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.
ESNs trained with Tikhonov least squares approximate ergodic dynamical systems in L2(μ) norm.
Improved regression analysis using Padé approximants with new residuals and regularization.
Paper improves learning rates for GSC loss functions using iterated Tikhonov regularization.
New learning rates derived for Tikhonov-regularized problems without kernel assumptions.
We find the optimal Tikhonov regularizer for linear inverse problems without prior knowledge.
We consider the problem of selecting the best estimator among a family of Tikhonov regularized estimators, or, alternatively, to select a linear combination of these regularizers that is as good as the best regularizer in the family. Our theory reveals that if the Tikhonov regularizers share the same penalty matrix wit…
Paper introduces a new IV regression method for mixed-frequency data.
Proposes RDIV for IV estimation avoiding limitations of existing methods.
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization, MOR) approach to reconstruct the estimator of the quantity for the non-…
CD converges linearly for MCP/SCAD penalized least squares.
Tikhonov regularization is robust under specific martingale constraints in distributionally robust optimization.
Kernel method improves instrumental variable regression rates.
Unified framework recovers exact input from SOM activation patterns.
We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account perturbations of the surfaces, in particular when the surfaces are approximated by spl…
Kaczmarz++ accelerates convergence for ill-conditioned systems.
New framework assesses regularization norms in ill-posed problems, revealing L2 instability and proposing adaptive fractional RKHS solutions.
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 …
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 …
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.
Proposes a partitioned least squares model for feature grouping.
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.
The paper analyzes Tikhonov regularization in Hilbert scales for statistical inverse problems.
The paper identifies saddlepoints in unsupervised auto-encoding neural nets.
Nyström subsampling with Tikhonov regularization for covariate shift adaptation under misspecified case
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…
New insights into learning for blind inverse problems with theoretical guarantees.
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.
The paper analyzes the risk of a least squares estimator under a spike covariance model.
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…
A new method for learning function parameters in operators using data-adaptive RKHS.
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…
Improved MMD test for non-Euclidean data with spectral regularization.
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.
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).