Study minimax regret in sequential probability assignment with and without side information.
problem Minimax regret analysis in sequential probability assignment.
method Upper and lower bounds on minimax regret using square-root entropy.
result Lower bound matches upper bound for Donsker classes, up to log factors.
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…
Gradient flow expands curves to round shapes.
problem Expanding curves to round shapes.
method Steepest descent L2-gradient flow of entropy.
result Flow converges to a round expanding circle for various initial curves.
Thanks to a recent result by Jean-Marc Schlenker, we establish an explicit linear inequality between the normalized entropies of pseudo-Anosov automorphisms and the hyperbolic volumes of their mapping tori. As its corollaries, we give an improved lower bound for values of entropies of pseudo-Anosovs on a surface with f…
Agent-based market shows herding cycles with square-root price impact.
problem Understanding herding cycles in agent-based markets.
method Agent-based model with 20,000 retail traders interacting with a single institutional agent.
result Agent discovers multi-cycle predatory strategy with 8-11 complete cycles over 2000 trading days.
Study differential properties of matrix square roots in specific cases.
problem Understanding matrix square roots in semi-simple, symmetric, and orthogonal cases.
method Analysis of differential and metric structures of real square roots of matrices under specific conditions.
result Differential properties of matrix square roots in semi-simple, symmetric, and orthogonal cases.
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
Guarantees uniform convergence for square-root Lipschitz losses.
problem Uniform convergence guarantees for square-root Lipschitz losses.
method Using Rademacher complexity and square root of scalar loss function Lipschitz constant.
result Generalizes previous results and handles non-smooth loss functions.
Adapting Hedge algorithm for semi-adversarial data with root-entropy regularization.
problem Minimizing regret in prediction with expert advice under varying distributions.
method Follow-the-Regularized-Leader (FTRL) with root-entropy regularization.
result Adaptive minimax optimal regret across all levels of constraint sets.
Study finds price impact follows a 'double' square-root law, suggesting mechanical origin.
problem Understanding the origin of price impact in markets.
method Detailed dataset of Tokyo Stock Exchange orders, analyzing single and metaorders.
result Price impact follows a 'double' square-root law, indicating mechanical origin rather than information.
A new method solves large-scale sparse group square-root Lasso problems efficiently.
problem Large-scale linearly constrained sparse group square-root Lasso problems.
method Dual semismooth Newton based augmented Lagrangian method (ALM).
result The proposed method efficiently solves the problem with numerical experiments demonstrating its effectiveness.
Square-root natural-gradient improves variational inference convergence.
problem Challenges in establishing theoretical convergence guarantees for natural-gradient descent.
method Square-root parameterization for Gaussian covariance.
result Establishes novel convergence guarantees for natural-gradient Gaussian inference.
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.
problem Non-uniqueness of limiting distributions in the Volterra square-root process.
method Establishing existence of limiting distributions using integrability of the Volterra convolution kernel and exponential-affine transformation.
result The limiting distributions of the Volterra square-root process depend on the initial state and belong to weighted Besov spaces.
The paper studies entropy of harmonic metrics on cyclic Higgs bundles.
problem Quantifying the degree of mutual misalignment of Hermitian metrics.
method Introduces entropy function and estimates its bounds for cyclic Higgs bundles.
result Entropy difference converges to a finite real number for β>−1. The study confirms that market volatility can be explained by correlated metaorders impacting prices in a square-root fashion.
problem Explaining market volatility using metaorders and their impact.
method Generated synthetic market data and analyzed the correlation between order flow and returns.
result The square-root law of market impact is confirmed and can be measured from anonymized trade data.
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…
Linear-Core Surrogates combine fast optimization and statistical efficiency in classification and structured prediction.
problem The trade-off between smoothness and margin-based losses in classification and structured prediction.
method Linear-Core (LC) Surrogates, a family of convex loss functions that stitch a linear core to a smooth tail.
result LC Surrogates achieve fast linear consistency rates while maintaining differentiability and strict H-consistency bounds. Solves non-Abelian Rainich problem for SU(2) gauge fields.
problem Existence of local SU(2) Yang-Mills fields with prescribed stress-energy tensor.
method Canonically identifying tensors with Hermitian forms and defining internal square roots of stress-energy tensors.
result Existence of local SU(2) Yang-Mills field is equivalent to a single differential condition on internal square roots of stress-energy tensor.
The paper studies entropy and free energy for harmonic metrics on cyclic Higgs bundles.
problem Quantifying the degree of mutual misalignment of metrics on Higgs bundles.
method Introduced entropy and free energy to quantify mutual misalignment; provided conditions for entropy and free energy to change.
result Extended work on boundedness of functions related to entropy and free energy on the unit disc.
In this paper we apply a compressibility loss that enables learning highly compressible neural network weights. The loss was previously proposed as a measure of negated sparsity of a signal, yet in this paper we show that minimizing this loss also enforces the non-zero parts of the signal to have very low entropy, thus…
Revisiting Trade-sign Long-memory and Square-root Law price impact
problem Revisiting the Lillo-Mike-Farmer (LMF) theory and the square-root law (SQRL) of meta-order impact
method Using a coupled discrete reaction-diffusion formulation
result Long-memory of trade signs and square-root law of meta-order impact
We confirm the square-root law of market impact on Apple Inc. using a large dataset.
problem Testing the square-root law of market impact on a single U.S. large-cap equity.
method Using a full market-by-order feed, we reconstruct metaorders and calibrate impact using the square-root formula.
result The square-root law is confirmed with a prefactor of 0.34, consistent with worldwide data.
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 …
Efficiently computes matrix square roots and their inverses for large matrices.
problem Computing matrix square roots and inverses for large matrices efficiently.
method Combines Krylov subspace methods with rational approximation for quadratic-time computation.
result Achieves 4 decimal places of accuracy with fewer than 100 matrix-vector multiplications.
Paper connects surface shape analysis and unbalanced optimal transport.
problem Computing the SRNF shape distance on piecewise linear surfaces.
method Characterizes SRNF shape distance as WFR distance pullback, proposes new algorithm for WFR distance computation.
result Direct computation of SRNF shape distance on piecewise linear surfaces.
Novel approach integrates Multivariate Square-root Lasso into Synthetic Control for high-dimensional data.
problem Challenges in practical implementation and computational efficiency of Synthetic Control method for high-dimensional disaggregated data.
method Integrates Multivariate Square-root Lasso into Synthetic Control framework.
result Demonstrates superior computational efficiency without compromising estimation accuracy.
This thesis examines the accuracy of scaling VaR estimates for longer holding periods.
problem The accuracy of VaR estimates for longer holding periods using the square root of time rule.
method Examined VaR scaling for longer holding periods using empirical analysis.
result Scaling can provide good estimates of VaR but may lead to significant losses over time.
TPSQRs model longitudinal event data, detecting ADRs from EHRs.
problem Detecting adverse drug reactions from longitudinal event data.
method Learned by estimating a collection of interrelated PSQRs, using Poisson pseudo-likelihood for estimation.
result TPSQRs effectively and efficiently recover ADR signals from EHRs.
This paper explains how predictable order flow can lead to Brownian motion in financial prices.
problem Why financial prices exhibit Brownian motion despite predictable order flow.
method Generalized Lillo-Mike-Farmer model to nonlinear price-impact dynamics, mapping to Lévy-walk model.
result Price dynamics remain diffusive under the square-root law, even with persistent order flow.
Improved survival analysis using square root Cox's models and neural networks.
problem Feature selection in survival analysis.
method Square root Cox's survival analysis by the fittest linear and neural networks model, directly tuning penalty parameter λ.
result Substantially improved over traditional methods, achieving phase transition in feature selection.
The paper establishes a uniform Lipschitz bound on the square root of the systole function in Teichmüller space.
problem Uniform Lipschitz bounds on geometric functions in Teichmüller space.
method Injectivity radius analysis and Lipschitz bounds on systole function.
result Uniform Lipschitz constant for the square root of the systole function on Teichmüller space.
In this paper, we prove that on any contact manifold, there exists an arbitrary C^{\infty}-small contactomorphism which does not admit a square root. In particular, there exists an arbitrary C^{\infty}-small contactomorphism which is not "autonomous". This result is the first step to study the topology of non-autonomou…
The chapter reviews metrics for comparing curves, focusing on quotient elastic and square root velocity metrics.
problem Comparing and analyzing shapes of curves.
method Construction and theoretical properties of quotient elastic metrics, special case of square root velocity metric, numerical approaches for estimation.
result Simplified expression for the square root velocity metric distance.
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 …
Root Laplacian Eigenmaps help in spectral embedding of graphs.
problem Efficient spectral embedding of graphs.
method Square root of graph-Laplacian operator.
result Improved spectral embedding techniques.
We study two--generated subgroups ⟨f,g⟩<Homeo+(I) such that ⟨f2,g2⟩ is isomorphic to Thompson's group F, and such that the supports of f and g form a chain of two intervals. We show that this class contains uncountably many isomorphism types. These include examples with n…
New method differentiates square-root Kalman filters robustly.
problem Gradient calculation issues in square-root Kalman filters.
method Closed-form chain rule derived from Gramian identity, resolves non-orthogonal and rank-deficient issues.
result Robust automatic differentiation for Kalman filters, resolving numerical stability and gradient issues.
We develop an efficient method to calibrate CDS spreads using asymptotic approximations.
problem Calibrating CDS spreads in the SSRD model with correlated processes.
method Asymptotic coefficient expansion to approximate solutions of nonlinear PDEs.
result Our approximation does not require uncorrelated interest rate and default intensity processes.
Paper develops efficient AltMin algorithm for SRPCP robust matrix recovery.
problem SRPCP model robust matrix recovery with universal penalty parameter.
method Tuning-free alternating minimization (AltMin) algorithm with closed-form subproblems.
result Efficient AltMin algorithm confirms robustness and efficiency.
Algorithm generates realistic metaorders from public trade data.
problem Generating realistic metaorders from public data.
method Novel algorithm that recovers stylized facts of metaorders impact.
result Average realized short-term price impact has a mechanical origin.
We generalize the reaction-diffusion model A + B -> 0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that linear response breaks down: the average displacement of the reaction front grows as the square-root of the imbalance. We argue t…
New algorithms reduce contextual bandits' regret without knowing reward noise variances.
problem Reducing regret in contextual bandits with unknown reward noise variances.
method Developed new algorithms based on the optimism principle.
result Regret scales as the square root of the sum of measurement variances, not the time horizon.
We show the existence of a smooth solution for the flow deformed by the square root of the scalar curvature multiplied by a positive anisotropic factor ψ given a strictly convex initial hypersurface in Euclidean space suitably pinched. We also prove the convergence of rescaled surfaces to a smooth limit manifold whic…
Improves probability distribution compression with KT algorithm.
problem Efficiently compressing probability distributions.
method Kernel thinning (KT) algorithm with four improvements.
result KT yields tighter, dimension-free guarantees for any kernel.
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 …
Volterra square-root process boundary behavior and martingale measures
problem Boundary behavior of the Volterra square-root process
method Comparison principles for Volterra integral equations and generalized Riemann-Liouville fractional equations
result Finiteness of negative p-moments and atom at the boundary for rough kernels