We consider the problem of estimating , where denotes a random vector with uniformly distributed marginals. In general, Latin hypercube sampling (LHS) is a powerful tool for solving this kind of high-dimensional numerical integration problem. In the case of depende…
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48 results for “Latin Hypercube Sampling”
A new sampling strategy improves reliability and robustness optimization for complex designs.
problem High sample requirements for optimizing reliability and robustness in complex designs.
method Local Latin Hypercube Refinement (LoLHR) for multi-objective design uncertainty optimization.
result LoLHR achieves better results compared to other surrogate-based strategies.
This paper studies convergence of risk aggregation methods using empirical margins and copulas.
problem Convergence of risk aggregation distributions in multivariate models.
method Empirical margins, Latin Hypercube Sampling, and convergence of sum distributions.
result Strong uniform consistency of estimated sum distribution function with convergence rate .
Improves ICA via novel mutual dependence measures.
problem Improving Independent Component Analysis (ICA) for better component independence.
method Combines distance-based and kernel-based mutual dependence measures, introduces Latin hypercube sampling and Bayesian optimization for initialization.
result MDMICA outperforms other methods in terms of mutual independence of estimated components, especially when the ICA model is misspecified.
Sampling strategies significantly affect feature approximations in ELA, impacting classifier accuracy.
problem The impact of sampling strategies on feature approximations in ELA.
method Analysis of feature approximations from different sampling strategies and sample sizes.
result Feature approximations from different sampling strategies do not converge, affecting classifier accuracy.
A co-evolutionary approach for Heston model calibration reduces overfitting with diverse datasets.
problem Overfitting and lack of generalization in Heston model calibration.
method Coupling a genetic algorithm with an evolving neural inverse map, using both GA-history sampling and Latin hypercube sampling.
result Diverse datasets improve out-of-sample stability and calibration accuracy.
ALAMO builds simple yet accurate models from data.
problem Creating accurate models from complex data.
method Building a linear model with non-linear transformations, refining through adaptive sampling, and incorporating constraints.
result ALAMO generates simple and accurate models for reaction problems.
ISOMORPH: A Supply Chain Digital Twin for Simulation, Dataset Generation, and Forecasting Benchmarksstat.ML
ISOMORPH creates a digital twin for supply chain logistics, advancing time-series forecasting benchmarks.
problem Lack of public benchmarks for supply chain logistics time-series forecasting.
method Developed a digital twin simulator with interpretable parameters and modular topology, generating datasets and verifying conservation laws.
result Foundation models achieve MASE values exceeding public benchmarks at low-to-moderate horizons, supporting UQ.
New infill criterion identifies local optima in multimodal models.
problem Identify challenging test scenarios for physical systems.
method Model-based optimization with efficient global optimization and infill criterion.
result New infill criterion outperforms existing methods in identifying local optima.
This paper develops efficient surrogate models for optimization of complex dynamical systems.
problem Computational expense in solving complex dynamical systems through numerical simulation.
method Combination of proper orthogonal decomposition and radial basis functions for constructing low-dimensional surrogate models.
result Surrogate models reduce computational time for optimization problems while maintaining accuracy.
StackMC improves Monte Carlo estimates by learning control variates from data.
problem Reducing error in Monte Carlo estimates, especially in high dimensions.
method StackMC uses in-sample/out-sample techniques to fit control variates to data samples, improving MC estimators without additional samples.
result StackMC significantly reduces estimation error across various MC sampling methods.
Surrogate model construction for vector-valued outputs
problem Improving surrogate model accuracy and stability for complex engineering systems
method Adaptive sequential sampling for polynomial chaos expansion
result Improves surrogate accuracy and stability
New reshaping method improves hyperparameter search over random search.
problem Improving hyperparameter search efficiency.
method Introducing reshaping techniques to optimize search distributions.
result Substantial gains over random search in various experiments.
Adaptive SAA solves large-scale stochastic linear programs efficiently.
problem Solving large-scale two-stage stochastic linear programs.
method Iterative algorithm with adaptive sample size and warm starts.
result The algorithm converges to the true solution set with a probabilistic guarantee.
Develops an SSBO algorithm for global optimization of expensive models.
problem Global optimization of expensive black-box models.
method Asynchronous hybrid-criterion with interval reduction.
result Improves global search ability and local search efficiency.
Study finds nonlinear dependence and co-movement between US and Latin American stock markets.
problem Understanding nonlinear dependence and co-movements between US and Latin American stock markets.
method Used Brooks and Hinich cross-bicorrelation test to analyze stock market indexes.
result Windows of nonlinear dependence and co-movement found between SP500 and Latin American stock markets.
This paper ranks Latin American countries based on AI potential.
problem Identifying emerging AI powers in Latin America.
method Ranking based on infrastructure, education, and finance.
result Argentina, Colombia, Uruguay, Costa Rica, and Ecuador are new emerging powers in AI.
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice of the directions of stratification and the allocation rule within each strata. S…
A tailored HTR system improves CER to 0.015 for medieval Latin.
problem Digitizing handwritten medieval Latin records for a low-resource language.
method End-to-end pipeline using image segmentation and transformer-based models with extensive data augmentation.
result Best-performing setup achieved CER of 0.015, superior to commercial models.
Paper develops an efficient approach to reduce HPO time.
problem Challenges in determining optimal hyperparameters due to large number and training time.
method Nested Latin hypercube design for initialization, truncated additive Gaussian process model for calibration, sequential model-based algorithm for optimization.
result Demonstrates competitive performance on various machine learning models.
Efficiently learns Gaussian and Boolean hypercube distributions privately.
problem Learning high-dimensional distributions privately.
method Recursive private preconditioning.
result Sample complexity nearly matches non-private optimal learners.
Paper tackles medieval Latin sequence tagging using deep learning.
problem Complex orthographic variation in medieval Latin.
method Integrated neural network architecture for part-of-speech tagging and lemmatization.
result Single, integrated approach outperforms traditional methods.
ALMAB-DC optimizes expensive black-box experiments using active learning and distributed computing.
problem Efficiently optimizing expensive, gradient-free objectives in computational statistics and machine learning.
method Combines active learning, multi-armed bandits, and distributed asynchronous computing.
result Achieves lower simple regret and superior performance in various tasks compared to non-ALMAB baselines.
This work extends score-based methods to binary data on the Boolean hypercube.
problem Learning and sampling binary data on the Boolean hypercube.
method Adopting Bernoulli noise as a smoothing device, deriving a TMF-like expression for the optimal denoiser, and using a Langevin-like sampler.
result The method successfully samples noisy binary data and reduces effective noise through multiple measurements.
Study reveals structural constraints on income inequality in Latin America.
problem Income inequality in Latin America compared to other economies.
method Product space, Product Gini Index, Xgini coefficient.
result LAC economies are more dependent on products related to high income inequality.
New algorithm learns halfspaces over hypercube with random bit flips.
problem Agnostic learning of Boolean halfspaces over discrete domains is computationally hard.
method Smoothed analysis with random bit flips for discrete inputs.
result First efficient algorithm for smoothed agnostic learning of halfspaces over Boolean hypercube.
RNN model predicts handwritten characters from accelerometer and gyroscope data.
problem Online handwritten character recognition using sensor data.
method RNN-based neural network trained on gyroscope and accelerometer data.
result High accuracy on test data, achieving character prediction.
The hypercube's perimeter is significantly larger than expected near half volume.
problem Understanding the isoperimetric profile of the hypercube.
method Analytical proof of perimeter bounds and comparison to Gaussian isoperimetric profile.
result The isoperimetric profile of the hypercube does not converge to the Gaussian profile as dimension increases.
In this paper we introduce a representation of a embedded knotted (sometimes Lagrangian) tori in $\BR^4$ called a hypercube diagram, i.e., a 4-dimensional cube diagram. We prove the existence of hypercube homology that is invariant under 4-dimensional cube diagram moves, a homology that is based on knot Floer homology.…
Defined by Joyce and Matveev, the fundamental quandle is a complete invariant of oriented classical knots. We consider invariants of knots defined from quotients of the fundamental quandle. In particular, we introduce the fundamental Latin Alexander quandle of a knot and consider its Gröbner basis-valued invariants, wh…
Algorithm completes symmetric tensors from few entries, learns product mixtures.
problem Learning product mixtures over the hypercube from incomplete data.
method Tensor completion algorithm applied to matrix completion for adversarially missing entries.
result Recover distributions with many centers in polynomial/quasi-polynomial time.
New Fourier analysis method for non-uniform Boolean hypercube.
problem Non-uniform probability measures on the Boolean hypercube.
method ANOVA-based decomposition, explicit basis, least squares problem.
result Generalization of Fourier analysis for arbitrary probability measures.
Rigidity properties of hypercube graphs via curvature methods.
problem Rigidity of hypercube graphs under curvature constraints.
method Semigroup methods and new direct methods translating curvature to combinatorial properties.
result Sharp inequalities for diameter and eigenvalues only hold for hypercubes.
Study applies HRP to Latin American markets, showing smoother risk-return profile.
problem Lack of empirical analyses of HRP in Latin American markets.
method Hierarchical Risk Parity (HRP) with hierarchical clustering and recursive bisection.
result HRP portfolio outperforms Max Sharpe portfolio in NUAM markets, with smoother risk-return profile.
Hypercube graphs are optimal in spectral rigidity due to Bakry--Émery curvature.
problem Spectral rigidity of hypercube graphs
method Interplay between global spectral embedding and local curvature analysis
result Hypercube graphs are optimal in spectral rigidity due to Bakry--Émery curvature.
Stock market integration in the Latin American markets: further evidence from nonlinear modelingq-fin.ST
This article studies the financial integration between the six main Latin American markets and the US market in a nonlinear framework. Using the threshold cointegration techniques of Hansen and Seo (2002), we show significant threshold stock market linkages between Mexico, Chile and the US. Thus, the dynamics of these …
Unified Growth Theory contradicted by Latin American economic data.
problem Unified Growth Theory fails to explain Latin American economic growth.
method Analysis of historical economic growth data from Maddison.
result Unified Growth Theory is inconsistent with Latin American data.
Paper improves variational inference on Boolean hypercube using quantum methods.
problem Improving variational inference for pairwise Markov random fields on the Boolean hypercube.
method Quantum relaxations of the Kullback-Leibler divergence for upper-bounds, primal-dual optimization, and greedy selection of hierarchies.
result Efficient algorithm and improved bounds for variational inference.
The paper solves a problem related to dimensions at hypercube vertices using matrix models.
problem Finding functions of cycle numbers as dimensions of graded spaces at hypercube vertices.
method Matrix model technique, inspired by AMM/EO topological recursion.
result Most powerful versions of the formalism can convert ordinary knots/links to virtual and back.
In this paper, we focus on developing efficient sensitivity analysis methods for a computationally expensive objective function in the case that the minimization of it has just been performed. Here "computationally expensive" means that each of its evaluation takes significant amount of time, and therefore our m…
Polynomial-time algorithm improves online linear optimization on hypercube.
problem Online linear optimization on hypercube with regret minimization.
method PolyExp algorithm for full information and bandit feedback.
result PolyExp achieves better regret bound than Exp2 in full information setting.
Simplified Khovanov polynomials for bipartite links.
problem Computing Khovanov polynomials for bipartite links.
method Reduced Khovanov-Rozansky technique to Kauffman-Khovanov cycle calculus.
result Consistency demonstrated between reduced technique and bipartite Khovanov polynomials.
The study shows how discrete graphs can resemble hypercube structures under certain curvature conditions.
problem Understanding the structure of graphs with specific curvature conditions.
method Analyzing weighted graphs with lower Ricci curvature bounds and eigenvalue closeness to establish structural similarity.
result Discrete graphs with specific curvature conditions are close to hypercube structures in terms of Frobenius distance and eigenfunctions.
Regular integer lattices are characterized by k unit vectors that build up their generator matrices. These have rank k for D-lattices, and are rank-deficient for A-lattices, for E_6 and E_7. We count lattice points inside hypercubes centered at the origin for all three types, as if classified by maximum infinity norm i…
Polynomial-time algorithm finds planted hypercube vectors in Gaussian mixtures.
problem Clustering d-dimensional Gaussian mixtures with unknown covariance.
method Lattice-based methods using Lenstra--Lenstra--Lovasz reduction.
result Achieves statistically-optimal sample complexity of d+1 samples.
ROMs predict thermal power output in EGS systems, accounting for uncertainties.
problem Predicting transient thermal power output in enhanced geothermal systems (EGS) with subsurface uncertainties.
method Developed regression-based ROMs using physics-based simulations and Latin Hypercube Sampling.
result Three ROMs (1, 2, 3) accurately describe power production curves, with ROM-2 and ROM-3 outperforming ROM-1 for typical EGS applications.
A quandle is a self-distributive algebraic structure that appears in quasi-group and knot theories. For each abelian group A and c \in A we define a quandle G(A, c) on \Z_3 \times A. These quandles are generalizations of a class of non-medial Latin quandles defined by V. M. Galkin so we call them Galkin quandles. Each …
New variational family approximates non-Gaussian posteriors efficiently.
problem Approximating non-Gaussian posteriors in Bayesian models.
method Copula-like variational distributions with efficient sampling and normalizing flows.
result The proposed method performs comparably to state-of-the-art approximations.