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.
New analysis of stock market correlations reveals unique properties and optimal portfolio construction.
problem Understanding the unique properties of stock market correlations at different magnitudes.
method Used q-dependent cross-correlation analysis, random matrix theory, and complex network representation.
result Optimal multifractal order for portfolio optimization is approximately q=2.
This paper introduces anti-correlation networks to study China's stock market.
problem Previous studies ignored anti-correlation in financial networks.
method Constructed weighted temporal anti-correlation and positive correlation networks.
result Unveiled differences in topological measurements between anti-correlation and positive correlation networks.
PCA improves with correlated noise, achieving nearly optimal sample complexity.
problem PCA in data-dependent noise, where noise and true data are correlated.
method SVD with bounded noise and simple correlation assumption.
result Nearly optimal sample complexity bound, improving over previous work.
CADGMM detects anomalies by capturing complex correlations in data.
problem Detecting anomalies in complex, unstructured data.
method CADGMM uses a graph structure to encode correlations, then a dual-encoder to learn low-dimensional latent space, followed by a Gaussian Mixture Model for anomaly detection.
result CADGMM effectively detects anomalies in real-world datasets.
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.
Clusters cryptocurrency market states via cross correlation analysis.
problem Analyse cryptocurrency market dynamics.
method Cross correlation structure analysis over 5 years.
result Cryptocurrency market clusters into 4 states.
Novel method calculates complex correlation for high-frequency financial data.
problem Analyzing lead-lag relations in high-frequency financial data.
method Hilbert transform based complex correlation for unevenly spaced data.
result Identifies market components with small but significant delays.
Complex network analysis reveals dominant stocks in financial stock returns correlations.
problem Inferring financial stock returns correlations from complex network analysis.
method Simulated geometric Brownian motion for stocks, complex network analysis, eigenvector centrality, clustering.
result Returns correlation matrix is dominated by stocks with high eigenvector centrality and clustering.
A new method detects long-range cross correlations in complex systems.
problem Detecting long-range cross correlations in complex systems.
method Joint multifractal analysis based on wavelet leaders (MF-X-WL).
result MF-X-WL detects cross correlations in synthetic and real-world data.
This study analyzes cryptocurrency market dynamics using a novel q-dependent detrended cross-correlation method.
problem Capturing correlations at varying fluctuation amplitudes and time scales in complex systems.
method Extends traditional metrics with q-dependent detrended cross-correlation coefficient ρ(q,s) and qMSTs. result Significant shifts in network structures during major disruptions, leading to decentralized correlations.
Study analyzes stock market correlations using multivariate distributions.
problem Capturing the correlation structure of complex, non-stationary systems.
method Applied Random Matrix Model to empirical data of 479 US stocks.
result Described and quantified changes in empirical distributions due to non-stationarity.
A new method for analyzing multifractal cross correlations in complex systems.
problem Characterizing long-range cross-correlations in complex systems.
method Multifractal Cross Wavelet Analysis (MFXWT)
result MFXWT accurately captures joint multifractality in binomial multifractal measures but may produce spurious results for bivariate fractional Brownian motions.
Study shows memory and communication constraints impact correlation detection in data.
problem Detecting correlations with limited memory and communication resources.
method Proves a tight trade-off between memory/communication complexity and sample complexity.
result Optimal sample complexity requires quadratic memory/communication complexity in dimension.
CDEFs reduce model complexity and uncover time correlations.
problem Model complexity and data efficiency in probabilistic modeling.
method Builds on deep exponential families, ties weights for reduced parameters.
result CDEFs uncover time correlations with fewer parameters.
Paper models dynamic multivariate functional data with sparse subspace learning.
problem Complex, high-dimensional multivariate functional data with evolving cross-correlations.
method Sparse subspace learning for automatic subspaces formulation and cross-correlation dynamics description.
result Efficient estimation and feature extraction of multivariate functional data.
Transformer predicts Ethereum prices using cross-currency correlation and sentiment analysis.
problem Predicting Ethereum cryptocurrency prices with limited data.
method Transformer-based neural network with cross-currency correlation and sentiment analysis.
result Transformer model outperforms other models on some parameters.
Machine learning detects non-local correlations in complex scenarios.
problem Systematic derivation of non-local correlations becomes unfeasible in complex scenarios.
method Ensemble of multilayer perceptrons blended with genetic algorithms.
result High performance in relevant Bell scenarios.
Paper develops efficient algorithms for learning rationalizable equilibria in multiplayer games.
problem Learning rationalizable behavior in multiplayer games under bandit feedback.
method New algorithms for finding rationalizable Coarse Correlated Equilibria and Correlated Equilibria with polynomial sample complexity.
result Achieved polynomial sample complexity for learning rationalizable equilibria, improving over existing exponential complexity.
Diffusion models learn simple statistics before complex ones, revealing a sample complexity exponent.
problem Understanding the learning dynamics of diffusion models.
method Empirical observations and theoretical analysis of diffusion models and denoisers.
result Diffusion models learn simple statistics (pair-wise correlations) at linear sample complexity, while higher-order statistics (e.g., fourth cumulant) require cubic sample complexity.
Financial markets analyzed by reducing correlation matrix complexity.
problem Understanding complex financial market correlations.
method Coarse graining Pearson correlation matrices into Guhr matrices by market sectors.
result Significant reduction in the number of relevant variables.
It is ubiquitous in natural and social sciences that two variables, recorded temporally or spatially in a complex system, are cross-correlated and possess multifractal features. We propose a new method called multifractal detrended cross-correlation analysis (MF-DXA) to investigate the multifractal behaviors in the pow…
A new way to describe correlation matrices makes modeling easier.
problem Describing correlation matrices in a flexible and positive-definite way.
method Introduces a novel parametrization that allows unrestricted vectors for correlation matrices.
result The new parametrization ensures positive definiteness without additional constraints.
Study on estimating CCA with stochastic methods and sample complexity.
problem Estimating canonical correlation and directions from samples.
method Exact and approximate solutions using stochastic optimization and power iterations.
result Achieve optimal alignment with minimal samples and passes.
The detrended cross-correlation coefficient ρDCCA has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, non-stationary time series. It is based on the detrended cross-correlation and detrended fluctuation analyses (DCCA and DFA, respectively) and c…
We analyze the daily stock data of the Nasdaq Composite index in the 22-year period 1992-2013 and identify market states as clusters of correlation matrices with similar correlation structures. We investigate the stability of the correlation structure of each state by estimating the statistical fluctuations of correlat…
Study uses detrended cross-correlation to analyze cryptocurrency market, revealing robust collective modes and distinguishing interdependencies.
problem Nonstationarity, long-range memory, and heavy-tailed fluctuations obscure traditional correlations in complex systems.
method Constructs detrended correlation matrices using multifractal detrended cross-correlation coefficient ρr to emphasize different fluctuations. result Detrending and fluctuation analysis reveal distinct spectral properties from random case, identifying market and sectoral components.
We develop a framework for analyzing extreme values in correlated financial data.
problem Quantifying and mitigating risk in complex financial systems.
method Developed a practical framework for handling finite, multivariate, and correlated time series in finance.
result We successfully analyze high-frequency stock returns using univariate extreme value tools.
Improved eigenvalue distribution method for financial data.
problem Noise and complexity in financial markets.
method Matrix H theory, hierarchical structure, informational cascade.
result Captures a larger fraction of data variance in financial markets.
This paper explores the relationships between migration and trade using a complex-network approach. We show that: (i) both weighted and binary versions of the networks of international migration and trade are strongly correlated; (ii) such correlations can be mostly explained by country economic/demographic size and ge…
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random…
Study identifies precursors of financial crashes using correlation patterns.
problem Identifying long-term precursors of financial market crashes.
method Comparative analysis of S&P 500 and Nikkei 225, using cross-correlation patterns, power mapping, and intra-cluster distance method.
result Identified four market states in USA and five in Japan, with transitions mainly to adjacent states.
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.
Fast online algorithm for nonparametric correlations.
problem Computing nonparametric correlations on streaming data.
method Novel online algorithm with O(1) time and memory complexity.
result 10 to 1,000 times faster than batch algorithms.
Study the structure of international trade through hypergraphs.
problem Understanding the complex relationships in international trade networks.
method Analyzing the mean hyperdegree of adjacent vertices and decomposing correlation properties.
result Identifies bias in trade relationships not visible in pairwise networks.
The paper analyzes long-range correlations in bond markets using DMA method.
problem Understanding long-range auto- and cross-correlations in bond markets.
method Detrended Moving Average (DMA) method and complex network analysis.
result Long-range correlations in bond markets are persistent and show market segmentation.
A study on the communication complexity of estimating correlations between variables.
problem Estimating the correlation between two sets of correlated random variables with limited communication.
method One-way interactive protocol exchanging k bits, optimizing over interaction protocol and estimator.
result Achieves optimal performance with communication complexity of 1/k, improving over naive schemes.
Richer prior for neural networks with correlated weights.
problem Weak priors limit neural network complexity and flexibility.
method Latent variables represent network units, conditional weights.
result Richer meta-representations and representations.
Method detects phase transitions in financial markets using eigenvalue decomposition.
problem Detecting tipping points and fluctuation patterns in financial markets.
method Eigenvalue decomposition and eigen-entropy from cross-correlation matrix.
result Market events undergo phase separation and order-disorder transitions.
Complex systems are typically represented by large ensembles of observations. Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and identify in a quantifiable way patterns of activity that are reproducible with statistically significant frequency compared…
Study analyzes landscape complexity of empirical loss functions with correlated data.
problem Understanding the complexity of loss landscapes in machine learning with structured data.
method Kac-Rice formula and random matrix theory applied to high-dimensional empirical loss functions.
result Characterizes the average number of critical points in loss functions with structured data.
We investigate the properties of correlation based networks originating from economic complex systems, such as the network of stocks traded at the New York Stock Exchange (NYSE). The weaker links (low correlation) of the system are found to contribute to the overall connectivity of the network significantly more than t…
Deep neural nets predict stock market trend changes using lagged correlations.
problem Predicting directional trend changes in financial time series with noisy data.
method Lagged correlations and deep neural networks with step-wise linear regressions and exponential smoothing.
result Deep learning approach achieves state-of-the-art accuracy in predicting stock market trend changes.
Bootstrapping regularizes singular correlation matrices, reducing the need for complex regularization.
problem Singular correlation matrices in large datasets.
method Averaging bootstrapped correlation matrices to ensure positive-definiteness.
result The averaged correlation matrix is almost surely positive-definite with a sufficient number of bootstraps.
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.
Financial markets are highly correlated systems that reveal both the inter-market dependencies and the correlations among their different components. Standard analyzing techniques include correlation coefficients for pairs of signals and correlation matrices for rich multivariate data. In the latter case one constructs…
We present an outlook of the studies on correlations in the price timeseries of stocks, discussing the construction and applications of "asset tree". The topic discussed here should illustrate how the complex economic system (financial market) enrichens the list of existing dynamical systems that physicists have been s…
Deep learning reveals lagged correlations in stock markets, showing accuracy decreases with shorter prediction horizons.
problem Capturing non-linear interactions in financial prediction problems using large-scale datasets.
method Applying deep learning to econometrically constructed gradients to learn and exploit lagged correlations among S&P 500 stocks.
result Model accuracies decrease with shorter prediction horizons, but remain significant in both stable and volatile markets.