We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider…
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48 results for “Non-linear Relationships”
Nonlinear wave equation, nonlinear Riemann problem, and the twistor transform of Veronese websmath-ph
Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but in the case dim =3 they reduce to a special flavor of a non-linear wave equation. The symmetries embedded in the definition of a Veronese web…
Unified framework for non-linear attention using modern Hopfield networks.
problem Improving transformer model's understanding of complex relationships and efficiency.
method Proposes an energy functional based on Modern Hopfield Networks (MNH) to unify linear and non-linear attention mechanisms.
result Context wells encapsulate contextual relationships among tokens, offering a richer representation of non-linear data.
Causal inference concerns the identification of cause-effect relationships between variables. However, often only linear combinations of variables constitute meaningful causal variables. For example, recovering the signal of a cortical source from electroencephalography requires a well-tuned combination of signals reco…
Financial markets are complex adaptive systems, and are commonly studied as complex networks. Most of such studies fall short in two respects: they do not account for non-linearity of the studied relationships, and they create one network for the whole studied time series, providing an average picture of a very long, e…
Rhino learns causal relationships from time series data with history-dependent noise.
problem Discovering causal relationships from time series data with non-linear relations, instantaneous effects, and history-dependent noise.
method Combines vector auto-regression, deep learning, and variational inference.
result Demonstrates better causal relationship discovery performance compared to baselines.
We show that classical Wilczynski--Se-ashi invariants of linear systems of ordinary differential equations are generalized in a natural way to contact invariants of non-linear ODEs. We explore geometric structures associated with equations that have vanishing generalized Wilczynski invariants and establish relationship…
Proposes using DII to identify non-linear causal relationships in EU Allowances returns.
problem Identifying causal relationships in non-linear data of EU Allowances returns.
method Uses Differentiable Information Imbalance (DII) for non-parametric causal discovery compared to multivariate Granger causality.
result Significant overlap and differences in causal variables identified by linear and non-linear methods.
We present function preserving projections (FPP), a scalable linear projection technique for discovering interpretable relationships in high-dimensional data. Conventional dimension reduction methods aim to maximally preserve the global and/or local geometric structure of a dataset. However, in practice one is often mo…
New method uses SEMs to uncover cause-effect in manufacturing processes.
problem Complex cause-and-effect relationships in manufacturing processes.
method Using Structural Equation Models with non-linear relationships.
result More informative cause-effect relationships derived from data.
Estimates causal effects using neural autoregressive density estimators.
problem Estimating causal effects in non-linear systems.
method Neural autoregressive density estimators within Pearl's do-calculus framework.
result Retrieves causal effects from non-linear systems without explicit modeling.
Deep learning improves sensor performance optimization.
problem Optimizing sensor performance based on key metrics.
method Re-approach non-linear regression using deep learning with Keras and Tensorflow.
result Deep learning models improve sensor performance optimization.
Improves BN graph learning with splines for scalability.
problem Learning accurate BN graph structures from data.
method Score-and-search approach with MARS for CPD modeling.
result Improves BN graph accuracy and scalability.
We consider the clustering problem of attributed graphs. Our challenge is how we can design an effective and efficient clustering method that precisely captures the hidden relationship between the topology and the attributes in real-world graphs. We propose Non-linear Attributed Graph Clustering by Symmetric Non-negati…
Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the reproducing kernel Hilbert space and develop a method for learning prediction func…
Recently the interest of researchers has shifted from the analysis of synchronous relationships of financial instruments to the analysis of more meaningful asynchronous relationships. Both of those analyses are concentrated only on Pearson's correlation coefficient and thus intraday lead-lag relationships associated wi…
DREAM model improves computational efficiency for non-linear effects in relational event models.
problem Efficiently modeling non-linear effects in dynamic relational networks.
method Introduces Deep Relational Event Additive Model (DREAM) using Neural Additive Models.
result Demonstrates superior computational efficiency compared to traditional REM approaches.
New method for learning causal relationships in PNL models.
problem Learning causal relationships from empirical observations in PNL models.
method Rank-based methods to estimate non-linear functions, disentangling from independence tests.
result Consistent method for PNL causal discovery, validated in experiments.
Improved interpretability methods for ML models using local regressions and variable importance.
problem Inability of existing interpretability methods to provide reliable explanations for ML models, especially in high-dimensional problems with irrelevant features and non-linear relationships.
method Introduces VarImp and SupClus methods using local regressions with weighted distance considering variable importance.
result VarImp and SupClus methods yield better explanations than state-of-the-art approaches, especially in high-dimensional problems with irrelevant features and non-linear relationships.
Two new algorithms reduce feature space while preserving non-linear relationships.
problem High-dimensional data and overfitting issues.
method Bias-variance analysis for non-linear transformations and generalized linear models.
result Competitive performance on regression and classification tasks.
Wavelet analysis reveals non-linear dynamics in cryptocurrency prices.
problem Understanding non-linear dynamics in high-frequency cryptocurrency prices.
method Wavelet analysis of frequency and time variables.
result Cyclical persistence at different frequencies in cryptocurrency prices.
A basic problem in machine learning is to find a mapping from a low dimensional latent space to a high dimensional observation space . Modern tools such as deep neural networks are capable to represent general non-linear mappings. A learner can easily find a mapping which perfectly fits a…
Study finds sales forecasters overreact to extreme news.
problem Understanding how forecasters react to sales growth news.
method Proposes a framework with fat-tailed dynamics and linear forecasting rule.
result Forecasters overreact to significant sales growth news.
This study develops a multi-factor framework where not only market risk is considered but also potential changes in the investment opportunity set. Although previous studies find no clear evidence about a positive and significant relation between return and risk, favourable evidence can be obtained if a non-linear rela…
Proposes a new dependency function for measuring non-linear relationships.
problem Need for a general-purpose measure of dependency between random variables.
method Revision of ideal properties and proposal of a new dependency function.
result Proposes a new dependency function that meets all desired properties.
We investigate the joint dynamics of spot and implied volatility from an empirical perspective. We focus on the equity market with the SPX Index our underlying of choice. Using only observable quantities, we extract the instantaneous variance curves implied by the market and study their daily variations jointly with sp…
Heterosis is the improved or increased function of any biological quality in a hybrid offspring. We have studied yet the largest maize SNP dataset for traits prediction. We develop linear and non-linear models which consider relationships between different hybrids as well as other effect. Specially designed model prove…
Improved CAEs reduce training time and enhance generalization.
problem Stability issues in Concrete Autoencoders (CAEs) for feature selection.
method Indirectly Parameterized Concrete Autoencoders (IP-CAEs) learn parameters of Gumbel-Softmax distributions.
result IP-CAEs achieve significant improvements in generalization and training time.
SLEM: Machine Learning for Path Modeling and Causal Inference with Super Learner Equation Modelingstat.ML
SLEM uses machine learning to improve causal inference from observational data.
problem Improving causal inference from observational data using non-linear relationships.
method Super Learner Equation Modeling integrating machine learning ensembles.
result SLEM provides consistent and unbiased estimates of causal effects.
We address the problem of causal discovery from data, making use of the recently proposed causal modeling framework of modular structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce σ-connection graphs (σ-CG), a new class of mixed graphs (containing undirected, bidirected…
Least-Squares Independence Regression for Non-Linear Causal Inference under Non-Gaussian Noisestat.ML
The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model…
New method discovers causal relationships in complex time series data.
problem Discovering causal relationships in multivariate time series is challenging.
method Temporal Dependency to Causality (TD2C) framework using mutual information.
result TD2C achieves state-of-the-art performance in causal discovery.
DANCE optimizes neural network and accelerator design for faster, more efficient DNN execution.
problem Challenges in optimizing neural network and accelerator design for efficient DNN execution.
method Differentiable approach to co-exploration of accelerator and network architecture design.
result Significantly shorter time to achieve superior accuracy and hardware cost metrics.
This paper analyzes the direction of the causality between crude oil, gold and stock markets for the largest economy in the world with respect to such markets, the US. To do so, we apply non-linear Granger causality tests. We find a nonlinear causal relationship among the three markets considered, with the causality go…
The prediction of workers' safety behaviour can help identify vulnerable workers who intend to undertake unsafe behaviours and be useful in the design of management practices to minimise the occurrence of accidents. The latest literature has evidenced that there is within-population diversity that leads people's intend…
New model handles complex non-linear relationships with hidden graph structures.
problem Modeling non-linear relationships with hidden graph-structured interactions.
method Block-diagonal localized mixture of polynomial experts (BLoMPE) regression model with penalized maximum likelihood selection criterion.
result Strong theoretical guarantee for finite-sample oracle inequality.
Proposes a deep neural network for predicting survival times with cure fractions.
problem Predicting survival times with cure fractions in medical studies.
method Flexible survival models integrated into a deep neural network framework.
result Better predictive performance and realistic covariate effects.
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variatio…
Deep Causal Graphs model complex causal relationships using neural networks.
problem Limited applicability of parametric causal models to real-life datasets with non-linear relationships.
method Deep Causal Graphs, an abstract specification for neural networks to model causal distributions.
result Demonstrates expressive power in modelling complex interactions and provides true causal counterfactuals.
This paper reviews Gaussian process-based multi-fidelity techniques for different fidelity relationships.
problem Combining accurate and cheap models for complex system design.
method Gaussian process-based multi-fidelity modeling techniques for varying fidelity relationships.
result Comparison of techniques on analytical and aerospace engineering problems.
Granger causality analysis, as one of the most popular time series causality methods, has been widely used in the economics, neuroscience. However, unobserved confounders is a fundamental problem in the observational studies, which is still not solved for the non-linear Granger causality. The application works often de…
In our previous study we have presented an approach to studying lead--lag effect in financial markets using information and network theories. Methodology presented there, as well as previous studies using Pearson's correlation for the same purpose, approached the concept of lead--lag effect in a naive way. In this pape…
A neural network model tackles high-dimensional data with latent structures.
problem Modeling high-dimensional data with latent low-dimensional structures.
method Integrates PCA and Soft PCA layers into neural network architecture for factor modeling and non-linear transformations.
result Demonstrates improved performance in forecasting and nowcasting with real-world data.
New approach predicts stock price synchronization using RNNs and LSTMs.
problem Forecasting synchronization of stock prices in the Indian market.
method Utilizing recurrence plots and CRQA for non-linear analysis, RNNs and LSTMs for prediction.
result Accuracy of 0.98 and F1 score of 0.83 in predicting stock price synchronization.
Statistical properties of order-driven double-auction markets with Bid-Ask spread are investigated through the dynamical quantities such as response function. We first attempt to utilize the so-called {\it Madhavan-Richardson-Roomans model} (MRR for short) to simulate the stochastic process of the price-change in empir…
Bayesian method estimates intervention effects in non-linear data.
problem Causal discovery from observational data with non-linear relationships.
method Gaussian Process Networks (GPN) with Bayesian estimation and Monte Carlo methods.
result Approach accurately identifies and reflects uncertainty of causal estimates.
The one-class kernel spectral regression (OC-KSR), the regression-based formulation of the kernel null-space approach has been found to be an effective Fisher criterion-based methodology for one-class classification (OCC), achieving state-of-the-art performance in one-class classification while providing relatively hig…
New method infers causal relationships from nonstationary time series data.
problem Challenges in inferring causal relationships from nonstationary time series data.
method Proposes a new class of restricted SCM with time-varying filters and stationary noise, leveraging asymmetry from nonstationarity.
result Demonstrates effectiveness of the proposed methodology on various synthetic and real datasets.