A new method reduces the computational time for pricing financial derivatives with complex models.
problem Pricing financial derivatives with a large number of variables.
method Chebyshev reduced basis function for polynomial interpolation and hierarchical orthogonalization.
result A significant reduction in computational time for pricing various financial contracts.
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.
New method uses low-fidelity data to improve neural network predictions.
problem Improving predictive capability of neural networks for parameterized problems.
method Combines POD and shallow neural network; incorporates low-fidelity data features.
result Improves predictive capability of neural network predictions.
Calibrating American options is sped up using model reduction techniques.
problem Calibrating American options is computationally challenging due to their flexibility and constraints.
method Two model reduction strategies: reduced basis method and de-Americanization.
result Calibration process is significantly faster with reduced model complexity.
Introduces tunable basis functions for Gaussian processes.
problem Reduces computational complexity in Gaussian process approximations.
method Introduces tunable, local, and bounded basis functions for kernel approximation.
result Demonstrates superior performance compared to state-of-the-art methods, especially with poorly chosen kernel functions.
New method models PDEs from noisy, limited data.
problem Modeling PDEs with incomplete, noisy data.
method Learned linear transformation of spatial grid points, followed by dynamics learning in a reduced basis, then back transformation.
result Rapid high-resolution simulations with smaller training data sets.
The paper explains the fair basis in bond-CDS trading during financial crises.
problem Large basis trading losses during financial crises are not explained by reduced form models.
method Dynamic spread model with bond repo financing, economic capital approach.
result Unhedged and unhedgeable residual jump to default risk exists, affecting fair basis level.
New framework quantifies uncertainty in reduced-order models for PDEs.
problem Quantifying reliability of reduced-order model predictions for PDEs.
method Combining stochastic representation of reduced bases with conformal-type methods.
result Provides prediction sets with coordinate miscoverage guarantees.
We consider the problem of designing a sparse Gaussian process classifier (SGPC) that generalizes well. Viewing SGPC design as constructing an additive model like in boosting, we present an efficient and effective SGPC design method to perform a stage-wise optimization of a predictive loss function. We introduce new me…
We study natural bases for two constructions of the irreducible representation of the symmetric group corresponding to [n,n,n]: the {\em reduced web} basis associated to Kuperberg's combinatorial description of the spider category; and the {\em left cell basis} for the left cell construction of Kazhdan and Lusztig. I…
BASIS improves LLM reasoning by sharing batchwise rollout info, reducing MSE by 69%.
problem Improving large language model reasoning with limited rollouts and batch information.
method BASIS samples only one rollout per prompt but uses batch information to improve value function estimation.
result BASIS reduces MSE in value function estimation by 69% compared to REINFORCE++.
Upper bounds on neural network complexity for PDE solutions.
problem Approximating solutions of parametric PDEs without knowing their exact form.
method Using low-dimensionality of solution manifolds and a small reduced basis.
result Neural networks can approximate PDE solutions with sizes dependent only on the reduced basis.
Option Encoder compresses reinforcement learning options into a policy basis.
problem Redundant options in reinforcement learning frameworks.
method Auto-encoder framework with constrained weights to discover a policy basis.
result Option Encoder reduces the number of options while maintaining performance.
Paper projects GP basis functions using tensor networks to reduce complexity.
problem Efficiently approximating Gaussian process regression with a large number of basis functions.
method Develops a method using tensor networks to approximate GP regression with an exponential number of basis functions without exponential computational complexity.
result Shows efficient GP regression on an 18-dimensional benchmark data set.
New sparse Gaussian process method tackles unconstrained regression problems.
problem Dealing with physical systems that satisfy inequality constraints.
method Extends constrained Gaussian process by redefining hat basis functions.
result Reduces computational complexity from O(n3) to O(nm2). A new optimizer for deep learning improves accuracy and reduces training time.
problem Training deep neural networks for classification tasks.
method Hybrid Newton/Gradient Descent (NGD) method exploiting convexity of cross-entropy loss.
result Improves validation error and provides qualitative differences in hidden layer basis functions.
Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address this problem and reduce the arithmetic and storage cost. However, we observed tha…
New methods reduce computational cost for Gaussian Markov Random Fields with sparse constraints.
problem Inference and simulation of GMRFs are computationally prohibitive with many constraints.
method Proposes a basis transformation into blocks of constrained and non-constrained subspaces.
result Significantly outperforms existing alternatives in computational cost.
Active learning method reduces labeling cost for regression models with aggregated data.
problem Reducing labeling cost for training regression models with aggregated data.
method Sequentially selects sets to be labeled using mutual information quantifying model parameter uncertainty.
result Achieves better predictive performance with fewer labeled sets.
A new kernel improves statistical surrogates for stochastic manifolds with diverse data.
problem Handling statistical surrogates for stochastic manifolds with heterogeneous data.
method A transient anisotropic kernel is introduced to improve statistical surrogates for stochastic manifolds with heterogeneous data.
result The transient anisotropic kernel provides a better representation of statistical dependencies in the learned probability measure.
This study tackles basis risk in weather parametric insurance using Monte Carlo simulations.
problem Mismatch between actual loss and payout in weather parametric insurance leads to loss without payout or payout without loss.
method Empirical research using Monte Carlo simulations to test diversification and hedging strategies.
result Portfolio basis risk and volatility decrease with more contracts, and spatial relationships significantly impact basis risk.
Improves multi-output regression speed.
problem High computation time in multi-output relevance vector regression.
method Optimized algorithm reducing time complexity.
result Significantly faster computation time compared to existing methods.
DDD reformulated for sparse matrices, integrating trajectory and snapshot time series data.
problem Efficiently integrate trajectory and snapshot time series data.
method Reformulate DDD to use compact basis functions, reducing parameter scaling.
result Inference of sparse matrices reduces the number of parameters in DDD.
This work proposes a novel method for interpolating ROMs without solving FEM models.
problem Interpolating ROMs for unseen parameter values without solving FEM models.
method Non-intrusive Space-Time POD interpolation on compact Stiefel manifolds.
result Robust ROMs derived for unseen parameter values with strong correlations to high-fidelity simulations.
This paper improves Gaussian process predictions by integrating prior knowledge.
problem Gaussian processes lack predictive power when prior information is ignored.
method Derive mean and covariance functions from previous data using weighted sums of basis functions.
result Integrating prior knowledge significantly increases look-ahead time and accuracy.
Subspace recovery from corrupted and missing data is crucial for various applications in signal processing and information theory. To complete missing values and detect column corruptions, existing robust Matrix Completion (MC) methods mostly concentrate on recovering a low-rank matrix from few corrupted coefficients w…
Adapts POD basis for parametric ROMs using pGP.
problem Updating POD basis for accurate system behavior over parameter space.
method Formulates problem as supervised statistical learning, uses pGP to learn mapping between parameter space and Grassmann manifold.
result Proposes pGP for optimal estimation of POD basis parameters and quantifies uncertainty.
New capacity measure for ReLU networks reduces generalization error.
problem Improper influence of path norm on ReLU network capacity.
method Basis-path Norm, optimization algorithms.
result Basis-path Norm better explains ReLU network generalization.
New basis for permutation equivariant layers reduces computation costs.
problem Efficiently computing permutation equivariant layers in neural networks.
method Generalized partition algebra basis with low-rank tensors.
result Low-rank tensors enable faster computation compared to orbit basis.
New ODE-Block handles stateful layers with continuous-in-depth functions using basis functions.
problem Handling stateful layers in ODE-Nets.
method Formulate ODE-Block using continuous-in-depth functions with basis function expansions.
result Enables state-of-the-art performance and reduces memory footprint.
Paper uses autoencoders for efficient reduced-order modeling of eigenvalue problems.
problem Efficiently modeling eigenvalue problems in high dimensions.
method Autoencoder-based reduced-order modeling for eigenvalue problems.
result Autoencoder-based models outperform standard POD-Galerkin methods in neutron diffusion applications.
By using the HOMFLY skein theory. We prove a strong integrality theorem for the reduced colored HOMFLYPT invariants defined by a basis in the full HOMFLY skein of the annulus.
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.
New method speeds up sparse Gaussian processes for large datasets.
problem Efficiently modeling large datasets with many inducing variables.
method Projecting a GP onto B-spline basis functions for sparse linear algebra.
result Efficiently models fast-varying spatial phenomena with tens of thousands of inducing variables.
In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings on high dimensional data. The supervised learning problem can be formulated as an…
This paper introduces Haar convolution for GNNs to reduce computational cost.
problem High computational cost in GNNs for large graph sizes.
method Introduces Haar basis for graph convolution and Fast Haar Transforms.
result State-of-the-art results on graph-based regression and node classification tasks.
RI-DeepONet learns neural operators from arbitrary sensor data.
problem Discretization of input functions limits practical applications of DeepONet.
method Introduces RI-DeepONet and two dictionary learning algorithms for INRs.
result RINO handles arbitrary sensor data robustly and applies to various problems.
Self-guided ALPs improve MDP policies without domain knowledge.
problem Improving MDP policies with minimal domain knowledge.
method Self-guided sequence of ALPs with random basis functions and state-relevance distribution.
result High probability error bounds and improved policy performance.
New algorithm improves polynomial chaos approximations using compressive sensing.
problem Improving the efficiency and accuracy of polynomial chaos expansions.
method Develops a two-step optimization procedure combining compressive sensing with basis adaptation.
result Optimal sparsity in polynomial chaos approximations with reduced dimensionality.
The paper offers methods to estimate causal functions using machine learning.
problem Estimating causal effects and their derivatives accurately.
method Neyman-orthogonal signal adjustment, best linear predictor, Gaussian bootstrap inference.
result Automatic targeting of smooth structural functions and group average effects.
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.
A model order reduction framework reduces financial risk analysis models efficiently.
problem Simulating high-dimensional financial risk models.
method Adaptive greedy sampling based on POD and surrogate modeling.
result Reduced models provide significant speedup with excellent accuracy.
Unified framework for imbalanced data resampling improves classification performance.
problem Data imbalance negatively impacts machine learning performance.
method Unified framework combining over- and undersampling with radial basis functions optimization.
result Potential Anchoring outperforms state-of-the-art resampling algorithms.
SONMF reduces ED crowding by predicting patient dispositions from triage notes.
problem Crowded Emergency Departments and delayed patient admissions.
method Semi-orthogonal Non-negative Matrix Factorization (SONMF) for text mining.
result SONMF improves classification accuracy and interpretability of patient notes.
A new decoupled approach for Gaussian processes reduces complexity and improves performance.
problem Superlinear complexity in sparse variational inference methods for Gaussian processes.
method Orthogonally decoupling the mean and covariance functions of Gaussian processes to achieve linear complexity and expressive posterior mean functions.
result Our method achieves significantly faster convergence compared to state-of-the-art approaches.
This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact subset of Rd. On this approximate eigenbasis the eigenvalues of the c…
A new algorithm tackles incomplete multi-view clustering.
problem Incomplete multi-view clustering where views have missing instances.
method DAIMC algorithm using weighted semi-NMF and L2,1-Norm regularized regression. result DAIMC effectively handles missing instances and improves clustering accuracy.
New algorithm speeds up online mapping of unknown terrains.
problem Increasing computational demands of GP mapping as area expands.
method Recursive GP mapping using local basis functions in an information filter.
result Reduces overall computational complexity and speeds up mapping.