Bayesian non-linear matrix completion tackles large, sparse data.
problem Predict missing elements in large, sparsely observed matrices.
method Bayesian Gaussian process latent variable models with data-parallel distributed computation.
result Scalable Bayesian non-linear matrix completion outperforms linear methods.
New classifier combines locally linear kernels for fast and accurate non-linear classification.
problem Developing a fast and accurate non-linear classifier.
method Combines locally linear classifiers using a ℓ 1 \ell_1 ℓ 1 Multiple Kernel Learning (MKL) problem with scalable MKL training for streaming kernels. result The resulting classifier achieves high accuracy with fast inference time.
In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its par…
Develops a Riemannian archetypal analysis for interpretable non-linear data.
problem Limited performance of classical archetypal analysis on non-linear data.
method Riemannian geometry for data-driven pullback, geodesic convex combinations, convex relaxation followed by non-convex refinement.
result Combines interpretability of classical archetypal analysis with expressive power of modern non-linear models.
Develops Chained Gaussian Processes for non-linear likelihoods.
problem Handling non-linear combinations of Gaussian process parameters.
method Introduces Chained Gaussian Processes and develops scalable approximate inference.
result Demonstrates scalability and applicability to various likelihood functions.
Combining neural networks and multiscale decomposition for financial market analysis.
problem Financial markets' complexity and mainstream models' limitations in capturing non-linear structures.
method Neural networks for non-linear associations combined with multiscale decomposition.
result Improved understanding of financial market data substructures.
This paper tackles efficient and scalable estimation of a complex model involving stochastic linear combinations of non-linear regressions.
problem Estimating a model involving stochastic linear combinations of non-linear regressions efficiently and scalably.
method The paper provides algorithms for estimating the model under specific assumptions about the variate vector and sample size, using techniques like zero-bias transformation and sub-sampling.
result The paper provides theoretical guarantees for the estimation of the model, showing that the estimation errors are of the order O ( p n ) O(\sqrt{\frac{p}{n}}) O ( n p ) and O ( 1 p + p n ) O(\frac{1}{\sqrt{p}}+\sqrt{\frac{p}{n}}) O ( p 1 + n p ) with high probability. New algorithm recovers non-linear cause-effect relationships from mixed neuroimaging data.
problem Recovering meaningful cause-effect relationships from linearly mixed neuroimaging data.
method MERLiN (Mixture Effect Recovery in Linear Networks) algorithm, extended to handle non-linear cause-effect relationships.
result The algorithm can recover non-linear cause-effect relationships from linearly mixed neuroimaging data.
AAnet learns non-linear archetypes from complex data.
problem Non-linear relationships in data make existing archetypal analysis methods ineffective.
method Archetypal Analysis network (AAnet) for non-linear data.
result AAnet effectively recovers and generates archetypes in non-linear domains.
This paper considers method of creation of an advisor and indicator based on the spectral stochastic analysis model, both with linear and non-linear approximation. The problem of entrance to one or another trade position is solved on the basis of combined analysis of dynamics of quotations of all currency pairs, what a…
Detects adversarial examples with non-linear dimensionality reduction.
problem Vulnerability of deep neural networks to adversarial examples.
method Combining non-linear dimensionality reduction and density estimation.
result Effective detection of adversarial examples by non-adaptive attackers.
Endogenous business cycles explain higher comovement across countries.
problem Standard models struggle to explain high comovement in business cycles across countries.
method Developed a demand-driven reduced-form model with strategic complementarities and international trade linkages.
result Combining endogenous business cycles with exogenous shocks matches empirical comovement levels.
BAVART model combines VAR and BART for non-linear forecasting.
problem Overly restrictive linearity assumption in VAR models.
method Combining VAR with Bayesian additive regression trees (BART).
result BAVART model yields highly competitive forecasts.
New numerical method for quantile hedging in imperfect markets.
problem Quantile hedging in non-linear markets with imperfections.
method Piecewise Constant Policy Timestepping (PCPT) coupled with monotone finite difference approximation.
result Convergence of the proposed numerical scheme proved using BSDE arguments.
Enhances Cox model for survival analysis with symbolic non-linear log-risk functions.
problem Limited interpretability and non-linearity in traditional Cox models.
method Introduces GCPH model using Kolmogorov-Arnold Networks for symbolic non-linear log-risk functions.
result GCPH achieves competitive performance and superior interpretability.
Paper establishes limits for accurately estimating low-rank matrices from noisy, non-linear data.
problem Estimating low-rank matrices from noisy, non-linear observations.
method Proves strong universality result with equivalent Gaussian model and effective prior parameters.
result Signal-to-noise ratio requirement grows as $N^{ rac 12 (1-1/k_F)}$ for accurate reconstruction.
TailCoR measures co-movement of financial crises events.
problem Measuring co-movement of financial crises events.
method Combines linear and non-linear dependencies using tail inter quantile range.
result TailCoR performs well in small samples and no optimisations are needed.
Improved electricity price forecasting model combining linear and non-linear structures.
problem Day-ahead electricity price forecasting in energy systems.
method Recurrent neural networks with embedded linear structures.
result Approximately 11% higher accuracy than state-of-the-art models.
PEA improves PCA and k-means for non-linear data and complex clusters.
problem Non-linear dimensionality reduction and clustering challenges.
method Principal Elliptical Analysis (PEA) for efficient non-linear approximation.
result PEA outperforms k-means in complex data clustering.
The paper tackles noisy combinations of continuous and step functions, providing conditions for their identification.
problem Recovering noisy observations as a combination of continuous and step functions.
method Topological and local properties of the functions are used to determine conditions for identification. A practical estimation algorithm is provided.
result Conditions for the identification of continuous and step functions based on their global and local properties.
Proposes HSIC-Lasso for selective inference in non-linear data.
problem Detecting influential features in non-linear and high-dimensional data.
method Model-free HSIC-Lasso based on truncated Gaussians and polyhedral lemma.
result Tight control of type-I error even for small sample sizes.
DiffKnock improves feature selection in neural networks with complex dependencies and non-linear associations.
problem Selecting important features in neural networks with complex dependencies and non-linear associations.
method DiffKnock uses diffusion models to generate knockoffs and neural network statistics to measure feature importance.
result DiffKnock outperforms existing methods in detecting non-linear associations and preserving feature dependencies.
In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear features on the original input space. After a finite number of iterations N, the n…
A new hierarchical forecasting method using machine learning improves forecast accuracy.
problem Improving forecast accuracy in hierarchical forecasting systems.
method Non-linear combination of base forecasts, focusing on both accuracy and coherence.
result The proposed method outperforms existing approaches, especially for diverse series.
This paper tackles non-linear reward optimization in resource allocation problems.
problem Optimizing a non-linear function of long-term average rewards in resource allocation problems.
method Proposes model-based and model-free algorithms to learn optimal policies.
result Model-based algorithm achieves a regret of $\Tilde{O}\left(LKDS\sqrt{\frac{A}{T}}
ight)$ for K K K objectives combined with a concave L L L -Lipschitz function. Sparse manifold transform linearizes non-linear signal transformations.
problem Non-linear signal transformations in sensory data.
method Combines sparse coding, manifold learning, and slow feature analysis.
result Models sparse discreteness and low-dimensional manifold structure in natural scenes.
Bayesian model merges multi-view latent models and kernel methods.
problem Handling high-dimensionality and non-linear issues in multi-view data.
method Combines probabilistic factor analysis with kernelized observations.
result Compact solutions for kernelized observations and feature selection.
Improves tree-based models' interpretability for medical applications.
problem Lack of explainability in tree-based models.
method Developed new algorithms and tools for local and global model understanding.
result Combining local explanations reveals global model structure and identifies non-linear interactions.
A new method learns state and proposal dynamics in state-space models using neural networks.
problem Inference in non-linear state-space models.
method StateMixNN method using neural networks for proposal and transition distributions.
result Significantly improved recovery of hidden state, especially in highly non-linear scenarios.
Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional observations. In these cases, system identification, i.e., finding the measurement map…
A new model simulates non-linear adsorption using Gaussian KDEs.
problem Simulating non-linear adsorption processes in porous materials.
method Combines random walk particle tracking with Gaussian Kernel Density Estimators for nonlinear modeling.
result Effective reproduction of Langmuir and Freundlich isotherms.
LQF linearizes deep models for better interpretability.
problem Lack of interpretability in deep neural networks.
method Simple modifications to architecture, loss function, and optimization.
result Comparable performance to non-linear fine-tuning, with interpretability.
Hadwiger's Theorem states that Euclidean-invariant convex-continuous valuations of definable sets are linear combinations of intrinsic volumes. We lift this result from sets to data distributions over sets, specifically, to definable real-valued functions on n-dimensional Euclidean space. This generalizes intrinsic vol…
The article presents a fast wind power forecasting model combining time series models.
problem Accurate short- to medium-term wind power forecasting for individual wind turbines.
method Combines multivariate TVARMA and power-TGARCH models with shrinkage techniques.
result The approach provides accurate forecasts of wind power up to 48 hours ahead.
Non-linear control rules improve smart inverter performance in fluctuating grids.
problem Optimizing smart inverter control for voltage regulation and energy efficiency in fluctuating grids.
method Customized non-linear control rules designed as a kernel-based regression task, leveraging a linearized grid model and convex optimization.
result Non-linear control rules achieve near-optimal performance in real-world tests, minimizing voltage deviations and ohmic losses.
The paper calibrates SLV models to LV models using an adjoint method.
problem Calibrating stochastic local volatility models to their underlying local volatility models.
method An adjoint semidiscretization of the forward Kolmogorov equation to solve for the leverage function.
result The method ensures that the fair values of European-style options in SLV and LV models match.
DECI combines causal discovery and inference in a single model for diverse data types.
problem Combining causal discovery and inference methods for diverse data types.
method Develops a single flow-based non-linear additive noise model (DECI) for causal discovery and inference.
result DECI can recover ground truth causal graphs and perform (C)ATE estimation.
Geometric matrix completion learns graph patterns and non-linear diffusion efficiently.
problem Efficiently learn graph patterns and non-linear diffusion from user/item graphs.
method Geometric deep learning on graphs with graph convolutional and recurrent neural networks.
result Outperforms state-of-the-art techniques on synthetic and real datasets.
Introduces MFVDM for high-dimensional data analysis.
problem Non-linear dimensionality reduction of high-dimensional datasets.
method Combines multiple unitary irreducible representations for nonlinear embeddings.
result Achieves better nearest neighbor search and alignment estimation on noisy data.
Paper compresses deep neural networks by eliminating redundant neurons.
problem Challenges in deploying deep learning models due to high parameter count.
method Exploits non-linear redundancy to compress neural networks without loss.
result Reduces network size by up to 99% with minimal performance loss.
Develops a data-driven smoothing technique for high-dimensional, non-linear panel data.
problem Improving prediction accuracy in high-dimensional, non-linear panel data models.
method Adaptive discrete smoothing with data-driven weights based on individual function similarity.
result Significant improvement in prediction accuracy compared to traditional linear panel data estimators.
Paper introduces non-linear discounting models for default compensation and climate valuation.
problem Valuation of non-replicable value and damage under default risk.
method Develops two models: one for risk-neutralising discounting and another for survival probability dependent discounting.
result Non-decaying discount factors (negative discount rates) are possible under certain scenarios.
A new framework learns shared features from multi-view data with many-to-many associations.
problem Learning shared features from multi-view data with many-to-many associations.
method Probabilistic Multi-view Graph Embedding (PMvGE) using neural networks.
result PMvGE outperforms existing multi-view methods in large-scale datasets.
Paper tackles intervention extrapolation using identifiable representations.
problem Predicting effects of unseen interventions on outcomes.
method Combines identifiable representation learning with autoencoders to enforce linear invariance.
result Identifiable representations enable non-linear extrapolation of interventions.
Unified framework for multi-user bandits using Laplacian kernels.
problem Multi-user contextual bandits with graph-related users and non-linear rewards.
method Joint penalty combining graph smoothness and individual roughness in a unified RKHS.
result Unified multi-user RKHS and effective dimension for regret bounds.
L 3 ^3 3 -SVMs clusters data, reduces dimensions, and learns linear models.
problem Capturing non-linearities and scaling to large datasets.
method Clusters input space, projects data onto landmarks, learns linear combination of local models.
result L 3 ^3 3 -SVMs achieves generalization guarantees and competitive performance. AuxiLearn combines auxiliary tasks into a single loss function.
problem Improving neural network performance on a main task using auxiliary tasks.
method Implicit differentiation to learn a network that combines auxiliary tasks into a single coherent objective function.
result AuxiLearn consistently outperforms competing methods in various tasks and domains.
New statistical tests detect interactions in clinical trials.
problem Detecting interactions between treatments and patient descriptors.
method Univariate and combined statistical tests based on random walk theory.
result Demonstrated utility and robustness of the proposed method.