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.
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arXiv research
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48 results for “nonparametric correlations”
Recent advances in topic models have explored complicated structured distributions to represent topic correlation. For example, the pachinko allocation model (PAM) captures arbitrary, nested, and possibly sparse correlations between topics using a directed acyclic graph (DAG). While PAM provides more flexibility and gr…
Proposes a new method to estimate variable importance in black box models, mitigating correlation effects.
problem Correlation between covariates affects the interpretation of variable importance parameters.
method Develops a modified LOCO (Leave Out COvariates) method and uses semiparametric models for estimation.
result Shows how to estimate a modified LOCO method that mitigates correlation effects.
A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonp…
We are often interested in explaining data through a set of hidden factors or features. When the number of hidden features is unknown, the Indian Buffet Process (IBP) is a nonparametric latent feature model that does not bound the number of active features in dataset. However, the IBP assumes that all latent features a…
Correlated Random Measuresstat.ML
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…
Canonical Correlation Analysis (CCA) is a classical tool for finding correlations among the components of two random vectors. In recent years, CCA has been widely applied to the analysis of genomic data, where it is common for researchers to perform multiple assays on a single set of patient samples. Recent work has pr…
Unified framework for interpreting complex regression models with many predictors.
problem Interpreting nonparametric regression models with many predictors.
method Derivative-based approach for existing tools like partial-dependence plots.
result New technique called accumulated total derivative effects plot for complex models.
Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep neural network methods. These approaches seek maximally correlated projections …
New estimator for joint entropy outperforms existing methods in various distributions.
problem Estimating joint entropy in high-dimensional spaces.
method Partitioned sample spacing (PSS) for nonparametric estimation.
result PSS consistently outperforms k-NN and normalizing flow methods.
The paper introduces a new method for modeling correlations in high-dimensional data.
problem Modeling correlations among multiple dimensions in high-dimensional data.
method Population random measure embedding (PRME) using random functions and neural networks.
result The proposed method can efficiently learn correlations among multiple dimensions.
CATVI improves variational inference for Bayesian nonparametric models by reducing divergence and improving prediction accuracy.
problem Limitations of current variational inference methods in characterizing latent correlations and inferring true posterior dimensions.
method CATVI integrates conditional and adaptive truncation into variational inference, maximizing nonparametric evidence lower bound and using Monte Carlo integration.
result CATVI outperforms traditional methods in Bayesian nonparametric topic models, reducing perplexity and improving topic-word clustering.
Method predicts which high-dimensional correlation signs will change in the future.
problem Predicting which correlation matrix coefficients will change signs in high-dimensional data.
method Stability of correlation signs depends on three-by-three relationships, inspired by Heider social cohesion theory.
result The method accurately predicts the stability of correlation signs in high-dimensional data.
Portfolio Allocation under Asymmetric Dependence in Asset Returns using Local Gaussian Correlationsq-fin.PM
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.
In this paper, a class of statistics named ART (the alternant recursive topology statistics) is proposed to measure the properties of correlation between two variables. A wide range of bi-variable correlations both linear and nonlinear can be evaluated by ART efficiently and equitably even if nothing is known about the…
Model dynamic customer sensitivities across categories.
problem Dynamic heterogeneity in customer sensitivities to marketing elements.
method Hierarchical dynamic factor model with Bayesian nonparametric Gaussian processes.
result Dynamic heterogeneity can be explained by a few global trends.
This paper solves nonparametric estimation of continuous DPPs using kernel methods.
problem Estimating continuous Determinantal Point Processes (DPPs) without assuming a parametric form.
method Developed a fixed point algorithm based on a representer theorem for nonnegative functions in RKHS.
result Demonstrated a finite-dimensional problem for nonparametric MLE of continuous DPPs.
In the presence of weak overall correlation, it may be useful to investigate if the correlation is significantly and substantially more pronounced over a subpopulation. Two different testing procedures are compared. Both are based on the rankings of the values of two variables from a data set with a large number n of o…
Genetic sequence data are well described by hidden Markov models (HMMs) in which latent states correspond to clusters of similar mutation patterns. Theory from statistical genetics suggests that these HMMs are nonhomogeneous (their transition probabilities vary along the chromosome) and have large support for self tran…
GNet uses Gaussian processes for scalable, flexible neural networks.
problem Large-scale predictive modeling with high computational and storage costs.
method GNet employs Gaussian processes with nonparametric activation functions and a fast algorithm for training and predictions.
result GNet achieves competitive performance across various test problems, including nonlinear function prediction and real-world data regression.
GNet uses Gaussian processes for scalable, flexible neural networks.
problem Large-scale predictive modeling with high computational and storage costs.
method GNet employs Gaussian processes with nonparametric activation functions and a fast algorithm for efficient training and predictions.
result GNet achieves competitive performance across various test problems, including nonlinear function prediction and real-world data regression.
An Extreme-Value Approach for Testing the Equality of Large U-Statistic Based Correlation Matricesmath.ST
There has been an increasing interest in testing the equality of large Pearson's correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more robust to outliers and nonlinearity. Unlike the Pearson's case, testing the equality…
Multilayer bootstrap network builds a gradually narrowed multilayer nonlinear network from bottom up for unsupervised nonlinear dimensionality reduction. Each layer of the network is a nonparametric density estimator. It consists of a group of k-centroids clusterings. Each clustering randomly selects data points with r…
Proposes a method for valid inference in GPLSIMs with longitudinal data.
problem Challenges in longitudinal data inference due to within-subject correlation and unstable variance estimation.
method Profile estimating-equation approach using spline approximation and block empirical likelihood.
result Block empirical likelihood ratio statistic with Wilks-type chi-square limit for joint inference.
New Hermite series estimator for Spearman rank correlation in non-stationary data.
problem Estimating time-varying Spearman rank correlation efficiently.
method Hermite series based sequential estimator for both stationary and non-stationary settings.
result Competitive performance compared to existing algorithms in simulations and real data.
A new nonparametric test measures dependence between variables using decision trees.
problem Measuring statistical dependence between two variables robustly and efficiently.
method An ensemble of decision trees discriminates between observed and permuted samples without generating the latter.
result The method effectively detects complex relationships from noisy data.
Estimates self- and cross-impact concavity and decay patterns in financial markets.
problem Understanding the impact of financial transactions on market dynamics.
method Nonparametric estimation of concave multi-asset propagator models using metaorders and order flow data.
result Concave self-impact with shifted power-law decay, significant gain from cross-impact, and improved predictive accuracy.
Parametric divergences are effective for generative modeling despite being non-optimal.
problem Training high-dimensional distributions with GANs.
method Generalization of GAN losses to parametric divergences, focusing on sensitivity to specific distribution moments.
result Parametric divergences are more suitable for learning high-dimensional distributions due to their sensitivity to specific aspects of the distribution.
Sum-Product Networks simplify building models for mixed data types.
problem Building probabilistic models for mixed data types is difficult and time-consuming.
method Proposes Sum-Product Networks (SPNs) with piecewise polynomial leave distributions and novel decomposition and conditioning steps.
result Sum-Product Networks can effectively approximate any continuous distribution and are efficient for learning and inference.
Proposes logistic-beta process for modeling dependent probabilities with beta marginals.
problem Limited work on flexible and computationally convenient stochastic process extensions for dependent random probabilities.
method Introduces logistic-beta process with logistic transformation and beta marginals, capable of modeling dependence in discrete and continuous domains.
result Logistic-beta processes enable effective posterior inference and design of computationally tractable dependent Bayesian nonparametric models.
Unsupervised learning of observation functions in state-space models by nonparametric moment methodsstat.ML
Method estimates observation functions in state-space models without supervision.
problem Unsupervised learning of non-invertible observation functions in nonlinear state-space models.
method Nonparametric generalized moment method using constrained regression.
result Estimates function space of identifiability from state process.
The paper presents a novel approach to multi-output regression using probabilistic circuits.
problem Capturing correlations between multiple output dimensions in large-scale regression problems.
method Employing a mixture of single-output Gaussian process experts encoded via a probabilistic circuit.
result The method can capture correlations between output dimensions and often outperforms other approaches.
The paper proposes a method to construct well-calibrated prediction sets for correlated target variables.
problem Constructing well-calibrated prediction sets for correlated target variables.
method The method uses vine copulas to estimate the joint cumulative distribution function of non-conformity scores and improves the asymptotic efficiency of the quantile estimate.
result The method guarantees asymptotically exact coverage and competitive efficiency on real-world regression problems.
A two-step nonparametric method estimates financial systemic risk.
problem Estimating CoVaR due to unobservability of multivariate-quantiles.
method Two-step nonparametric approach using Monte-Carlo simulation and kernel method.
result Consistency and asymptotic normality of the two-step estimator established.
We consider the problem of providing nonparametric confidence guarantees for undirected graphs under weak assumptions. In particular, we do not assume sparsity, incoherence or Normality. We allow the dimension to increase with the sample size . First, we prove lower bounds that show that if we want accurate infe…
MT-HAL learns features and task associations for multiple tasks with a shared sparse structure.
problem Learning features and task associations for multiple tasks with shared structure.
method Fully nonparametric approach that learns features, samples, and task associations with a shared sparse structure.
result MT-HAL achieves a powerful convergence rate and outperforms other methods across various simulation settings.
Geometric QHD tests improve hub detection in correlated data.
problem Detecting hubs in correlated data with evolving correlations.
method Geometric QHD tests combining QCD and QHD, clustering.
result Improved hub detection in correlated data.
This appendix proves CORN's universal consistency. One of Bin's PhD thesis examiner (Special thanks to Vladimir Vovk from Royal Holloway, University of London) suggested that CORN is universal and provided sketch proof of Lemma 1.6, which is the key of this proof. Based on the proof in Gyprfi et al. [2006], we thus pro…
This paper deals with the problem of nonparametric independence testing, a fundamental decision-theoretic problem that asks if two arbitrary (possibly multivariate) random variables are independent or not, a question that comes up in many fields like causality and neuroscience. While quantities like correlation o…
One popular approach to model the limit order books dynamics of the best bid and ask at level-1 is to use the reduced-form diffusion approximations. It is well known that the biggest contributing factor to the price movement is the imbalance of the best bid and ask. We investigate the data of the level-1 limit order bo…
The article compares predictor importance in classification problems with categorical outcomes.
problem Comparing predictor importance in classification problems with categorical response variables.
method The approach is based on the categorical Gini correlation (CGC) and tests differences in CGCs across predictor groups.
result The proposed methodology accommodates predictors of arbitrary and unequal dimensions and allows for dependence between predictor groups.
Genome-wide association studies have proven to be essential for understanding the genetic basis of disease. However, many complex traits---personality traits, facial features, disease subtyping---are inherently high-dimensional, impeding simple approaches to association mapping. We developed a nonparametric Bayesian re…
Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices appropriate for the intended applications. The method has been widely used for unsupervised learning tasks, including recommender systems (rating matrix of users by items) and document clustering (weighting matrix …
We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN is a generalization of the hierarchical Dirichlet process (HDP) that models correlation structure between the weights of the atoms at the group level. We derive a representation of DILN…
Unsupervised two-view learning, or detection of dependencies between two paired data sets, is typically done by some variant of canonical correlation analysis (CCA). CCA searches for a linear projection for each view, such that the correlations between the projections are maximized. The solution is invariant to any lin…
Method learns software resource usage from snapshots.
problem Challenges in learning time-varying, correlated resource usage.
method Graph structured Schrödinger bridge problem for nonparametric learning.
result Predicts most-likely resource distributions.
The Nonparanormal SKEPTICstat.ME
We propose a semiparametric approach, named nonparanormal skeptic, for estimating high dimensional undirected graphical models. In terms of modeling, we consider the nonparanormal family proposed by Liu et al (2009). In terms of estimation, we exploit nonparametric rank-based correlation coefficient estimators includin…
Simplex Random Featuresstat.ML
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.