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.
Agents learn state ambiguity from non-linear sensor data using Gaussian approximations.
ENIAC method optimizes and explores complex RL problems with non-linear policies.
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…
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative …
We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.
Papers learn from data to make decisions without interacting, improving on previous methods.
New method recovers causal graphs from data scores in non-linear models.
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 …
Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant extension of the "anchored regression" method formulated and analyzed in [10] f…
We consider the numerical approximation of the quantile hedging price in a non-linear market. In a Markovian framework, we propose a numerical method based on a Piecewise Constant Policy Timestepping (PCPT) scheme coupled with a monotone finite difference approximation. We prove the convergence of our algorithm combini…
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…
New algorithm improves dynamic mode decomposition for high-dimensional data.
Improved disability insurance model with collective health claims.
Improved bounds for non-linear SA with fast convergence.
New method distinguishes feature relevance in non-linear contexts.
Agent optimizes perpetual contract liquidation with transaction costs and risk.
Develops an efficient method for real-time data analysis and visualization.
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…
We provide several new depth-based separation results for feed-forward neural networks, proving that various types of simple and natural functions can be better approximated using deeper networks than shallower ones, even if the shallower networks are much larger. This includes indicators of balls and ellipses; non-lin…
Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are analytically intractable for such a model, they need to be approximated numerically. In [Po…
Quantile Temporal-Difference learning proved convergent with proof.
Privacy concern has been increasingly important in many machine learning (ML) problems. We study empirical risk minimization (ERM) problems under secure multi-party computation (MPC) frameworks. Main technical tools for MPC have been developed based on cryptography. One of limitations in current cryptographically priva…
Since their introduction a year ago, distributional approaches to reinforcement learning (distributional RL) have produced strong results relative to the standard approach which models expected values (expected RL). However, aside from convergence guarantees, there have been few theoretical results investigating the re…
This paper introduces a method to approximate Gaussian process regression by representing the problem as a stochastic differential equation and using variational inference to approximate solutions. The approximations are compared with full GP regression and generated paths are demonstrated to be indistinguishable from …
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…
We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations, which arise, e.g., in non-linear option pricing problems or in probabilistic dis…
Paper presents a machine learning method to improve significance tests for misspecified linear models.
Paper introduces non-linearity signature to measure deep neural network performance.
Quantum computing offers a quadratic speedup for estimating non-linear functionals.
Sparse Bayesian learning improves rational approximations for complex-valued models.
A new method learns state and proposal dynamics in state-space models using neural networks.
New filters for non-linear systems achieve closed-form solutions.
Paper establishes limits for accurately estimating low-rank matrices from noisy, non-linear data.
New method for interpreting non-linear models using forward marginal effects.
Tractable model explains market dynamics using Langevin and SUSY QM.
We introduce a prototype model in an attempt to capture some aspects of market dynamics simulating a trading mechanism. The model description starts with a discrete-space, continuous-time Markov process describing arrival and movement of orders with different prices. We then perform a re-scaling procedure leading to a …
This research uses DPPs to improve semi-parametric regression models.
Broadens Jourdain and Martini's method to non-linear stochastic processes.
New proof of Riemannian Penrose Inequality for manifolds with corners
When approximating a black-box function, sampling with active learning focussing on regions with non-linear responses tends to improve accuracy. We present the FLOLA-Voronoi method introduced previously for deterministic responses, and theoretically derive the impact of output uncertainty. The algorithm automatically p…
Improves financial instrument pricing using neural networks.
Study -parabolicity on graphs using various energy functionals.
Develops deep learning methods for non-linear PDEs in credit risk.
Study reward-free RL in non-linear settings, improving efficiency and removing assumptions.
We present a general existence proof for a wide class of non-linear elliptic equations which can be applied to problems with barrier conditions without specifying any assumptions guaranteeing the uniqueness or local uniqueness of particular solutions. As an application we prove the existence of closed hypersurfaces wit…
PEA improves PCA and k-means for non-linear data and complex clusters.
Kernel -means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear -means clustering algorithm. However, kernel -means clustering is computationally expensive when the non-linear feature map is high-dimensional and there are many input points. Kernel …