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…
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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
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48 results for “non-linear parameters”
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.
Method estimates mixture components without discretizing parameters.
problem Learning from mixtures of continuous features with noise.
method Off-the-grid optimization method for continuous parameter space.
result Prediction error bound similar to Lasso predictor.
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.
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…
We propose a new Bayesian tracking and parameter learning algorithm for non-linear non-Gaussian multiple target tracking (MTT) models. We design a Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distribution of the target states, birth and death times, and association of observations to targets, …
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.
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.
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.
The goal of a recommendation system is to predict the interest of a user in a given item by exploiting the existing set of ratings as well as certain user/item features. A standard approach to modeling this problem is Inductive Matrix Completion where the predicted rating is modeled as an inner product of the user and …
This tutorial introduces the CMA Evolution Strategy (ES), where CMA stands for Covariance Matrix Adaptation. The CMA-ES is a stochastic, or randomized, method for real-parameter (continuous domain) optimization of non-linear, non-convex functions. We try to motivate and derive the algorithm from intuitive concepts and …
Estimates signals from a continuous dictionary with sparse mixtures using optimization.
problem Estimating signals from a continuous dictionary with unknown mixtures and noise.
method Formulates a regularized optimization problem with data fidelity and -penalty.
result High probability bounds on prediction error for the Group-Nonlinear-Lasso solution.
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.
Bayesian neural networks improve uncertainty quantification in non-linear dimensionality reduction.
problem Current neural network models lack adequate uncertainty quantification.
method Deploy Markov chain Monte Carlo sampling algorithms for Bayesian inference in ANN models with latent variables.
result New research directions are needed due to fundamental challenges in neural networks with latent variables.
Improved regret bound for multinomial logistic bandits with non-linearity.
problem Maximizing rewards in multinomial logistic bandits with non-linear feedback.
method Extended the definition of to multinomial setting and proposed an efficient algorithm.
result Minimax-optimal regret bound of , improving over existing guarantees.
New deep learning method simplifies parameter estimation design.
problem Optimal experimental design for parameter estimation with non-linear systems.
method Training a deep network as a Likelihood Free Estimator to simplify design process.
result Deep design improves parameter recovery quality and simplifies design process.
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.
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…
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 …
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.
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…
We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of di…
New method estimates SDE parameters efficiently using WCE and SGD.
problem Parameter estimation for stochastic differential equations.
method Wiener Chaos Expansion and Stochastic Gradient Descent.
result Accurate parameter recovery from noisy observations.
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.
Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such scenarios. In particular, a random process generated by the autoregressive moving…
On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex multi-dimensional integrals that are not amenable to analytical solution. While basic sequentia…
Paper tackles robust control of SDEs with ambiguity, proving value function existence and applying to investment problems.
problem Robust control of SDEs with ambiguity parameters and non-Lipschitz coefficients.
method Existence and uniqueness of value function established through BSDEs with non-linear growth conditions.
result Existence and uniqueness of value function in proper space, verified through BSDEs.
We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a non-linear Black-Scholes Equation that provides an exact replication strategy. This equation is fully non-linear and singular, but we show that it is well posed, and we prove existence o…
Agent optimizes perpetual contract liquidation with transaction costs and risk.
problem Optimizing perpetual contract liquidation with transaction costs and risk.
method Solving stochastic control problem for optimal trading strategy.
result Closed-form expression and approximations for optimal strategy.
Develops polynomial diffusion models for multi-factor commodity futures dynamics.
problem Modeling futures prices using latent state variables for short and long-term stochastic factors.
method Polynomial diffusion models to incorporate non-linear effects, two filtering methods for estimation.
result Accurate estimation of futures prices despite parameter identification issues in polynomial diffusion models.
Two Fisher information matrix estimators are analyzed for neural networks, focusing on their variances and trade-offs.
problem Estimating the Fisher information matrix in neural networks due to its high computational cost.
method Examined two popular diagonal Fisher information matrix estimators and their variances in neural networks for regression and classification.
result The variances of the estimators depend on the non-linearity with respect to different parameter groups and should not be neglected.
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.
We develop a general theory for the goodness-of-fit test to non-linear models. In particular, we assume that the observations are noisy samples of a submanifold defined by a \yao{sufficiently smooth non-linear map}. The observation noise is additive Gaussian. Our main result shows that the "residual" of the model fit, …
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.
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…
Paper proposes a bias-constrained deep learning approach to non-linear estimation.
problem Designing unbiased estimators for non-linear models.
method Bias Constrained Estimator (BCE) using deep learning with bias constraints.
result Asymptotic MVUEs with Cramer Rao bound performance.
Method infers parameters in complex diffusion processes.
problem Parameter inference in high-dimensional, non-linear diffusion processes.
method Differentiable score matching to approximate diffusion bridges, used in an importance sampler.
result Numerically stable framework for parameter inference and diffusion mean estimation.
Dynamic linear models improve travel time prediction for congested freeways.
problem Accurate travel time prediction for congested freeways.
method Dynamic linear models (DLMs) with time-varying parameters.
result Significant improvements in travel time prediction accuracy, especially for short-term predictions.
The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power…
We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein-Maxwell equations: If one perturbs the initial data of a slowly rotating Kerr-Newman-de Sitter (KNdS) black hole, then in a …
We propose a new efficient online algorithm to learn the parameters governing the purchasing behavior of a utility maximizing buyer, who responds to prices, in a repeated interaction setting. The key feature of our algorithm is that it can learn even non-linear buyer utility while working with arbitrary price constrain…
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extendin…
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.
We introduce a method for constructing skills capable of solving tasks drawn from a distribution of parameterized reinforcement learning problems. The method draws example tasks from a distribution of interest and uses the corresponding learned policies to estimate the topology of the lower-dimensional piecewise-smooth…
We provide an explicit description of all rigid hypersurfaces that are equivalent to a Heisenberg sphere. These hypersurfaces are determined by 4 real parameters. The defining equations of the rigid spheres can also be viewed as the complete solution of a non-linear PDE that expresses the vanishing Cartan curvature con…
Affine models with path-dependence under parameter uncertainty and their application in financeq-fin.MF
Study path-dependent affine models under uncertain parameters for financial applications.
problem Valuation of path-dependent financial derivatives under parameter uncertainty.
method Developed path-dependent setting for value function, established dynamic programming principle, approximated functional derivatives with neural networks.
result Efficient numerical methods for valuation of complex financial derivatives under parameter uncertainty.
Proves stability of Schwarzschild black holes without symmetry assumptions.
problem Stability of Schwarzschild black holes under general conditions.
method Teleologically normalised double null gauges, analysis of linear stability, and control of non-linearities.
result Proves non-linear asymptotic stability of Schwarzschild family as solutions to Einstein vacuum equations.
This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed …