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.
New analysis of Muon and SignSGD on matrix-valued least squares problems.
We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis and the ordinary least squares, we consider an efficient nuclear norm penalized …
Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
New bounds show current methods overestimate system parameter errors.
Classifies contravariant matrix-valued valuations on polytopes without continuity assumptions.
CD converges linearly for MCP/SCAD penalized least squares.
The paper extends log-Sobolev inequalities to matrix-valued settings using combinatorial methods.
Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.
Study finds weak solutions for complex map flows with optimal lifespan.
Illustrates interleaved learning with Kalman Filter for linear least squares.
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the quadratic objective function (cost approximation), or in terms of some distance meas…
Cross validation residuals are well known for the ordinary least squares model. Here leave-M-out cross validation is extended to generalised least squares. The relationship between cross validation residuals and Cook's distance is demonstrated, in terms of an approximation to the difference in the generalised residual …
Method learns molecular Hamiltonian for accurate electron dynamics predictions.
We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that …
Holomorphic functions from knot complements link to quantum modular forms.
The paper improves Kaczmarz algorithm with momentum for linear least squares.
New algorithm improves online binary classification with constant time complexity.
Reduced-rank method improves least-squares regression under output regularity.
Paper improves matrix-valued data classification using nonparametric LDA.
Researchers developed a new Riemannian manifold for SPD matrix-valued optimal transport problems.
Proposes a partitioned least squares model for feature grouping.
ESNs trained with Tikhonov least squares approximate ergodic dynamical systems in L2(μ) norm.
Recovering matrix valued potentials from wave equation data on stationary spacetimes.
Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it for…
The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm is closely related to the Kalman filtering, and thus, the KLMS can be interpreted…
A new algorithm solves nonnegative least squares faster with nonnegative data.
We extend Kyle's model to include stochastic liquidity and multiple assets.
The paper identifies saddlepoints in unsupervised auto-encoding neural nets.
The paper proposes a least squares method for binary compressive sampling with low intrinsic dimension signals.
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional construction and employs least-squares functionals as loss functions to determine para…
We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our numerical experiments demonst…
We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-supervised method…
New method speeds up solving L0-regularized least-squares problems.
Least squares estimator fails to achieve optimal risk in bounded distributions, but non-linear predictors can.
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an -constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm sequentially selects the features (i.e., columns of the coefficient matrix) to greedil…
We introduce the implicitly constrained least squares (ICLS) classifier, a novel semi-supervised version of the least squares classifier. This classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-s…
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as…
Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking solutions quality and accuracy becomes the trade-off. In this paper, we investi…
This book introduces linear models and their theories rigorously.
The ratio of two probability densities can be used for solving various machine learning tasks such as covariate shift adaptation (importance sampling), outlier detection (likelihood-ratio test), and feature selection (mutual information). Recently, several methods of directly estimating the density ratio have been deve…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The proposed methods are based on randomized block kernel matrices, and we show that t…
Efficiently estimates private least squares with linear error growth.
Paper introduces a new kernel model for PSD-valued functions with theoretical guarantees and applications.
Here, we provide a supplementary material for Takayuki Osogami, "Uncorrected least-squares temporal difference with lambda-return," which appears in {\it Proceedings of the 34th AAAI Conference on Artificial Intelligence} (AAAI-20).
We prove strong consistency and asymptotic normality of least squares estimators for the subcritical Heston model based on continuous time observations. We also present some numerical illustrations of our results.
We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified parameters.
Improved Least-Squares Monte Carlo with finite-difference ansatz.
Consider Least Squares Monte Carlo (LSM) algorithm, which is proposed by Longstaff and Schwartz (2001) for pricing American style securities. This algorithm is based on the projection of the value of continuation onto a certain set of basis functions via the least squares problem. We analyze the stability of the algori…