Paper models non-linear dynamics from time series data.
problem Modeling non-linear dynamical systems from time series data.
method Introduces latent state modeling and a novel alternating minimization algorithm.
result LaNoLem achieves competitive performance in dynamics estimation and prediction.
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…
New method for interpreting non-linear models using forward marginal effects.
problem Interpreting non-linear models' feature effects is challenging.
method Introducing forward marginal effects and partitioning feature space for better interpretation.
result Improved interpretation of non-linear prediction functions.
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.
TaCo prevents non-linear classifiers from detecting sensitive attributes.
problem Ensuring fairness in NLP models by preventing sensitive attribute detection.
method Targeted Concept Erasure (TaCo) removes sensitive information from final latent representations, even against non-linear classifiers.
result TaCo outperforms state-of-the-art methods in reducing sensitive attribute prediction accuracy while preserving overall task performance.
We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call non-linear affine processes. This is done as follows: given a set of parameters for the process, we construct a corresponding non-linear expectation on the path space of continuous processes. By a general dynamic programm…
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.
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 model for Knightian uncertainty with jumps.
problem Knightian uncertainty and non-linear jumps.
method Probabilistic construction of non-linear affine processes with jumps.
result Tractable model for Knightian uncertainty with sublinear expectations.
RNN-HAR model improves VaR forecasting with long-memory and non-linear dynamics.
problem Efficiently forecasting Value at Risk (VaR) with long-memory and non-linear realized volatility.
method Loss-based generalized Bayesian inference with Sequential Monte Carlo for model estimation and prediction.
result RNN-HAR model consistently outperforms other VaR forecasting models.
Improves sparse recovery with non-linear Fourier features.
problem Sparse recovery challenges with non-linear Fourier features.
method Characterizes sufficient data points for perfect recovery.
result Sufficient data points depend on kernel matrix.
Optimal algorithms for non-linear ridge bandits reduce burn-in cost.
problem Non-linear models introduce a burn-in period with fixed cost.
method Two-stage algorithm: find initial action, then treat locally linear.
result Two-stage algorithm is statistically optimal.
The study introduces a new stickiness parameter for stock prices using a non-linear model.
problem Understanding how closely individual stocks follow a stock index's price movements.
method Developed a non-linear pricing model inspired by tectonic plate movements to measure stickiness.
result Defined a stickiness parameter for stock price returns using a novel model.
This paper studies the dynamic generator model for spatial-temporal processes such as dynamic textures and action sequences in video data. In this model, each time frame of the video sequence is generated by a generator model, which is a non-linear transformation of a latent state vector, where the non-linear transform…
PatternLocal improves XAI for non-linear models by suppressing suppressor variables.
problem Suppressor variables cause false-positive feature attributions in non-linear models.
method PatternLocal uses locally linear surrogate models and transforms weights into a generative representation.
result PatternLocal reduces false-positive attributions and provides more reliable explanations.
New neural network models for functional data.
problem Handling non-linear functional data.
method Functional Direct Neural Network (FDNN) and Functional Basis Neural Network (FBNN) with gradient-based optimization.
result Demonstrated effectiveness in complex functional models.
SSL framework identifies non-linear systems without labeled data.
problem System identification in non-linear environments without labeled data.
method Dynamics contrastive learning framework.
result SSL can identify non-linear dynamics in latent space.
Non-linear source separation is a challenging open problem with many applications. We extend a recently proposed Adversarial Non-linear ICA (ANICA) model, and introduce Cramer-Wold ICA (CW-ICA). In contrast to ANICA we use a simple, closed--form optimization target instead of a discriminator--based independence measure…
Machine learning improves joint default assessment by capturing non-linear dependencies.
problem Capturing non-linear dependencies among covariates for accurate joint default assessment.
method Application of machine learning techniques to credit card dataset, comparing with logistic regression.
result Machine learning outperforms logistic regression in assessing portfolio riskiness.
The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We provide closed-form expressions for the mean function and the covariance function of t…
Non linear sigma models are quantum field theories describing, in the large deviations sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci fl…
New model explains market dynamics with phase transitions and non-linear interactions.
problem Understanding complex multi-asset market dynamics with phase transitions.
method Developed a Multi-Asset Non-Equilibrium Skew (MANES) model based on Langevin dynamics and McKean-Vlasov equation.
result The model accurately predicts market returns and phase transitions in both benign and distressed markets.
An approach is proposed to determine structural shift in time-series assuming non-linear dependence of lagged values of dependent variable. Copulas are used to model non-linear dependence of time series components.
Improved texture synthesis using wavelet-based statistics with rectifier non-linearity.
problem Improving texture synthesis quality using wavelet representations.
method Proposes a family of statistics based on non-linear wavelet representations with a generalized rectifier non-linearity.
result Significantly improves visual quality of texture synthesis compared to classical wavelet-based models.
fmeffects package interprets non-linear models in plain language.
problem Interpreting complex non-linear models.
method Forward marginal effects for model-agnostic explanations.
result First software implementation of forward marginal effects.
New models learn stable latent clusters without side info.
problem Stability of non-linear ICA representations without side information.
method Deep generative models with latent clusterings, compared to standard VAEs and auxiliary labeled models.
result Deep generative models with latent clusterings are as stable as models with side information.
GP-KAN uses Gaussian Processes in KANs for robust, parameter-efficient non-linear modeling.
problem Non-linear modeling with limited parameters and uncertainty estimates.
method Integrates Gaussian Processes into Kolmogorov Arnold Networks (KANs) for robust non-linear modeling.
result GP-KAN achieves 98.5% accuracy on MNIST with 80k parameters compared to 1.5M for state-of-the-art models.
New method recovers causal graphs from data scores in non-linear models.
problem Recovering causal graphs from data scores in non-linear models.
method Score matching algorithms and efficient Jacobian approximation.
result New method, SCORE, is competitive and faster than state-of-the-art methods.
This work optimizes reservoir computing models by linking recurrence and non-linear dynamics.
problem Understanding how recurrence and non-linear dynamics in cortical networks contribute to their function.
method Transformed time-continuous, recurrent dynamics into an effective feed-forward structure of linear and non-linear temporal kernels.
result Optimal time-series classifiers can be built from random reservoir networks, demonstrating significant performance gains.
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…
Inference-aware meta-alignment of LLMs reduces computational cost.
problem Aligning LLMs to diverse human preferences is challenging due to conflicting criteria.
method IAMA trains a base model to be aligned to multiple tasks via different inference-time alignment algorithms, using non-linear GRPO for optimization.
result IAMA enables effective alignment of LLMs to multiple criteria with limited computational budget.
ENIAC method optimizes and explores complex RL problems with non-linear policies.
problem Theoretical understanding of non-linear policies in RL with strategic exploration.
method ENIAC, an actor-critic method for non-linear function approximation.
result ENIAC finds near-optimal policies in polynomial exploration rounds under bounded eluder dimension.
Study confirms complex crypto market dynamics via non-linear potentials.
problem Linear models fail to capture complex financial market dynamics.
method Analyzed high-frequency crypto currency data to confirm non-linear drift and potential functions.
result Markets exhibit either single-well or double-well potentials, indicating varying levels of uncertainty or stress.
Develops inverse EKF for non-linear systems with stability guarantees and learning unknown dynamics.
problem Estimating adversary's Kalman-filtered estimates in highly non-linear systems.
method Proposes inverse extended Kalman filter (I-EKF) for second-order, Gaussian sum, and dithered forward models. Uses reproducing kernel Hilbert space for learning unknown dynamics.
result Derives theoretical stability guarantees for inverse second-order EKF.
Latent force models are systems whereby there is a mechanistic model describing the dynamics of the system state, with some unknown forcing term that is approximated with a Gaussian process. If such dynamics are non-linear, it can be difficult to estimate the posterior state and forcing term jointly, particularly when …
SAFLe solves federated learning's trade-off between non-linearity and scalability.
problem Federated Learning's high communication overhead and performance collapse on non-IID data.
method SAFLe introduces a structured head of bucketed features and sparse, grouped embeddings, mathematically equivalent to a high-dimensional linear regression.
result SAFLe achieves a new state-of-the-art in analytic FL, outperforming linear AFL and multi-round DeepAFL.
New Shapley values reveal non-linear feature dependencies.
problem Understanding non-linear dependencies in machine learning models.
method Model-independent Shapley values using non-parametric measures of dependence.
result Model-independent Shapley values can uncover non-linear dependencies.
New method distinguishes feature relevance in non-linear contexts.
problem Finding relevant features with preserved redundancies.
method Random forest models and statistical methods.
result Distinguishes strong from weak feature relevance in non-linear problems.
Extends model uncertainty framework to non-linear affine processes for longevity bonds and contingent claims.
problem Model uncertainty and non-linear affine processes in financial markets.
method Extended reduced-form setting with affine process intensities, introduced longevity bond, and priced contingent claims.
result Consistent valuation of longevity bonds and arbitrage-free market under sublinear operator.
This paper conditions non-linear infinite-dimensional diffusion processes.
problem Conditioning non-linear and infinite-dimensional diffusion processes.
method Infinite-dimensional Girsanov's theorem to condition function-valued stochastic processes.
result Conditioning of non-linear infinite-dimensional diffusion processes is achieved.
New method adds all interactions in non-linear models without high computational cost.
problem Missing interactions in interpretable machine learning models.
method Additive higher-order factorization machines using tensor product splines.
result Scalable model with interactions at low computational cost.
Tractable model explains market dynamics using Langevin and SUSY QM.
problem Understanding non-linear market dynamics and option pricing.
method Langevin dynamics mapped to QM, using SUSY to find solutions.
result NES model provides accurate option pricing with a single volatility parameter.
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.
Broadens Jourdain and Martini's method to non-linear stochastic processes.
problem Applying pricing methods to non-linear stochastic processes.
method Analyzes from probabilistic and analytic viewpoints, extending Jourdain and Martini's method.
result Broadens applicability of pricing methods to non-linear frameworks.
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization, which predicts unobserved entries as linear combinations of latent variables. We g…
In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily highe…
DPLS improves asset pricing by capturing non-linear risk factor structures.
problem Estimating asset pricing models with non-linear risk factor structures.
method Deep Partial Least Squares (DPLS) for dynamic and flexible factor modeling.
result DPLS models outperform linear models in asset pricing, capturing non-linear risk factor interactions.
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.