arXiv research

ENIAC method optimizes and explores complex RL problems with non-linear policies.

Agents learn state ambiguity from non-linear sensor data using Gaussian approximations.

Papers learn from data to make decisions without interacting, improving on previous methods.

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…

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…

Agent optimizes perpetual contract liquidation with transaction costs and risk.

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…

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 …

Quantum computing offers a quadratic speedup for estimating non-linear functionals.

We propose a new method for learning deep neural network models that is based on a greedy learning approach: we add one basis function at a time, and a new basis function is generated as a non-linear activation function applied to a linear combination of the previous basis functions. Such a method (growing deep neural …

Paper presents a machine learning method to improve significance tests for misspecified linear models.

New method for interpreting non-linear models using forward marginal effects.

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…

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…

Study $p$-parabolicity on graphs using various energy functionals.

Paper establishes limits for accurately estimating low-rank matrices from noisy, non-linear data.

GP-KAN uses Gaussian Processes in KANs for robust, parameter-efficient non-linear modeling.

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…

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 propose fast approximations for the generalized sliced-Wasserstein distance.

Universal approximation theorem for differentiable maps on infinite-dimensional manifolds

Generalizes neural network approximation to infinite-dimensional manifolds and derivatives.

Matrix completion works well for smooth non-linear structures, even without low-rank assumptions.

New algorithm tackles non-linear utility in MNL bandits with $ilde{O}(\sqrt{T})$ regret.

We propose a Laplace approximation that creates a stochastic unit from any smooth monotonic activation function, using only Gaussian noise. This paper investigates the application of this stochastic approximation in training a family of Restricted Boltzmann Machines (RBM) that are closely linked to Bregman divergences.…

A new method learns state and proposal dynamics in state-space models using neural networks.

We extend neural networks with fractional and mixed activation functions for better function approximation.

Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic tools called "codes" is an emerging technique to alleviate the adverse effects …

Improved learning bounds for corrupted data using thresholded gradient descent.

Develops deep learning methods for non-linear PDEs in credit risk.

Broadens Jourdain and Martini's method to non-linear stochastic processes.

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.

Feature selection problems have been extensively studied for linear estimation, for instance, Lasso, but less emphasis has been placed on feature selection for non-linear functions. In this study, we propose a method for feature selection in high-dimensional non-linear function estimation problems. The new procedure is…

The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including con…

VO$Q$L optimizes RL with sparse rewards using weighted bounds.

Study reward-free RL in non-linear settings, improving efficiency and removing assumptions.

Sparse Bayesian learning improves rational approximations for complex-valued models.

Functional input neural networks approximate continuous functions on weighted spaces.

A risk-averse agent hedges her exposure to a non-tradable risk factor $U$ using a correlated traded asset $S$ and accounts for the impact of her trades on both factors. The effect of the agent's trades on $U$ is referred to as cross-impact. By solving the agent's stochastic control problem, we obtain a closed-form expr…

The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilizing a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimat…

New framework for analyzing games with multi-dimensional singular controls and non-linear jumps.

Tractable model explains market dynamics using Langevin and SUSY QM.

Sharp bounds on neural network approximation rates and widths.

New method recovers causal graphs from data scores in non-linear models.

Kernel $k$-means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear $k$-means clustering algorithm. However, kernel $k$-means clustering is computationally expensive when the non-linear feature map is high-dimensional and there are many input points. Kernel …

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 …

This paper deals with the exact calibration of semidiscretized stochastic local volatility (SLV) models to their underlying semidiscretized local volatility (LV) models. Under an SLV model, it is common to approximate the fair value of European-style options by semidiscretizing the backward Kolmogorov equation using fi…

This paper studies how to sketch element-wise functions of low-rank matrices. Formally, given low-rank matrix A = [Aij] and scalar non-linear function f, we aim for finding an approximated low-rank representation of the (possibly high-rank) matrix [f(Aij)]. To this end, we propose an efficient sketching-based algorithm…