New method for estimating lead-lag times between non-synchronously observed point processes.
problem Estimating lead-lag relationships between non-synchronously observed point processes.
method Formulate lead-lag estimation as CPCF shape estimation; propose kernel density estimation-based lead-lag time estimator.
result Proposed method delivers superior numerical performance and effective lead-lag time estimation.
Study on Gaussian ensemble of matrix products with mixed moments computed.
problem Understanding the statistical properties of matrix products of Gaussian matrices.
method Analysis of a multi-Wishart ensemble and enumeration of non-crossing pairings.
result Mixed moments of the product matrix are computed and found to be weighted by Fuss-Catalan numbers at large N. Log-conformal projective pairs restrict to simple geometric structures.
problem Characterizing pairs of projective manifolds with logarithmic conformal tensors.
method Analyzing the nefness and triviality of KX+Δ to deduce geometric properties. result Pairs of projective manifolds with logarithmic conformal tensors are restricted to simple geometric structures.
Study on bit threads and their locking properties in holographic spacetimes.
problem Understanding the conditions under which regions can be locked in holographic spacetimes.
method Investigation of different density bounds and their implications on the locking of regions.
result Non-crossing regions can be locked under the most stringent bound, but crossing regions cannot.
Universal functions derived for topological correlators in Yang-Mills theory.
problem Expressing correlation functions of topologically twisted Yang-Mills theory.
method Combining Seiberg-Witten geometry, u-plane integral, and blowup formula.
result Closed expressions for universal functions determined.
Using first principles from inference, we design a set of functionals for the purposes of \textit{ranking} joint probability distributions with respect to their correlations. Starting with a general functional, we impose its desired behaviour through the \textit{Principle of Constant Correlations} (PCC), which constrai…
The paper proposes new cross-correlators using Price's Theorem and piecewise-linear decomposition.
problem Optimal method for estimating cross-correlations using finite samples.
method General mathematical framework using Price's Theorem and piecewise-linear decomposition.
result Some cross-correlators based on Huber's loss functions, MP functions, and LSE functions have higher SNR.
Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar features, while some others may have almost no cross-correlations with quite di…
We conduct an empirical study using the quantile-based correlation function to uncover the temporal dependencies in financial time series. The study uses intraday data for the S\&P 500 stocks from the New York Stock Exchange. After establishing an empirical overview we compare the quantile-based correlation function to…
Symmetry of neural network densities can be determined from correlation functions.
problem Determining symmetries of neural network densities without knowing the density itself.
method Symmetry-via-duality approach using invariance properties of correlation functions.
result Symmetries of neural network densities can be determined via dual computations of correlation functions.
Neurons in the visual cortex are correlated in their variability. The presence of correlation impacts cortical processing because noise cannot be averaged out over many neurons. In an effort to understand the functional purpose of correlated variability, we implement and evaluate correlated noise models in deep convolu…
Study neural networks by mapping correlations, revealing essential statistics.
problem Understanding information processing in trained neural networks.
method Characterize neural network as distribution transformations, focusing on correlation functions.
result Higher-order correlations are crucial for internal layers, while input layer captures more.
A new geometric framework embeds correlation matrices into Euclidean space for scalable brain network analysis.
problem Inefficient and unstable analysis of functional brain networks in high-dimensional contexts.
method Diffeomorphic transformations to embed correlation matrices into Euclidean space, preserving manifold properties.
result Improved computational speed and enhanced accuracy compared to conventional manifold-based approaches.
We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. We derive closed-form expressions for the correlation functions and leverage for a general form of the stochastic term. We also discuss correlation functions and leverage for three specific models -- multiplicative,…
The paper uses distance correlation for brain connectivity and a novel multi-task learning model for age prediction.
problem Estimating age-related gender differences in brain functional connectivity.
method Estimates functional connectivity using distance correlation and proposes a non-convex multi-task learning model.
result The proposed non-convex multi-task learning model outperforms other models in age prediction and gender-specific connectivity.
We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is convergent and scale invariant in the large but finite number limit. We demonstra…
The study examines correlations of logarithms of integers at different scalings.
problem Analyzing pair correlations of logarithms of integers at various scalings.
method Examined correlations of logarithms of positive integers at different scalings, proving the existence of pair correlation functions.
result Level repulsion at linear scaling, total loss of mass at superlinear scalings, and Poissonian behavior at sublinear scalings.
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only o…
Derives stress-energy identities in Liouville theory on compact surfaces.
problem Stress-energy tensor correlation functions on compact Riemann surfaces.
method Varying correlation functions with respect to background metric, treating different types of variations separately.
result Stress-energy correlation functions expressed as differential operators acting on primary field correlation functions.
This paper sets thresholds for recovering vertex correspondences in partially correlated graphs.
problem Recovering hidden vertex correspondences in partially correlated graphs.
method Proposed partially correlated Erdős-Rényi graphs model; information-theoretic thresholds; correlated functional digraphs.
result Optimal rates for partial and exact recovery of vertex correspondences.
Abstract result on correlations of pairs in exponentially growing discrete subsets.
problem Pair correlations in exponentially growing discrete subsets with weight functions.
method Proved abstract result on correlations of pairs of elements in an exponentially growing discrete subset with a weight function.
result Distribution function of unscaled differences is t↦2δe−∣t∣, and pair correlation exhibits Poissonian behavior under certain conditions. We construct a price impact model between stocks in a correlated market. For the price change of a given stock induced by the short-run liquidity of this stock itself and of the information about other stocks, we introduce a self- and a cross-impact function of the time lag. We model the average cross-response function…
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 shows decay of correlations on specific types of flows.
problem Analyzing decay of correlations in specific flow types.
method Asymptotic expansion of correlation function on Abelian covers.
result Established an expansion in inverse powers of time.
The u-plane integral is the contribution of the Coulomb branch to correlation functions of N=2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group SU(2), for an arbitrary four-manifold with (b1,b2+)…
We study the character of the infinite wedge projective representation of the algebra of differential operators on the circle. We prove quasi-modularity of this character and also compute certain generating functions for traces of differential operators which we call correlation functions. These correlation functions a…
We study historical correlations and lead-lag relationships between individual stock risk (volatility of daily stock returns) and market risk (volatility of daily returns of a market-representative portfolio) in the US stock market. We consider the cross-correlation functions averaged over all stocks, using 71 stock pr…
The article proposes optimal learning strategies for machine learning-based reliability analysis.
problem Improving computational efficiency and accuracy in machine learning-based reliability analysis.
method Theorems and mathematical proofs for optimal learning strategies considering and neglecting correlations among design samples.
result The optimal learning strategy considering Kriging correlation outperforms other methods in terms of reduced evaluations of performance functions.
Study feature representations induced by dependence between variables.
problem Learning feature representations from dependent random variables.
method Characterized sufficient and necessary conditions for dependence-induced representations, and provided a family of loss functions.
result Features learned from the family of loss functions can be expressed as the composition of a loss-dependent function and the maximal correlation function.
Study topological correlators for SU(2) SYM on four-manifolds, deriving explicit formulae and confirming S-duality.
problem Topological correlation functions of SU(2), N=2∗ SYM on four-manifolds. method Coupling to a Spin^c structure, deriving explicit formulae, and confirming S-duality.
result Topological correlators are mock modular forms for b2+=1. New method for analyzing multiple longitudinal data processes.
problem Exploring associations between multiple random processes observed jointly.
method Functional Generalized Canonical Correlation Analysis (FGCCA) based on multiblock Regularized Generalized Canonical Correlation Analysis (RGCCA).
result FGCCA framework is robust to sparsely and irregularly observed data.
Machine learning often needs to model density from a multidimensional data sample, including correlations between coordinates. Additionally, we often have missing data case: that data points can miss values for some of coordinates. This article adapts rapid parametric density estimation approach for this purpose: model…
We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorithms do not consider such temporal correlations and thus their performance degrades significantly with the correlations. I…
Geometrically constructs twist-field correlation functions in CFT.
problem Understanding entanglement entropy in quantum systems.
method Using Cauchy-Hadamard renormalization of Polyakov anomaly integral on surfaces with conical singularities.
result Provides a purely mathematical interpretation of entanglement entropy results.
The study shows how trade uncertainty affects stock-bond correlations over time.
problem Impact of trade policy uncertainty on stock-bond correlations.
method Daily data analysis using GARCH-based models (CCC, STCC, DCC) with TPU and political dummy variables.
result Time-varying correlation models better capture the dynamics of stock-bond correlations than constant models.
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equa…
Two new methods for analyzing repeated measures data using embeddings into Reproducing Kernel Hilbert Spaces.
problem Analyzing complex data structures with multiple features over time.
method Two generalizations of canonical correlation analysis for repeated measures data using embeddings into Reproducing Kernel Hilbert Spaces.
result Consistency rates for transformation and correlation estimators, relaxing common assumptions.
Enhances sensitivity analysis for correlated inputs.
problem Estimating sensitivity indices in models with correlated inputs.
method Proposes an extension of Sobol' estimator using a linear correlation model.
result Improves accuracy in variance-based sensitivity analysis.
Develops a method for stress testing correlations of financial portfolios.
problem Stress testing correlations in financial asset portfolios.
method Parametric representation of correlations, Bayesian variable selection, joint distribution of stress scenarios.
result Inference of worst-case correlation scenarios using stress tests.
Research examines correlations of complex logarithms of lattice points, showing level repulsion and Poissonian behavior.
problem Analyzing correlations of complex logarithms of lattice points.
method Proving existence of pair correlation functions and examining behavior at various scalings.
result Level repulsion observed at linear scaling, Poissonian behavior at sublinear scalings.
Resolves spurious correlations in causal models via intervention design.
problem Spurious correlations lead to incorrect causal models in reinforcement learning environments.
method Proposes a method to design interventions that improve causal models by incentivizing agents to find errors.
result Experimental results show improved causal models compared to baselines.
Proposes a flexible MGP model for dynamic, sparse correlations.
problem Handling dynamic and sparse correlations in multivariate data.
method Non-stationary MGP with dynamic spike-and-slab prior and EM algorithm.
result Captures dynamic and sparse correlations effectively.
Improved control approach for correlated bandits with better performance.
problem General multi-armed bandit problem with correlated elements.
method Introducing entropy regularisation to obtain a smooth asymptotic approximation of the value function, leading to a semi-index approximation of the optimal decision process.
result Performance of Asymptotic Randomised Control (ARC) algorithm compares favorably with other approaches.
Paper introduces a new cost function to improve deep learning model generalization.
problem Overfitting and poor extrapolation of deep learning models.
method Introduces a 'whitening' cost function based on the Ljung-Box statistic.
result Significant improvement in generalization for RNNs and image autoencoders.
An average instantaneous cross-correlation function is introduced to quantify the interaction of the financial market of a specific time. Based on the daily data of the American and Chinese stock markets, memory effect of the average instantaneous cross-correlations is investigated over different price return time inte…
Although modern recommendation systems can exploit the structure in users' item feedback, most are powerless in the face of new users who provide no structure for them to exploit. In this paper we introduce ImplicitCE, an algorithm for recommending items to new users during their sign-up flow. ImplicitCE works by trans…
Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification o…
We study the structure of locational marginal prices in day-ahead and real-time wholesale electricity markets. In particular, we consider the case of two North American markets and show that the price correlations contain information on the locational structure of the grid. We study various clustering methods and intro…