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.
Max-affine regression method converges linearly using GD and SGD.
Paper presents ABGD for efficient piecewise linear regression in high dimensions.
New AMP algorithm estimates signals and latent variables in mixed regression models.
Paper presents an efficient algorithm for estimating Lipschitz functions from noisy data.
Paper proposes Sp-GD for sparse max-affine regression with theoretical guarantees.
Single-head attention approximates any function under various norms.
This paper shows neural networks can solve complex graph problems efficiently.
Max-affine regression refers to a model where the unknown regression function is modeled as a maximum of unknown affine functions for a fixed . This generalizes linear regression and (real) phase retrieval, and is closely related to convex regression. Working within a non-asymptotic framework, we study th…
We build a rigorous bridge between deep networks (DNs) and approximation theory via spline functions and operators. Our key result is that a large class of DNs can be written as a composition of max-affine spline operators (MASOs), which provide a powerful portal through which to view and analyze their inner workings. …
New method uses DC functions for piecewise linear regression.
Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and extend both of them using weighted lattices and a max- algebra with an ar…
We connect a large class of Generative Deep Networks (GDNs) with spline operators in order to derive their properties, limitations, and new opportunities. By characterizing the latent space partition, dimension and angularity of the generated manifold, we relate the manifold dimension and approximation error to the sam…
Spectrahedral regression fits convex functions via a non-convex optimization problem.
We study the geometry of deep (neural) networks (DNs) with piecewise affine and convex nonlinearities. The layers of such DNs have been shown to be {\em max-affine spline operators} (MASOs) that partition their input space and apply a region-dependent affine mapping to their input to produce their output. We demonstrat…
Nonlinearity is crucial to the performance of a deep (neural) network (DN). To date there has been little progress understanding the menagerie of available nonlinearities, but recently progress has been made on understanding the rôle played by piecewise affine and convex nonlinearities like the ReLU and absolute value …
Improved iterative methods for risk parity portfolio weights.
We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems. Our method has only one parameter (a step size), and is radically simpler than o…
A new method combines Laplace and Variational Bayes for scalable inference.
Unified framework for model explanation methods based on feature removal.
This work reviews and evaluates methods for predicting prediction intervals in regression problems.
Derives kernel PCA with Nyström method for scalability.
In this paper, the author considers the numerical computation of CVA for large systems by Mote Carlo methods. He introduces two types of stochastic mesh methods for the computations of CVA. In the first method, stochastic mesh method is used to obtain the future value of the derivative contracts. In the second method, …
New method combines spectral and sparse methods for Gaussian processes.
A comprehensive benchmark of 15 scRNA-seq imputation methods across various datasets and analyses.
New methods using natural gradient for structured optimization.
Recently, {\it stochastic momentum} methods have been widely adopted in training deep neural networks. However, their convergence analysis is still underexplored at the moment, in particular for non-convex optimization. This paper fills the gap between practice and theory by developing a basic convergence analysis of t…
We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift, which makes it a time-changed Brownian motion. In general, the finite difference me…
A new method speeds up deep neural network training.
We propose a new stochastic dual coordinate ascent technique that can be applied to a wide range of regularized learning problems. Our method is based on Alternating Direction Multiplier Method (ADMM) to deal with complex regularization functions such as structured regularizations. Although the original ADMM is a batch…
NCG methods improve shape optimization efficiency.
We propose two localized Radial Basis Function (RBF) methods, the Radial Basis Function Partition of Unity method (RBF-PUM) and the Radial Basis Function generated Finite Differences method (RBF-FD), for solving financial derivative pricing problems arising from market models with multiple stochastic factors. We demons…
Proposes UTC method for stock price prediction with uncertainty quantification.
Survey of spectral, probabilistic, and deep metric learning methods.
Various approaches to gene selection for cancer classification based on microarray data can be found in the literature and they may be grouped into two categories: univariate methods and multivariate methods. Univariate methods look at each gene in the data in isolation from others. They measure the contribution of a p…
A novel weighted feature selection method using fuzzy sets improves classification accuracy and stability.
New method improves accuracy in computing implied volatility.
The paper examines Wiener process for LID estimation methods.
We evaluate how modern outlier detection methods perform in identifying outliers in e-commerce conversion rate data. Based on the limitations identified, we then present a novel method to detect outliers in e-commerce conversion rate. This unsupervised method is made more business relevant by letting it automatically a…
Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to model misspecification. In this paper we present a hierarchical approach to methods…
We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike SVRG, our method can be directly applied to non-strongly and strongly convex prob…
We discuss the relevance of the recent Machine Learning (ML) literature for economics and econometrics. First we discuss the differences in goals, methods and settings between the ML literature and the traditional econometrics and statistics literatures. Then we discuss some specific methods from the machine learning l…
R package for counterfactual explanation methods.
We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing s…
The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the …
Derives new optimization methods using variational integrators.
A new method for faster optimization in high dimensions.
We discuss various analytic and numerical methods that have been used to get option prices within a framework of the VG model. We show that some popular methods, for instance, Carr-Madan's FFT method could blow up for certain values of the model parameters even for an European vanilla option. Alternative methods - one …
The article derives a formula for predicting claims uncertainty using the GCC method.