arXiv research

Paper proposes an algorithm to recover full supervision from weakly labeled data.

The paper provides convergence guarantees for multicalibration gradient boosting.

Proves weak convergence equals mean convergence in GGC.

Gradient boosting is a prediction method that iteratively combines weak learners to produce a complex and accurate model. From an optimization point of view, the learning procedure of gradient boosting mimics a gradient descent on a functional variable. This paper proposes to build upon the proximal point algorithm, wh…

Sharp bounds on weak convergence rate for rough volatility models.

New bounds for generative models under weaker assumptions.

Studied SGD convergence under weak conditions.

New method estimates causal effects in complex spaces using topological structures.

The paper shows how MMD metrizes weak convergence for certain kernels.

In this paper we study utility maximization with proportional transaction costs. Assuming extended weak convergence of the underlying processes we prove the convergence of the corresponding utility maximization problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on …

The significance of the study of the theoretical and practical properties of AdaBoost is unquestionable, given its simplicity, wide practical use, and effectiveness on real-world datasets. Here we present a few open problems regarding the behavior of "Optimal AdaBoost," a term coined by Rudin, Daubechies, and Schapire …

Proves curvature tensor convergence for smoothable spaces.

Study shows financial value of weak information converges in discrete vs continuous markets.

Adaptive Bayesian quadrature (ABQ) is a powerful approach to numerical integration that empirically compares favorably with Monte Carlo integration on problems of medium dimensionality (where non-adaptive quadrature is not competitive). Its key ingredient is an acquisition function that changes as a function of previou…

Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.

New theory explains consistency of kernel methods with non-i.i.d. data.

In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify thi…

Neural networks trained with actor-critic algorithms converge to ODEs under weak convergence analysis.

New algorithm improves convergence of gradient boosting trees.

Develops robust MDPs for unknown disturbances with performance guarantees.

Preserves scalar curvature bounds under weak convergence of 3-manifolds.

Stability of Yang-Mills connections' Morse indices and nullity in 4D.

We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal gradient descent algorithm for computing the estimator and establish adaptive m…

In this paper, we prove that a sequence of weak almost Kähler-Ricci solitons under further suitable conditions converge to a Kähler-Ricci soliton with complex codimension of singularities at least 2 in the Gromov-Hausdorff topology. As a corollary, we show that on a Fano manifold with the modified K-energy bounded belo…

In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence result for the terminal wealths of the optimal portfolios. Finally,…

Paper studies identifiability and stability of drifting fields in generative modeling.

Study shows how neural networks generalize with minimal training data.

Optimal quantization of measures on Carnot groups

Study on error rates for approximating rough volatility models.

LMC algorithm receives first convergence guarantees under weak smoothness conditions.

The paper explores identifiability and stability in drifting fields using companion-elliptic kernels.

Paper studies central bank's strategy to control systemic risk in interbank system.

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient computational algorithm for this class is presented that easily scales to thousands of ob…

We provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by U- and V-statistics, Lipschitz L-statistics and various error f…

New KSDs control moments in approximations, improving diagnostics and tests.

Study rough volatility models using path-dependent PDEs and fractional Brownian motions.

Paper introduces HRPCFD for efficient training of stochastic processes.

Generative adversarial networks (GAN) approximate a target data distribution by jointly optimizing an objective function through a "two-player game" between a generator and a discriminator. Despite their empirical success, however, two very basic questions on how well they can approximate the target distribution remain…

The paper proves stability of critical points for conformally invariant Lagrangians.

Proves existence and uniqueness of weak solutions for specific equations.

The paper studies limits of flows on Kähler surfaces, proving convergence to solutions of equations.

New mechanism detects overlap density for weak-to-strong generalization.

In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, f…

Estimates ends of Ricci shrinkers, focusing on smooth and singular cases.

Establishes a microstructural foundation for a rough log-normal volatility model.

In this paper we consider Dynkin's games with payoffs which are functions of an underlying process. Assuming extended weak convergence of underlying processes $\{S^{(n)}\}_{n=0}^{\infty}$ to a limit process $S$ we prove convergence Dynkin's games values corresponding to $\{S^{(n)}\}_{n=0}^{\infty}$ to the Dynkin's game…

Gradient descent converges to minimum Bayes risk for two-layer ReLU networks in mean field regime.

We investigate the computational aspects of the basket CDS pricing with counterparty risk under a credit contagion model of multinames. This model enables us to capture the systematic volatility increases in the market triggered by a particular bankruptcy. The drawback of this problem is its analytical complication due…