencies to approximate GP inference.
problem Scalability issues in exact GP inference for large-scale GPVAEs.
method Neighbour-driven approximation strategy that confines computations to nearest neighbours.
result Outperforms other GPVAE variants in predictive performance and computational efficiency.
All too often measuring statistical dependencies between financial time series is reduced to a linear correlation coefficient. However this may not capture all facets of reality. We study empirical dependencies of daily stock returns by their pairwise copulas. Here we investigate particularly to which extent the non-st…
Algorithm recovers graph from Glauber dynamics trajectory without mixing.
problem Learning Gaussian graphical models from a single Glauber dynamics trajectory.
method Three components: conditional variance estimation, pairwise influence test, robust median aggregation.
result Polynomial-time recovery of conditional independence graph from a single trajectory.
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 apply a recently developed wavelet based approach to characterize the correlation and scaling properties of non-stationary financial time series. This approach is local in nature and it makes use of wavelets from the Daubechies family for detrending purpose. The built-in variable windows in wavelet transform makes t…
The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and thus invariant to the translations in the input space. The optimization of the hyp…
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.
Global inducing points improve Bayesian neural network performance.
problem Improving Bayesian neural network performance.
method Adapting correlated approximate posterior to all layers in a Bayesian neural network and deep Gaussian processes using learned global inducing points.
result State-of-the-art performance on CIFAR-10 (86.7%) without data augmentation or tempering.
Two algorithms learn Gaussian graphical models from Glauber dynamics trajectories.
problem Learning Gaussian graphical models from dependent data.
method Two complementary approaches: local edge-testing and burn-in/thinning reduction.
result Both approaches provide finite-sample recovery guarantees and empirical comparisons.
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.
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.
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.
Random Forests adapted for dependent data using GLS.
problem Random Forests' local nature fails for dependent data.
method RF-GLS: GLS loss for correlated data.
result Consistency of RF-GLS under beta-mixing processes.
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.
CaLoNet integrates spatial and local correlations for multivariate time series classification.
problem Ignoring spatial and local correlations in multivariate time series classification.
method Model spatial correlations using causality modeling, extract local correlations, integrate into graph neural network.
result Competitive performance compared to state-of-the-art methods on UEA datasets.
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.
Decor protects decentralized learning models from curious users.
problem Privacy violation in decentralized learning.
method Decor uses correlated Gaussian noises to protect local models in decentralized SGD with differential privacy guarantees.
result Decor matches central DP optimal privacy-utility trade-off for arbitrary connected graphs.
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.
PPM improves graph matching for correlated Gaussian Wigner models with high probability.
problem Graph matching in the Correlated Gaussian Wigner model with edge correlations.
method Seeded projected power method (PPM) for iterative improvement of initial partial matches.
result PPM recovers ground-truth matching with high probability in O(log n) iterations if seed is close enough.
We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a fe…
We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. Extending the exact recovery guarantees established in the companion paper for Gaussian weights, in this work,…
The paper explores local-correlation models for pricing complex financial contracts.
problem Calibrating synthetic quanto forward contracts and composite options.
method Design on-line calibration procedures for local and stochastic volatility models.
result Calibration performance of local-correlation models compared to simpler approximations.
The paper develops a test for independence of selected Gaussian variables after thresholding correlations.
problem Testing independence of selected Gaussian variables after thresholding correlations.
method The approach involves conditioning on the selection event and using a new characterization of the conditioning event in terms of canonical correlation.
result The proposed test has higher power than a naive approach that ignores selection effects.
Deep Gaussian Processes (DGPs) combine the expressiveness of Deep Neural Networks (DNNs) with quantified uncertainty of Gaussian Processes (GPs). Expressive power and intractable inference both result from the non-Gaussian distribution over composition functions. We propose interpretable DGP based on approximating DGP …
We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior distribution where we explicitly model the covariance among the input and output dimensions…
The statistical dependencies which independent component analysis (ICA) cannot remove often provide rich information beyond the linear independent components. It would thus be very useful to estimate the dependency structure from data. While such models have been proposed, they usually concentrated on higher-order corr…
Multifractality in time series arises from temporal correlations, not just fat tails.
problem Understanding the origin of multifractality in time series data.
method Mathematical arguments and numerical simulations using MFDFA approach.
result Genuine multifractality requires temporal correlations, not just fat tails.
Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical copulas with the same unconditional correlation. Furthermore, for Gaussian and Stude…
Study on MC dropout in wide neural networks and its convergence to Gaussian processes.
problem Understanding the behavior of Monte Carlo dropout in wide neural networks.
method Rigorously studied the limiting distribution of wide untrained NNs under dropout, proving convergence to Gaussian processes. Investigated correlations and non-Gaussian behavior in finite width NNs.
result Wide untrained neural networks under dropout converge to Gaussian processes for fixed sets of weights and biases.
We uncover scaling laws and statistical structure in complex datasets.
problem Understanding universal traits in complex datasets.
method Analogizing data to physical systems, using statistical physics and RMT.
result Real-world datasets and Gaussian data with long-range correlations share the same RMT universality class.
Distributed Quantum Gaussian Processes improve modeling in multi-agent systems.
problem Limited expressivity of classical kernels in complex domains.
method Distributed Quantum Gaussian Process (DQGP) with DR-ADMM algorithm.
result Enhanced modeling capabilities and scalability in multi-agent systems.