New approach for uninformed investors to optimize execution costs.
problem Optimizing execution costs for new investors with imperfect initial knowledge.
method Iterative derivation of OLS estimates of market parameters.
result Dynamic adjustment of trading strategies based on evolving market parameters.
Research calculates elasticities of energy demand in Ecuador, finding it highly income elastic.
problem Analyzing energy demand elasticities in Ecuador to inform policy.
method Cointegration analysis and Dynamic Ordinary Least Squares approach with structural breaks.
result Energy demand in Ecuador is highly income elastic, with no price elasticity and inverse relationship with industrial production.
OLS estimator nearly optimally identifies linear systems from single trajectory.
problem Identifying linear dynamical systems from a single observed trajectory.
method Generalized small-ball method for dependent data, avoiding mixing-time arguments.
result OLS estimator nearly matches minimax optimal performance for linear systems.
Develops algorithms for sparse signal reconstruction without needing signal sparsity or noise variance.
problem Sparse signal reconstruction challenges due to unknown signal sparsity and noise variance.
method TF-IGP and RRT-IGP frameworks for OMP and OLS without prior knowledge of k0 and σ2. result TF-IGP and RRT-IGP achieve successful sparse recovery under restricted isometry conditions.
A fast feature selection method using OLS and SOCC for classification.
problem Feature selection for linear classification.
method Orthogonal Least Squares (OLS) with Squared Orthogonal Correlation Coefficient (SOCC).
result The proposed method outperforms other feature selection methods in speed and accuracy.
OLS recovers sparse signals from noisy measurements with high probability.
problem Recovering sparse signals from noisy linear measurements.
method Orthogonal Least-Squares (OLS) algorithm under noisy conditions.
result OLS recovers true support in k iterations with high probability under certain conditions. The OLS estimator optimally identifies stable linear systems with a finite number of samples.
problem Identifying stable linear systems with a finite number of samples.
method Finite-time analysis of the Ordinary Least Squares (OLS) estimator for stable linear systems.
result The OLS estimator achieves optimal sample complexity for stable systems, matching existing lower bounds up to universal factors.
Estimates time-varying parameters from two OLS estimates.
problem Time-varying linear regression with hidden dynamics.
method Combines two OLS estimates for stable linear dynamics.
result Finite sample guarantee on estimation error.
This paper analyzes how BN affects GD convergence and stability.
problem The effect of batch normalization on gradient descent convergence and stability.
method Quantitative analysis of gradient descent with and without batch normalization on ordinary least squares.
result Gradient descent with batch normalization converges for arbitrary learning rates and remains linear under mild conditions.
This study examines the relationship between PLS and OLS regression using eigenvalue distributions.
problem Analyzing the difference between PLS and OLS regression in terms of eigenvalue distributions.
method Examined the distance between PLS and OLS regression coefficients using the Mahalanobis distance and eigenvalue distributions of the regressor covariance matrix.
result Provided a bound on the distance between PLS and OLS regression coefficients that depends only on the eigenvalue distribution of the regressor covariance matrix.
OLS predictions are shown to be similar to attention mechanisms in models.
problem OLS in traditional statistics and econometrics.
method Rewriting OLS as an attention mechanism in a transformed space.
result OLS can be understood as minimizing squared prediction errors via optimal embedding and decoding.
Every 4-dimensional infrasolvmanifold M with β1(M;Q)>0 or which is flat or has one of the geometries Nil4, Solm,n4, or Sol04 bounds. However there are non-orientable Sol14-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=β1(M;Q)≥2 or M is a Sol04- or a Solm,n4-manifold (with m=n) then M is parallelizable. There are non-parallelizable examples with β=1 for each of the other solvable Lie geometries $\ma…
Develops methods for reliable inference on batched bandit data.
problem Need for reliable inference methods based on adaptively-collected data from bandit algorithms.
method Introduces Batched OLS (BOLS) estimator for reliable inference on bandit data.
result BOLS is asymptotically normal and robust to non-stationarity in the baseline reward.
Polynomial Chaos Expansion improves operator learning for PDEs.
problem Approximating mappings between infinite-dimensional functional spaces.
method Polynomial Chaos Expansion (PCE) for operator learning.
result PCE achieves strong performance in operator learning and uncertainty quantification.
We show that Sol3×E1-manifolds are Seifert fibred, with general fibre the torus, and base one of the seven flat 2-orbifolds T,Kb,A,Mb,S(2,2,2,2),P(2,2) or D(2,2), and outline a classification of such 4-manifolds.
PCA-based dimensionality reduction improves robustness in overparameterized linear models.
problem Improving robustness in overparameterized linear models.
method PCA-based dimensionality reduction (PCA-OLS)
result PCA-OLS can achieve better generalization than ordinary least squares (OLS) in the overparameterized regime.
This paper investigates the hedging effectiveness of a dynamic moving window OLS hedging model, formed using wavelet decomposed time-series. The wavelet transform is applied to calculate the appropriate dynamic minimum-variance hedge ratio for various hedging horizons for a number of assets. The effectiveness of the dy…
Unified framework for online learning in click prediction for search ads.
problem Model staleness leading to accuracy and calibration degradation over time.
method Two paradigms of Batch Online Learning: early stopping and proximal regularization.
result Two OL schemes are closely related and can be traded-off between new and historical data.
Lower bounds show OLS outperforms basis pursuit in overparameterized linear regression.
problem Excess risk of sparse interpolating procedures in overparameterized linear regression.
method Proved lower bounds on excess risk for OLS and basis pursuit.
result Excess risk of basis pursuit can converge at an exponentially slower rate than OLS.
The paper analyzes risks and revenue dynamics of a liquid restaking protocol in decentralized finance.
problem Interconnected risks and revenue dynamics of a liquid restaking protocol in decentralized finance.
method Empirical analysis using OLS regression, Granger-causality, and random forest feature importance tests.
result Revenue is primarily driven by value locked in the ecosystem, yield of liquid restaking token, and multi-blockchain expansion.
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.
problem Differentially private linear regression with improved accuracy and efficiency.
method Iterative Hessian Mixing (IHM) for differentially private ordinary least squares (DP-OLS).
result IHM provides better utility guarantees and outperforms AdaSSP in empirical evaluations.
New bounds show current methods overestimate system parameter errors.
problem Current bounds overestimate parameter errors in system identification.
method Utilized asymptotic normality and second-order decomposition.
result Obtained finite-sample bounds matching optimal rates up to constants.
New algorithm selects variables from large datasets.
problem Automatic selection of variables from large datasets.
method Uses Graphical Models and combines with OLS method.
result Outperforms LASSO method in forecasting models.
Transformers learn a mesa-optimizer to implement in-context learning.
problem Understanding the convergence of autoregressive training to a mesa-optimizer.
method Investigated a one-layer linear causal self-attention model autoregressively trained by gradient flow.
result Proved that autoregressive training converges to a gradient descent step for an OLS problem, validating the mesa-optimizer hypothesis.
The paper tackles system identification via Hankel nuclear norm regularization, improving estimation rates and singular value gaps.
problem Identifying low-order linear systems from limited data.
method Hankel nuclear norm regularization to encourage low-rankness of the Hankel matrix.
result Hankel regularization enables optimal system recovery with fewer observations and better estimation rates.
OLS is a special case of Transformer, revealing its linear nature.
problem Understanding the statistical essence of Transformer architecture.
method Algebraic proof and spectral decomposition of covariance matrix.
result Attention mechanism in Transformers is mathematically equivalent to OLS.
We compare the random group model of Gromov and the model of generic groups of Arzhantseva and Ol'shanskii.
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…
Enhanced LSTM predicts equity trends, outperforming traditional methods.
problem Nonstationary and nonlinear market regimes challenge trend forecasting.
method LSTM-based framework for forecasting equity trend differences.
result LSTM framework outperforms traditional methods in terms of overall PNL.
Proposes a new test for validating multivariate dynamic regression models.
problem Inadequate exogeneity conditions for conventional model specification tests in dynamic systems.
method Develops a generalized Durbin estimator for multiple-equation systems with dynamic dependencies, and constructs Wald tests.
result Bootstrap-based Wald tests improve finite-sample size control and validate the null hypothesis in multifactor models.
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.
problem Stability of SEM findings under alternative estimation frameworks.
method Staged robustness analysis framework connecting SEM, OLS, and DML.
result Identifies stable and unstable relationships across SEM, OLS, and DML checks.
This work develops fast and accurate ROMs for AM models using OL methods.
problem Achieving specific material properties in AM by manipulating process parameters increases computational load.
method Operator learning (OL) approach with Fourier neural operator (FNO) and DeepONet.
result OL methods offer comparable performance and outperform DNN in accuracy and generalizability.
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…
New EiV models correct bias in operator learning with noisy data.
problem Bias in operator learning due to noisy independent variables.
method Developed EiV models for MOR-Physics and DeepONet.
result EiV models reduce bias in noisy operator learning.
Let f:Mm⟶Rm+k be an immersion where M is a smooth connected m-dimensional manifold without boundary. Then we construct a subspace Ω(f) of Rk, namely push-out space. which corresponds to a set of embedded manifolds which are either parallel to f, tubes around f or, in…
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.
problem High-dimensional regression with ICD-10 codes leads to unstable coefficient estimates.
method Log-linear analytics approach to cost model regularization through diagnostic code merging.
result Reducing ICD-10 code granularity from 7 characters to 6 or fewer improves model interpretability and consistency.
This work develops a fast-running ROM for MOOSE-based AM model using OL.
problem Achieving desired material properties in real-time manufacturing processes.
method Operator learning (OL) and Fourier neural operator for ROM development.
result OL-based ROM outperforms conventional deep neural network-based ROM in benchmark tests.
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…
Derives optimal dynamic trading strategies under Gaussian assumptions.
problem Understanding and optimizing dynamic trading strategies in finance.
method Assumes Gaussian returns and dynamic weights, derives closed-form expressions for strategy returns moments.
result Positive skewness and excess kurtosis are essential for positive Sharpe dynamic strategies.
We compute the rings H∗(N;F2) for N a closed Sol3-manifold and then determine the Borsuk-Ulam indices BU(N,φ) with φ=0 in H1(N;F2).
A new algorithm selects features efficiently for sparse linear regression.
problem Finding sparse solutions to underdetermined linear systems.
method Generalized Orthogonal Least-Squares (OLS) algorithm.
result The generalized OLS algorithm outperforms existing methods in efficiency and performance.
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…
Improves regression models' performance on covariate shift.
problem Out-of-distribution generalization for regression.
method Spectrally adapting the weights of a pre-trained neural regression model.
result Spectral adaptation improves out-of-distribution performance.