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.
Estimates fat-shattering dimension of aggregated function classes.
Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods. To provide a better theoretical understanding of the reasons for its success, we discuss the performance of deep learning and other methods on a nonparametric reg…
Papers learn from data to make decisions without interacting, improving on previous methods.
Introduces HTV to measure function complexity in learning schemes.
The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.
This work connects hardness of approximation and learning.
Study of linear classifiers in infinite imbalance scenarios.
We consider a class of continuous functions on that is of interest from two different perspectives. First, it is closely related to sets of functions that have been studied as generalizations of the Takagi function. Second, each function in admits a linear pathwise quadratic variatio…
We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger class includes functions whose second derivatives may be singular or unbounded at th…
New framework allows reinforcement learning with polynomial sample complexity.
Researchers classify cmc surfaces using Jacobi elliptic functions.
Study optimizes estimating linear functionals from observational data without strict overlap.
Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns linear factored functions (LFF). This class of functions has structural properties …
The paper analyzes methods for estimating linear functionals from observational data, proving upper bounds and showing optimal procedures.
We derive bounds for a notion of adversarial risk, designed to characterize the robustness of linear and neural network classifiers to adversarial perturbations. Specifically, we introduce a new class of function transformations with the property that the risk of the transformed functions upper-bounds the adversarial r…
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for minimizing a smooth convex function over a linear space spanned by a set of atoms…
Study shows long-term solutions for complex equations on curved spaces.
New particle-based VI algorithm expands function class and improves scalability.
In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an…
Symmetrizes loss functions to improve neural network robustness against noisy labels.
New proof shows efficient ReLU networks for piecewise linear functions.
VOL optimizes RL with sparse rewards using weighted bounds.
It is important to develop mathematically tractable models than can interpret knowledge extracted from the data and provide reasonable predictions. In this paper, we present a Linear Distillation Learning, a simple remedy to improve the performance of linear neural networks. Our approach is based on using a linear func…
New neural network models for functional data.
Improved algorithms solve multi-period multi-class packing problems with bandit feedback.
Transformers learn low-dimensional target functions efficiently in-context.
Optimizes experiment design for causal structure learning in linear models with cycles.
-learning with function approximation is one of the most popular methods in reinforcement learning. Though the idea of using function approximation was proposed at least 60 years ago, even in the simplest setup, i.e, approximating -functions with linear functions, it is still an open problem on how to design a pr…
The paper analyzes risk bounds and Rademacher complexity in batch RL.
This research sets limits on how complex multi-class learning problems can be.
New neural network models for complex functional data analysis.
Optimal algorithm for maximizing rewards in contextual bandits with resource constraints.
New RL algorithm achieves nearly optimal performance for linear MDPs.
New algorithm tackles non-linear utility in MNL bandits with regret.
New method uses DC functions for piecewise linear regression.
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 …
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop the explicit solution for this class of problem. The revealed optimal control poli…
We analyze different re-ranking algorithms for diversification and show that majority of them are based on maximizing submodular/modular functions from the class of parameterized concave/linear over modular functions. We study the optimality of such algorithms in terms of the `total curvature'. We also show that by adj…
Signature portfolios approximate optimal wealth in non-Markovian markets.
In this paper, we introduce a large class of convergent numerical methods, based on (linear) basis function regression technique, to approximate the solution to a forward-backward stochastic differential equation with jumps (FBSDEJ hereafter). Numerical experiment shows good applicability of the proposed method.
ENIAC method optimizes and explores complex RL problems with non-linear policies.
In this paper, we study a certain class of online optimization problems, where the goal is to maximize a function that is not necessarily concave and satisfies the Diminishing Returns (DR) property under budget constraints. We analyze a primal-dual algorithm, called the Generalized Sequential algorithm, and we obtain t…
Study nonparametric covariance function estimation for noisy data.
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and H…
We obtain the first positive results for bounded sample compression in the agnostic regression setting with the loss, where . We construct a generic approximate sample compression scheme for real-valued function classes exhibiting exponential size in the fat-shattering dimension but independen…
Supervised (linear) embedding models like Wsabie and PSI have proven successful at ranking, recommendation and annotation tasks. However, despite being scalable to large datasets they do not take full advantage of the extra data due to their linear nature, and typically underfit. We propose a new class of models which …
Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with graph-dependent linear operations. However, these graph-dependent linear operations are d…
We show that Newton's method converges globally at a linear rate for objective functions whose Hessians are stable. This class of problems includes many functions which are not strongly convex, such as logistic regression. Our linear convergence result is (i) affine-invariant, and holds even if an (ii) approximate Hess…