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.
Study differential properties of matrix square roots in specific cases.
Efficiently computes matrix square roots and their inverses for large matrices.
Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to compute the inverse or inverse square root of a matrix whose size is quadratic of …
Paper develops efficient AltMin algorithm for SRPCP robust matrix recovery.
Covariance pooling is a feature pooling method with good classification accuracy. Because covariance features consist of second-order statistics, the scale of the feature elements are varied. Therefore, normalizing covariance features using a matrix square root affects the performance improvement. When pooling methods …
New method differentiates square-root Kalman filters robustly.
This paper proposes the recursive and square-root BLS algorithms to improve the original BLS for new added inputs, which utilize the inverse and inverse Cholesky factor of the Hermitian matrix in the ridge inverse, respectively, to update the ridge solution. The recursive BLS updates the inverse by the matrix inversion…
We consider the problem of learning in Linear Quadratic Control systems whose transition parameters are initially unknown. Recent results in this setting have demonstrated efficient learning algorithms with regret growing with the square root of the number of decision steps. We present new efficient algorithms that ach…
Optimal data splitting improves covariance matrix estimation in large datasets.
New method for NMF without tuning parameter.
A new method simulates square-root processes efficiently.
We study -GenEV, the problem of finding the top generalized eigenvectors, and -CCA, the problem of finding the top vectors in canonical-correlation analysis. We propose algorithms and to solve the two problems with running times linearly dependent on the input size and…
Layer normalization (LayerNorm) has been successfully applied to various deep neural networks to help stabilize training and boost model convergence because of its capability in handling re-centering and re-scaling of both inputs and weight matrix. However, the computational overhead introduced by LayerNorm makes these…
EPMF factorizes matrices by adjusting their entries to match a specified power.
Guarantees uniform convergence for square-root Lipschitz losses.
We study the stability vis a vis adversarial noise of matrix factorization algorithm for matrix completion. In particular, our results include: (I) we bound the gap between the solution matrix of the factorization method and the ground truth in terms of root mean square error; (II) we treat the matrix factorization as …
Study finds price impact follows a 'double' square-root law, suggesting mechanical origin.
Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how to modify full-matrix adaptive regularization in order to make it practical and e…
Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan, Hebiri and Lederer (2017). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularize…
We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models [Yang et al. 2015] did not allow positive dependencies for the exponential and Poisson generalizat…
Root Laplacian Eigenmaps help in spectral embedding of graphs.
A new method solves large-scale sparse group square-root Lasso problems efficiently.
Alpha-based performance evaluation may fail to capture correlated residuals due to model errors. This paper proposes using the Generalized Information Ratio (GIR) to measure performance under misspecified benchmarks. Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is deriv…
New bounds for private matrix approximation using Gaussian noise and Dyson Brownian Motion.
Square-root natural-gradient improves variational inference convergence.
New insights into learning rates and batch sizes for neural networks using random matrix theory.
Many independent studies on stocks and futures contracts have established that market impact is proportional to the square-root of the executed volume. Is market impact quantitatively similar for option markets as well? In order to answer this question, we have analyzed the impact of a large proprietary data set of opt…
The notion of market impact is subtle and sometimes misinterpreted. Here we argue that impact should not be misconstrued as volatility. In particular, the so-called ``square-root impact law'', which states that impact grows as the square-root of traded volume, has nothing to do with price diffusion, i.e. that typical p…
The Volterra square-root process shows non-uniqueness of limiting distributions and regularity of its law.
Method detects lithium-ion battery knee onset for early warning.
In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling probabilities. The sampling dependent error bound (i) allows us to better understand the …
New CRB derived for curved models using extrinsic geometry.
New analysis of Muon and SignSGD on matrix-valued least squares problems.
The study confirms that market volatility can be explained by correlated metaorders impacting prices in a square-root fashion.
We apply an asymmetric version of Kirman's herding model to volatile financial markets. In the relation between returns and agent concentration we use the square root law proposed by Zhang. This can be derived by extending the idea of a critical mean field theory suggested by Plerou et al. We show that this model is eq…
Solves non-Abelian Rainich problem for SU(2) gauge fields.
New method efficiently learns positive-definite curvature for neural nets.
Efficient optimization method reduces Full AdaGrad complexity.
Revisiting Trade-sign Long-memory and Square-root Law price impact
We confirm the square-root law of market impact on Apple Inc. using a large dataset.
Agent-based market shows herding cycles with square-root price impact.
New algorithms reduce contextual bandits' regret without knowing reward noise variances.
Paper improves efficiency in matrix computations for Gaussian processes.
The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In this paper we study analytical and topological aspects of this construction for …
Paper connects surface shape analysis and unbalanced optimal transport.
We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation f…
Novel approach integrates Multivariate Square-root Lasso into Synthetic Control for high-dimensional data.
This thesis examines the accuracy of scaling VaR estimates for longer holding periods.