In the paper, we introduce a new measure of correlation between possibly non-stationary series. As the measure is based on the detrending moving-average cross-correlation analysis (DMCA), we label it as the DMCA coefficient with a moving average window length . We analytically show that the coefficient…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
Trend · papers per month
48 results for “correlation length”
The paper studies the correlation of Hilbert lengths for convex projective surfaces.
problem Understanding the correlation of Hilbert lengths for convex projective surfaces.
method Asymptotic formula for free homotopy classes with renormalized Hilbert length.
result The correlation number is not uniformly bounded away from zero but can be larger than a uniform strictly positive constant.
Study geodesics on flat tori, focusing on orthogonal lengths and their distribution.
problem Properties of geodesics on flat tori and their lengths.
method Fine study of dynamical correlation function and anisotropic Sobolev spaces.
result Properties of the length distribution and singularities of its Fourier transform.
We study the dynamics of the linear and non-linear serial dependencies in financial time series in a rolling window framework. In particular, we focus on the detection of episodes of statistically significant two- and three-point correlations in the returns of several leading currency exchange rates that could offer so…
This study examines how sequential correlations affect in-context learning in sequence models.
problem Understanding how in-context learning works with sequentially correlated data.
method Extended linear regression model to sequentially correlated data, tested on transformer architectures.
result Sequential correlations alter the effective context length and attention architecture effectiveness.
A simple method reduces bias in LLM auto-evaluators by controlling output length.
problem Bias in LLM auto-annotators, particularly length bias.
method Simple regression analysis to control for length difference and other mediators.
result Improved robustness and increased correlation with human preferences.
Compressibility Measures Complexity: Minimum Description Length Meets Singular Learning Theorystat.ML
Study shows LLC correlates with neural network compressibility.
problem Evaluating limits of neural network compression.
method Extended minimum description length principle using singular learning theory.
result Complexity estimates based on LLC are linearly correlated with compressibility.
The paper describes correlations of spectra for higher rank Anosov representations.
problem Understanding correlations of spectra for Anosov representations of higher rank groups.
method Relates correlation problem to counting projections in truncated hypertubes.
result Extends previous work on rank one representations to higher rank.
LaRT models LLMs' response accuracy and CoT length to evaluate reasoning ability and speed.
problem Valid evaluation of Large Language Models (LLMs) via response accuracy and chain-of-thought length.
method Introduces Latency-Response Theory (LaRT) to jointly model response accuracy and CoT length using latent ability and latent speed.
result LaRT yields higher estimation accuracy and shorter confidence intervals for latent traits compared to IRT.
Formula connects length and correlation functions via ghost polygons and Poisson bracket.
problem Understanding functions on moduli spaces of Anosov representations.
method Introduced ghost polygons and ghost algebra to compute Poisson bracket.
result Stability of length and correlation functions under Poisson bracket.
We examine Deep Canonically Correlated LSTMs as a way to learn nonlinear transformations of variable length sequences and embed them into a correlated, fixed dimensional space. We use LSTMs to transform multi-view time-series data non-linearly while learning temporal relationships within the data. We then perform corre…
New insights show embedding lengths correlate with semantic properties.
problem Contrastive embedding norms ignore embedding magnitudes but correlate with semantic properties.
method Formal theoretical framework and analysis of optimization dynamics.
result Embedding lengths encode semantic information as a byproduct of training.
We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types, which are useful to classify the ambiguous nature of knotting in open curves. Modell…
We study finite sample properties of estimators of power-law cross-correlations -- detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA) -- with a special focus on short-term memory bias as well as power-law coherency. Presen…
Entropy estimation of symbol sequencescond-mat.stat-mech
We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our interest is in describing their convergence with sequence length, assuming no limit…
ESS improves MCMC efficiency for correlated & multimodal distributions.
problem Slice Sampling's sensitivity to initial length scale and difficulty with correlated distributions.
method Adaptive tuning and parallel walkers for efficient sampling.
result ESS improves efficiency by more than an order of magnitude on correlated distributions.
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.
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.
This paper presents a novel adaptive-filter approach for predicting assets on the stock markets. Concepts are introduced here, which allow understanding this method and computing of the corresponding forecast. This approach is applied, as an example, through the prediction over the actual valuation of the PETR3 shares …
Preformer improves Transformer for long-term time series forecasting.
problem Transformer's quadratic complexity and lack of context-awareness for long-term forecasting.
method Introduces Multi-Scale Segment-Correlation mechanism for efficient time series segmentation and context-aware attention.
result Preformer outperforms other Transformer-based methods in long-term time series forecasting.
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.
Fine-tuning improves information conveyance in language models by reorganizing uncertainty into more informative sequences.
problem Uncertainty reduction in large language models through fine-tuning is not fully understood, especially regarding output length.
method Proposed Canopy Entropy () to measure uncertainty in both output length and sequence, capturing total Shannon entropy.
result Fine-tuned models exhibit stronger positive correlation between entropy rate and semantic diversity, indicating more informative and semantically meaningful generations.
Large bundles of myelinated axons, called white matter, anatomically connect disparate brain regions together and compose the structural core of the human connectome. We recently proposed a method of measuring the local integrity along the length of each white matter fascicle, termed the local connectome. If communicat…
We analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes. We use 100 highly-capitalized stocks from the American market and relate result to the corresponding ensemble of Wishart random matrices. It turns …
This paper studies the correlations of the average winnings of agents and the volatilities of systems based on mix-game model which is an extension of minority game (MG). In mix-game, there are two groups of agents; group1 plays the majority game, but the group2 plays the minority game. The results show that the correl…
Fractal approach towards power-law coherency to measure cross-correlations between time seriesq-fin.ST
We focus on power-law coherency as an alternative approach towards studying power-law cross-correlations between simultaneously recorded time series. To be able to study empirical data, we introduce three estimators of the power-law coherency parameter based on popular techniques usually utilized for studying pow…
VAE improves MCMC efficiency by generating diverse prior proposals.
problem Inefficient MCMC methods in Bayesian inverse problems, especially subsurface flow modeling.
method Uses Variational Autoencoder (VAE) to generate broader-spectrum prior proposals.
result VAE achieves comparable accuracy to Karhunen-Loève Expansion (KLE) and outperforms it when correlation length is unknown.
We examine the performance of six estimators of the power-law cross-correlations -- the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle e…
Traders adopt different trading strategies to maximize their returns in financial markets. These trading strategies not only results in specific topological structures in trading networks, which connect the traders with the pairwise buy-sell relationships, but also have potential impacts on market dynamics. Here, we pr…
Study validates Lillo-Mike-Farmer model predicting financial market long-range correlations.
problem Quantifying long-range correlations in financial markets.
method Analyzed nine years of market data to classify traders as order-splitting or random, measured metaorder-length distributions, and compared to LMF model predictions.
result Agreement between LMF model predictions and actual data, validating the model.
Study correlations of spectral lengths and displacements in higher rank groups.
problem Analyzing correlations of spectral lengths and displacements in higher rank groups.
method Study Jordan and Cartan projections in tubes of Anosov subgroups of semisimple real algebraic groups.
result Prove existence of δ_ρ(\mathsf{v}) such that correlations of spectral lengths and displacements follow specific exponential growth patterns.
Shorter adversarial prompts help protect LLMs from jailbreak attacks.
problem Protecting large language models from jailbreak attacks with long adversarial suffixes.
method Adversarial training on shorter adversarial suffixes to defend against longer adversarial suffixes.
result Aligning LLMs on shorter adversarial suffixes can effectively defend against jailbreak attacks with longer suffixes.
Quantum field theory connects deep neural networks to criticality.
problem Understanding the criticality and training dynamics of deep neural networks.
method Constructing quantum field theory for deep neural networks, computing corrections to correlation functions.
result Found precise analogy with vector model, providing corrections to correlation length.
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.
Agents Play Mix-gamephysics.soc-ph
In mix-game which is an extension of minority game, there are two groups of agents; group1 plays the majority game, but the group2 plays the minority game. This paper studies the change of the average winnings of agents and volatilities vs. the change of mixture of agents in mix-game model. It finds that the correlatio…
Standardizes weighted ranking correlation coefficients to maintain zero expected value.
problem Measuring correlation between weighted rankings of items.
method Develops a standardization function g(·) that transforms coefficients to zero expected value under randomness.
result A general standardization function g(Γ) that preserves the domain [-1,1] and reduces to the identity for coefficients already satisfying zero-expected-value property.
VBS improves sampling efficiency in cosmological data analysis.
problem High dimensionality of cosmological parameter space makes sampling computationally challenging.
method Developed a hybrid scheme combining variational self-boosted sampling with Hamiltonian Monte Carlo.
result VBS generates better quality samples and reduces auto-correlation length by a factor of 10-50.
Kullback-Leibler distance as a measure of the information filtered from multivariate dataphysics.data-an
We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation …
Paper tackles variable-length, incomplete wearable sensor data to improve personalized insights.
problem Variable-length and incomplete time series data from wearable sensors.
method HeartSpace integrates a time series encoding module and pattern aggregation network, along with a Siamese-triplet network for representation learning.
result Empirical evaluation shows significant performance gains in personality prediction, demographics inference, and user identification.
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.
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several graphical Markov models. Rules for comparing degree of association among the vertices of…
We investigate the time series of the degree of minimum spanning trees obtained by using a correlation based clustering procedure which is starting from (i) asset return and (ii) volatility time series. The minimum spanning tree is obtained at different times by computing correlation among time series over a time windo…
Study quantizes ropelength and writhe of 12-crossing knots.
problem Quantifying geometric and topological properties of knots.
method Computation of ropelength and space writhe for 12-crossing knots.
result Non-alternating knots show evidence of writhe quantization, while alternating knots do.
Algorithm minimizes regret and converges to equilibria in Markov games.
problem Regret minimization and convergence to equilibria in general-sum Markov games under adversarial opponents.
method Decentralized algorithm that uses policy optimization and controls path length to achieve sublinear regret.
result Sublinear regret guarantees for convergence to correlated equilibrium in Markov games.
Proposes a new model for EHR data using time-dependent Gaussian processes.
problem Joint modeling of multiple clinical variables over time.
method Multivariate nonstationary Gaussian processes with time-varying parameters and posterior inference via HMC.
result The proposed model outperforms stationary models and reveals latent correlations predictive of patient risk.
One of the ubiquitous representation of long DNA sequence is dividing it into shorter k-mer components. Unfortunately, the straightforward vector encoding of k-mer as a one-hot vector is vulnerable to the curse of dimensionality. Worse yet, the distance between any pair of one-hot vectors is equidistant. This is partic…
Circumventing the Curse of Dimensionality in Prediction: Causal Rate-Distortion for Infinite-Order Markov Processescond-mat.stat-mech
Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on fi…
Study how knots occupy space using topological methods.
problem Understanding how knots occupy a volume of space.
method Statistical analysis of persistent homology features from Vietoris-Rips complexes.
result Existence of correlations between geometric and topological features of knots.