A first-order model for a stock market assigns to each stock a return parameter and a variance parameter that depend only on the rank of the stock. A second-order model assigns these parameters based on both the rank and the name of the stock. First- and second-order models exhibit stability properties that make them a…
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48 results for “order parameter”
New method tackles catastrophic forgetting and order-sensitivity in continual learning.
problem Catastrophic forgetting and order-sensitivity in continual learning.
method Additive Parameter Decomposition (APD) to represent task parameters as a sum of shared and adaptive parts.
result Significantly outperforms state-of-the-art methods in accuracy, scalability, and order-robustness.
This paper solves parameter estimation with ordered regularization using ADMM.
problem Scaling up ordered regularization for large-scale data.
method Alternating Direction Method of Multipliers (ADMM) for ordered regularization.
result ADMM-O outperforms or matches state-of-the-art methods in parameter estimation.
Proposes a method to measure model parameter similarity for visual tasks.
problem Estimating relations between different visual tasks.
method LPS method using a second-order neural network to align model parameters and learn second-order similarity.
result Extensive experiments validate the effectiveness of the proposed method.
Proves limitations of higher-order optimization for convex problems.
problem Limitations of higher-order optimization methods for convex problems.
method Proves polynomial dependence on approximation guarantee and higher-order smoothness parameters.
result Nesterov's accelerated cubic regularization method is nearly tight.
Gaffke's bound is optimal for a specific parameter ordering in independent random vectors.
problem Finding optimal lower confidence bounds for a scalar parameter in independent random vectors.
method Revisiting classical work on lower confidence bounds, specializing to independent components, and proving optimality with respect to a specific parameter ordering.
result Gaffke's bound is Buehler optimal for the maximum marginal mean parameter.
A hybrid model reduces graph complexity for improved classification accuracy.
problem High computational complexity and large number of parameters in higher-order graph convolutional networks.
method Weight sharing mechanism and novel fusion pooling layer to reduce parameters and complexity.
result The proposed model achieves highest classification accuracy with fewer trainable parameters.
Artificial neural networks infer gravitational-wave parameters from reduced-order waveforms.
problem Efficiently infer gravitational-wave parameters from noisy data.
method Represent waveforms as weighted sums over reduced bases, train neural networks to map source parameters to coefficients.
result Fast and accurate interpolation of gravitational-wave coefficients.
Bayesian classification and regression with high order interactions is largely infeasible because Markov chain Monte Carlo (MCMC) would need to be applied with a great many parameters, whose number increases rapidly with the order. In this paper we show how to make it feasible by effectively reducing the number of para…
This Ph.D. thesis is devoted to the constructions of Lagrangian formulation on Finsler and Kawaguchi manifolds. While Finsler geometry is a natural extension of Riemannian geometry, Kawaguchi geometry is the extension of Finsler geometry to higher order derivatives and to k-dimensional parameter space. The latter exten…
RHOMP improves prediction accuracy for user trails.
problem Predicting user actions in web browsing and geolocation.
method Retrospective higher-order Markov process (RHOMP) for sequences of data.
result RHOMP outperforms higher-order Markov chains and other methods in prediction accuracy.
New method identifies structural parameters without assuming uncorrelated errors.
problem Identifying structural parameters in simultaneous equation models.
method Exploits higher-order cumulant restrictions, not requiring uncorrelated errors.
result Simple diagonality condition on th-order cumulants identifies structural parameter matrix.
We consider the problem of stochastic comparison of general Garch-like processes, for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the Garch process itself, and discuss their interpretations. We focus on the convex…
This paper proposes a new method to adapt ROMs for new parameter settings.
problem ROMs lack robustness when applied to new parameter settings.
method Regression trees on Grassmann Manifold to learn the mapping between parameters and POD bases.
result The proposed method is capable of establishing the mapping between parameters and POD bases, thus adapting ROMs for new parameters.
Paper introduces Bayesian EEF for model order selection using exponentially embedded family.
problem Model order selection in Bayesian statistics.
method Bayesian EEF method using exponentially embedded family.
result Bayesian EEF can use vague priors and reveals EEF mechanism for model selection.
We define a stochastic model of a two-sided limit order book in terms of its key quantities \textit{best bid [ask] price} and the \textit{standing buy [sell] volume density}. For a simple scaling of the discreteness parameters, that keeps the expected volume rate over the considered price interval invariant, we prove a…
Probing hidden spin order with interpretable machine learningcond-mat.stat-mech
Machine learning identifies hidden spin nematics in magnetic configurations.
problem Challenging identification of unconventional magnetic states.
method Interpretable machine learning protocol for detecting nematic order.
result Extracted analytical forms of nematic order parameters up to rank 6.
Method estimates parameters for disease spread models robustly.
problem Estimating parameters for disease spread models.
method Statistical Learning applied to Approximate Bayesian Computation.
result Qualitative properties of disease evolution can be assessed.
Parametric model reduction of mean-field and stochastic systems via higher-order action matchingstat.ML
This work learns models for population dynamics using variational methods and higher-order quadrature.
problem Modeling population dynamics of physical systems with stochastic and mean-field effects.
method Variational problem to infer gradient fields, combining Monte Carlo sampling with higher-order quadrature rules.
result Accurate prediction of population dynamics over a wide range of parameters.
Improves machine learning consistency with orthogonal moment equations.
problem Improving consistency of machine learning estimates with complex nuisance parameters.
method Employing Neyman-orthogonal moment equations to improve consistency from to .
result Second-order orthogonality can improve consistency to .
Study properties of self-similar continua with finite intersection property.
problem Characterize self-similar continua with finite intersection property.
method Prove intersection graph criterion, finite order theorem, and parameter matching theorem.
result All Jordan arcs starting from a intersection point in such continuum on a plane should have the same slope parameter at that point.
Impact Study of Numerical Discretization Accuracy on Parameter Reconstructions and Model Parameter Distributionsphysics.comp-ph
Study shows how numerical discretization affects reconstructions and parameter distributions in nano metrology.
problem Impact of numerical discretization on parameter reconstructions and model parameter distributions.
method Bayesian target vector optimization, finite element model, Gaussian process, stochastic machine learning surrogate models, Markov chain Monte Carlo sampler.
result Numerical discretization parameters impact the accuracy and distribution of reconstructed model parameters.
The short-time asymptotic behavior of option prices for a variety of models with jumps has received much attention in recent years. In the present work, a novel second-order approximation for ATM option prices under the CGMY Lévy model is derived, and then extended to a model with an additional independent Brownian com…
Extends knotted defect classification to bounded domains using handlebodies.
problem Classifying knotted defects in bounded domains.
method Using continuous maps and monodromies around meridional loops, global defects are described in terms of planar diagrams.
result Classification scheme for defects in handlebodies.
Estimating the Number of Components in Finite Mixture Models via the Group-Sort-Fuse Procedurestat.ME
New method estimates mixture model components efficiently.
problem Estimating the number of components in finite mixture models.
method Group-Sort-Fuse (GSF) procedure for simultaneous estimation of order and mixing measure.
result GSF achieves consistent estimation of true mixture order and convergence rate.
Privacy utility trade offs for parameter estimation in degree heterogeneous higher order networksstat.ML
Study privacy vs. utility in estimating network parameters with aggregated data.
problem Privacy-preserving estimation of network parameters from aggregated node degrees.
method β model, local and central differential privacy, minimax lower bounds, simple estimators.
result Achieved minimax-optimal risk bounds for parameter estimation under privacy constraints.
We describe a bottom-up framework, based on the identification of appropriate order parameters and determination of phase diagrams, for understanding progressively refined agent-based models and simulations of financial markets. We illustrate this framework by starting with a deterministic toy model, whereby indepe…
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.
Synthesis parameter effect detection using quantitative representations and high dimensional distribution distancescond-mat.mtrl-sci
Method detects effects of synthesis parameters on plutonium oxide microstructure.
problem Detecting effects of synthesis parameters on material microstructure.
method Copula theory, high dimensional distribution distances, and permutational statistics.
result Effects of strike order and oxalic acid feed on plutonium oxide microstructure detected.
New MOSC clusters networks by considering both second- and third-order structures.
problem Limited consideration of higher-order structures in spectral clustering.
method Mixed-Order Spectral Clustering (MOSC) combining GL and RW for second- and third-order structures.
result MOSC outperforms existing SC methods on real-world networks.
Order patterns, their variation and change points in financial time series and Brownian motionq-fin.ST
Study of financial time series and Brownian motion using order patterns and permutation entropy.
problem Analyzing order patterns and variation in financial time series and Brownian motion.
method Use of order patterns and permutation entropy to study financial data and Brownian motion, focusing on turning rate and up-down balance.
result For small lags, pattern frequencies in financial data remain constant. Up-down balance is better for change points in financial data.
New quantum states capture more information, enabling advanced processing tasks.
problem Quantum information processing challenges with limited statistical information.
method Introducing Random-Coefficient Pure States (RCPS) and exploiting their higher-order statistics.
result RCPS provide richer information than density operators, enabling new quantum tasks.
Bias-Variance Trade-Off in Hierarchical Probabilistic Models Using Higher-Order Feature Interactionsstat.ML
Study on bias-variance trade-off in hierarchical models with higher-order interactions.
problem Understanding the bias-variance trade-off in hierarchical probabilistic models with higher-order interactions.
method Proposed an efficient inference algorithm using Gibbs sampling and annealed importance sampling for log-linear higher-order Boltzmann machine.
result Higher-order interactions produce less variance for smaller sample size and comparable error with hidden layers.
Develops unbiased averaging methods for second order optimization in distributed systems.
problem Computing the Hessian is challenging and communication is a bottleneck in distributed optimization.
method Unbiased parameter averaging methods using sampling and sketching of the Hessian.
result Provably minimizes bias for sketched Newton directions.
Power-law model outperforms logarithmic model in estimating stock and warrant price impacts.
problem Estimating immediate price impacts of stock and warrant orders.
method Used order flow data to estimate price impacts using power-law and logarithmic models.
result Power-law model outperforms logarithmic model in robustness and forecasting accuracy.
New model captures long-term memory effects in epidemic dynamics.
problem Identifying memory effects in disease progression and recovery.
method Physics-informed neural networks (PINN) with fractional SEIRD model.
result Fractional memory order improves predictive performance over classical models.
An agent-based model for financial markets has to incorporate two aspects: decision making and price formation. We introduce a simple decision model and consider its implications in two different pricing schemes. First, we study its parameter dependence within a supply-demand balance setting. We find realistic behavior…
Proposes a new method for estimating non-pathwise differentiable functional parameters.
problem Estimating dose-response curves for continuous exposure.
method Targeted Highly Adaptive Lasso (HAL) for non-pathwise differentiable functional parameters.
result The Targeted HAL-MLE achieves dimension-free rates up to log(n) factors and outperforms other methods in simulations.
CDF2PDF improves SIC for high-dimensional data estimation.
problem Estimating PDF from CDF in high-dimensional data.
method CDF2PDF approximates PDF by approximating CDF, avoiding hyper-parameter tuning and enabling polynomial time higher order derivative computation.
result CDF2PDF shows promising results in one-dimensional data experiments.
We study first order local invariants of Vassiliev type for Lagrangian immersions with generic planar caustics. For this we produce some examples of 2-parameter families of Lagrangian maps and study their bifurcation diagrams.
New analysis shows black-box methods outperform action space methods in certain scenarios.
problem Comparing black-box methods vs. action space methods in exploration.
method Theoretical analyses and empirical comparisons of simple methods on various problems.
result Complexity of exploration in parameter space depends on parameter space dimensionality, while action space complexity depends on both action space and horizon length.
A new algorithm solves minimax problems without needing parameters.
problem Convex-concave minimax optimization problems in machine learning.
method Proposes a fully parameter-free LF-CR and FF-CR algorithms for solving these problems.
result The FF-CR algorithm achieves the best iteration complexity under gradient norm termination criterion.
We identify Melrose's suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space . For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone , we construct a uniq…
Hyperbolic 2-spheres with conical singularities, accessory parameters and Kaehler metrics on math.CV
We show that the real-valued function on the moduli space of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic 2-sphere with conical singularities of arbitrary orders , generates accessory parameters of the as…
Cayley's surface revisitedmath.DG
Cayley's (ruled cubic) surface carries a three-parameter family of twisted cubics. We describe the contact of higher order and the dual contact of higher order for these curves and show that there are three exceptional cases.
A parameter-invariant variational problem with a manifestly covariant Lagrangian function of second order is considered, which covers the case of the free relativistic top at constraint manifold of constant acceleration
GE-autoencoder identifies spontaneous symmetry breaking in systems.
problem Locating phase boundaries and identifying spontaneously broken symmetries in systems.
method Group-equivariant autoencoder using group theory to constrain parameters and learn invariant order parameters.
result GE-autoencoder accurately determines spontaneous symmetry breaking and estimates critical temperatures more efficiently.
For loop groups (free and based), we compute the exact order of the curvature operator of the Levi-Civita connection depending on a Sobolev space parameter. This extends results of Freed and Maeda-Rosenberg-Torres.