arXiv research

A fast feature selection method using OLS and SOCC for classification.

Orthogonal matching pursuit (OMP) and orthogonal least squares (OLS) are widely used for sparse signal reconstruction in under-determined linear regression problems. The performance of these compressed sensing (CS) algorithms depends crucially on the \textit{a priori} knowledge of either the sparsity of the signal ($k_…

The OLS estimator optimally identifies stable linear systems with a finite number of samples.

We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a $m$-dimensional $k$-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for OLS under certain condition on nonzero elements of the signal. The new result a…

This study examines the relationship between PLS and OLS regression using eigenvalue distributions.

OLS predictions are shown to be similar to attention mechanisms in models.

Every 4-dimensional infrasolvmanifold $M$ with $β_1(M;\mathbb{Q})>0$ or which is flat or has one of the geometries $\mathbb{N}il^4$, $\mathbb{S}ol_{m,n}^4$, or $\mathbb{S}ol_0^4$ bounds. However there are non-orientable $\mathbb{S}ol_1^4$-manifolds which do not bound. The question remains open for $\mathbb{N}il^3\times…

We show that if $M$ is an orientable 4-dimensional infrasolvmanifold and either $β=β_1(M;\mathbb{Q})\geq2$ or $M$ is a $\mathbb{S}ol_0^4$- or a $\mathbb{S}ol_{m,n}^4$-manifold (with $m\not=n$) then $M$ is parallelizable. There are non-parallelizable examples with $β=1$ for each of the other solvable Lie geometries $\ma…

Polynomial Chaos Expansion improves operator learning for PDEs.

We present a unified framework for Batch Online Learning (OL) for Click Prediction in Search Advertisement. Machine Learning models once deployed, show non-trivial accuracy and calibration degradation over time due to model staleness. It is therefore necessary to regularly update models, and do so automatically. This p…

We show that $\mathbb{S}ol^3\times\mathbb{E}^1$-manifolds are Seifert fibred, with general fibre the torus, and base one of the seven flat 2-orbifolds $T, Kb, \mathbb{A}, \mathbb{M}b, S(2,2,2,2), P(2,2)$ or $\mathbb{D}(2,2)$, and outline a classification of such 4-manifolds.

PCA-based dimensionality reduction improves robustness in overparameterized linear models.

Lower bounds show OLS outperforms basis pursuit in overparameterized linear regression.

As bandit algorithms are increasingly utilized in scientific studies and industrial applications, there is an associated increasing need for reliable inference methods based on the resulting adaptively-collected data. In this work, we develop methods for inference on data collected in batches using a bandit algorithm. …

When the design matrix has orthonormal columns, "soft thresholding" the ordinary least squares (OLS) solution produces the Lasso solution [Tibshirani, 1996]. If one uses the Puffer preconditioned Lasso [Jia and Rohe, 2012], then this result generalizes from orthonormal designs to full rank designs (Theorem 1). Theorem …

We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from $\…

Improved privacy-preserving linear regression via iterative Hessian mixing.

New algorithm selects variables from large datasets.

We compare the random group model of Gromov and the model of generic groups of Arzhantseva and Ol'shanskii.

The paper tackles system identification via Hankel nuclear norm regularization, improving estimation rates and singular value gaps.

Ordinary least squares (OLS) is the default method for fitting linear models, but is not applicable for problems with dimensionality larger than the sample size. For these problems, we advocate the use of a generalized version of OLS motivated by ridge regression, and propose two novel three-step algorithms involving l…

OLS is a special case of Transformer, revealing its linear nature.

Enhanced LSTM predicts equity trends, outperforming traditional methods.

Despite its empirical success and recent theoretical progress, there generally lacks a quantitative analysis of the effect of batch normalization (BN) on the convergence and stability of gradient descent. In this paper, we provide such an analysis on the simple problem of ordinary least squares (OLS). Since precise dyn…

We consider the question of learning in general topological vector spaces. By exploiting known (or parametrized) covariance structures, our Main Theorem demonstrates that any continuous linear map corresponds to a certain isomorphism of embedded Hilbert spaces. By inverting this isomorphism and extending continuously, …

Study combines SEM, OLS, and DML for robustness checks in survey-based research.

This work develops fast and accurate ROMs for AM models using OL methods.

Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm sequentially selects the features (i.e., columns of the coefficient matrix) to greedil…

The purpose of this note is to present several criteria for essential self-adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in the most general setting. Such a symmetric first order system of differential eq…

Let $f:M^m\longrightarrow \Bbb R^{m+k}$ be an immersion where $M$ is a smooth connected $m$-dimensional manifold without boundary. Then we construct a subspace $Ω(f)$ of $\mathbb{R}^k$, namely push-out space. which corresponds to a set of embedded manifolds which are either parallel to $f$, tubes around $f$ or, in…

New EiV models correct bias in operator learning with noisy data.

We apply the method of Arzhantseva-Ol'shanskii to prove that for an exponentially generic (in the sense of Ol'shanskii) class of one-relator groups the isomorphism problem is solvable in at most exponential time. This is obtained as a corollary of our more general result that for any fixed integers $m>1, n>0$ there is …

Reducing ICD-10 code granularity improves cost model accuracy and stability.

This work develops a fast-running ROM for MOOSE-based AM model using OL.

We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail specific metrics to compare the hedging effectiveness of short and long hedgers using crude oil futures contracts. The metrics used include Lower Partial Moments (LPM), Value at Risk (VaR) and Conditional Value…

We compute the rings $H^*(N;\mathbb{F}_2)$ for $N$ a closed $\mathbb{S}ol^3$-manifold and then determine the Borsuk-Ulam indices $BU(N,φ)$ with $φ\not=0$ in $H^1(N;\mathbb{F}_2)$.

Risk aversion is a key element of utility maximizing hedge strategies; however, it has typically been assigned an arbitrary value in the literature. This paper instead applies a GARCH-in-Mean (GARCH-M) model to estimate a time-varying measure of risk aversion that is based on the observed risk preferences of energy hed…

New approach for uninformed investors to optimize execution costs.

Improves regression models' performance on covariate shift.

The paper studies how submanifolds in Gaussian space behave under mean curvature flow, showing they typically blow up.

Ordinary least square (OLS) estimation of a linear regression model is well-known to be highly sensitive to outliers. It is common practice to (1) identify and remove outliers by looking at the data and (2) to fit OLS and form confidence intervals and p-values on the remaining data as if this were the original data col…

The paper optimizes asset selection for index trackers and enhanced trackers with varying cardinality constraints.

Extends knockoff filter for composite null hypotheses in variable selection.

Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce stable graphical (SG) models, a class of multivariate st…

Study evaluates scikit-learn regularization frameworks for machine learning models.

This study uses machine learning to predict sovereign credit ratings and identifies key factors.

New bounds show current methods overestimate system parameter errors.

'Ergodicity economics' is criticized as pseudoscience.