Flexible framework assesses multilevel data group heterogeneity.
problem Multilevel data structure complicates model selection.
method Flexible framework for assessing differences between levels of grouping variables.
result Framework reliably identifies relevant multilevel components.
A new multilevel framework speeds up ResNet training.
problem Training deep residual networks (ResNets) is time-consuming.
method Formulates ResNets as dynamical systems and uses time-dependent optimal control problems.
result Enhanced training of ResNets with multilevel auxiliary networks achieves significant speedup.
A multilevel framework speeds up sparse optimization for inverse covariance estimation and logistic regression.
problem Sparse optimization problems in machine learning and signal processing.
method Multilevel framework exploiting sparseness of solutions.
result Efficiently solves l1 regularized optimization problems for inverse covariance estimation and logistic regression.
A fast multilevel SVM framework tackles large-scale data challenges.
problem High computational complexity and quality vs. performance trade-off in SVMs.
method Generalized fast multilevel framework for regular and weighted SVMs.
result Significant speed up compared to state-of-the-art nonlinear SVM libraries.
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that scales efficiently to very large data sets. Instead of solving the whole training s…
Accelerates MCMC sampling for large-scale problems using machine learning.
problem Efficiently sampling large-scale Bayesian inference problems with high computational cost.
method Integrates low-fidelity machine learning models into a multilevel MCMC framework.
result Significantly accelerates multilevel sampling by a factor of two with similar accuracy.
A method learns to solve multilevel combinatorial problems with two players.
problem Multilevel combinatorial optimization problems with multiple players.
method Value-based multi-agent reinforcement learning in a graph neural network framework.
result Close to optimal solutions on graphs up to 100 nodes, with a significant speedup.
Framework detects covert financial market manipulation using LOB representations.
problem Detecting covert financial market manipulation (spoofing) from complex anomaly patterns in multilevel prices.
method Cascaded contrastive representation learning of LOB data.
result Transformer-based architectures achieve state-of-the-art results in detection performance.
Develops a multilevel Monte Carlo framework with dropout for efficient uncertainty quantification.
problem Efficiently quantify uncertainty in complex models using dropout.
method Integrates multilevel Monte Carlo with Monte Carlo dropout, creating coupled estimators to reduce variance.
result Demonstrates significant variance reduction and efficiency gains over single-level Monte Carlo dropout.
In medical domain, data features often contain missing values. This can create serious bias in the predictive modeling. Typical standard data mining methods often produce poor performance measures. In this paper, we propose a new method to simultaneously classify large datasets and reduce the effects of missing values.…
A multilevel model combines genetic and imaging data for AD diagnosis.
problem Classification from multimodal genetic and brain imaging data with unbalanced contributions.
method Multilevel model with structured penalties for joint effects between modalities.
result The model reveals relationships between genes, brain regions, and disease status.
A new training method uses multilevel minimization for machine learning.
problem Training machine learning models with high variance and low efficiency.
method Constructs a multilevel hierarchy by reducing sample size and internally trains surrogate models with fewer samples.
result The multilevel method enhances model training efficiency compared to subsampled Newton's and variance reduction methods.
New method improves classification of healthcare data with missing values.
problem Predictive analytics on noisy, missing data with class imbalance.
method Multilevel Weighted Support Vector Machine (SVM) with imputation.
result Multilevel SVM produces more accurate and robust results.
The paper improves Monte Carlo methods for optimization problems.
problem Efficiently solving optimization problems with biased Monte Carlo estimators.
method Introduces Multilevel Monte Carlo (MLMC) within Sample Average Approximation (SAA).
result Establishes uniform convergence and sample complexity for MLMC in SAA.
Adaptive Multilevel Splitting improves rare event pricing for financial derivatives.
problem Efficient pricing of binary options in rare event regimes with discontinuous payoffs.
method Adaptive Multilevel Splitting (AMS) reformulates rare-event problem as conditional events.
result AMS achieves up to 200-fold improvements over standard Monte Carlo, preserving unbiasedness.
Estimates log marginal likelihood using multilevel Monte Carlo.
problem Estimating log marginal likelihood accurately.
method Unbiased multilevel Monte Carlo estimator.
result Validates application in variational Bayes.
Improved multilevel scheme for value-at-risk computation.
problem Discontinuity in Heaviside function affects value-at-risk computation.
method Adaptive multilevel stochastic approximation to mitigate discontinuity.
result Best complexity improved to O(ε−2∣lnε∣25). We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of refining time-grids to reduce statistical approximation errors in an adaptive and…
A new clustering method using transportation distance for multilevel data.
problem Multilevel clustering problems, especially with large datasets.
method Probabilistic approach based on composite transportation distance, solving a joint optimization problem over probability measures.
result Efficient and scalable solution for multilevel datasets, demonstrated on synthetic and real data.
New training method for neural nets using multilevel entropic regularization.
problem Training efficiency and generalization bounds for neural nets.
method Multilevel relative entropy, chaining mutual information, Gibbs posterior distribution.
result Proves the Gibbs posterior achieves the unique minimum of the empirical risk minimization problem.
A multilevel optimization method for constrained problems.
problem Regularized constrained linear inverse problems with box constraints.
method Geometric multilevel optimization with varying discretization levels.
result Preserves feasibility of updates while speeding up computations.
Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the key features in achieving a high rate of multilevel variance convergence, and su…
Automates kernel discovery for longitudinal data analysis.
problem Handling irregularly sampled, sparse longitudinal data with multilevel correlation.
method Combines deep neural networks and non-parametric kernel methods to discover complex multilevel correlation structure.
result Significantly outperforms state-of-the-art methods on benchmark data sets.
New deep fusion methods improve human action recognition using depth and inertial sensor data.
problem Existing multimodal HAR frameworks lack mid-level feature fusion.
method Proposes three deep multilevel multimodal fusion frameworks, transforming depth and inertial sensor data into images and using convolution with Prewitt filter to create modality within modality.
result Supremacy of proposed fusion frameworks over existing methods on three publicly available datasets.
Develops a fast algorithm for fitting multilevel factor models.
problem Fitting multilevel factor models with covariance structure.
method Novel expectation-maximization algorithm tailored for multilevel factor models.
result Shows efficient computation of inverse of positive definite MLR matrix.
We investigate the extension of the multilevel Monte Carlo path simulation method to jump-diffusion SDEs. We consider models with finite rate activity, using a jump-adapted discretisation in which the jump times are computed and added to the standard uniform dis- cretisation times. The key component in multilevel analy…
A new ML-based framework improves variational inference efficiency.
problem Efficient and accurate gradient estimation in variational inference.
method Multilevel Monte Carlo (MLMC) with reparameterized gradient estimators and adaptive learning rate.
result Our method achieves faster convergence and reduces gradient variance.
Faster SVMs trained with multilevel approach.
problem Training time inefficiency for SVMs on large datasets.
method Label propagation algorithm to construct a hierarchy of smaller SVM problems.
result Up to orders of magnitude faster than previous fastest algorithm.
MiME learns EHR data structure for predictive healthcare tasks.
problem Data insufficiency in EHR for predictive healthcare tasks.
method Leverages multilevel structure of EHR data and learns multilevel embedding.
result MiME outperforms baseline methods in diverse evaluation settings.
Develops a multilevel method for solving BLUP and GLS models with high dimensional data.
problem Numerical instability and ill-conditioned covariance matrices in high-dimensional data.
method Multilevel basis construction and transformation of covariance matrices using kD-tree partitioning.
result The multilevel method solves BLUP and GLS models accurately and efficiently, scaling well with dimensions and observations.
A new method for multilevel clustering using Wasserstein distances.
problem Simultaneously partitioning data in groups and discovering group patterns.
method Joint optimization over spaces of discrete probability measures with Wasserstein distances.
result Consistency properties for estimates of local and global clusters established.
Paper proposes a new algorithm to reduce derivative pricing computation time.
problem Derivative pricing computational inefficiency.
method Combines multilevel Richardson-Romberg and importance sampling.
result Reduces computational time while maintaining accuracy.
Adaptive Multilevel Monte Carlo improves probability estimation for complex random variables.
problem Estimating probabilities of complex random variables with multiple approximations.
method Adaptive Multilevel Monte Carlo framework for discontinuous functionals.
result Achieves optimal computational complexities for both smooth and discontinuous functionals.
The paper discusses building ETF risk models using a multilevel classification taxonomy.
problem Building accurate risk models for ETFs.
method First, build a multilevel classification taxonomy for ETFs. Then, use this taxonomy to define risk factors and build risk models.
result The approach can accurately classify and model ETF risks.
A new method for multilevel clustering using Wasserstein means.
problem Simultaneously partitioning data in each group and discovering grouping patterns among groups.
method Joint optimization over spaces of discrete probability measures with Wasserstein distance metrics, including variants that admit fast optimization.
result Consistency properties for estimates of both local and global clusters are established.
In this paper, we are interested in the strong convergence properties of the Ninomiya-Victoir scheme which is known to exhibit weak convergence with order 2. We prove strong convergence with order 1/2. This study is aimed at analysing the use of this scheme either at each level or only at the finest level of a multil…
Improved Bayesian regression for large datasets using multilevel Gibbs sampling.
problem Efficiently handling large-scale Bayesian regression with complex posterior distributions.
method Developed a multilevel Gibbs sampler for linear mixed models, incorporating data clustering and correlated samples for variance reduction.
result Significant speed-up achieved for Bayesian regression without sacrificing predictive performance.
New neural network models speed up Bayesian multilevel modeling.
problem Complex computational challenges in Bayesian multilevel modeling.
method Probabilistic neural network architectures that leverage multilevel model factorization.
result Efficient posterior inference on unseen datasets with near-instant results.
The paper proposes a method to learn discriminative multilevel dictionaries for supervised image classification.
problem Improving sparse representation for supervised image classification.
method Learning structured multilevel dictionaries with discriminative constraints for each class, using reconstruction errors of image patches.
result Competitive results compared to state-of-the-art methods on texture image classification.
The paper introduces a multilevel initialization method for deep neural networks.
problem Training very deep neural networks with layer-parallel methods.
method Continuous interpretation of training as optimal control, using time-dependent ODEs for neural network discretization, and a refinement strategy across the time domain.
result The method creates deep networks with good initializations from coarser networks, reducing training time and providing regularization.
Efficiently price VIX options using multilevel Monte Carlo in rough Bergomi model.
problem Pricing VIX options in a rough Bergomi model with high computational complexity.
method Combining rectangle discretization, Cholesky sampling, and multilevel Monte Carlo.
result Reduced computational complexity to O(ε−2log2(ε)) and asymptotically optimal O(ε−2). Enhances SBI accuracy with multilevel Monte Carlo for expensive simulators.
problem Limited accuracy in SBI due to expensive simulators.
method Multilevel Monte Carlo techniques for cost-effective SBI.
result Significant enhancement in SBI accuracy with fixed computational budget.
A new algorithm estimates VaR and ES for financial risks.
problem Estimating Value-at-Risk and Expected Shortfall for financial losses.
method Multilevel Stochastic Approximation (MLSA) scheme for nested stochastic approximation problems.
result Optimal complexities for VaR and ES estimation are derived.
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when using the Milst…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizin…
Proposes a method for multilevel explanations of black-box models.
problem Need for explanations at intermediate or group levels, especially for GDPR compliance.
method Meta-method that builds a multilevel explanation tree using local explainability methods.
result Effective multilevel explanations for groups of data points, including novel test points.
We present a Bayesian nonparametric framework for multilevel clustering which utilizes group-level context information to simultaneously discover low-dimensional structures of the group contents and partitions groups into clusters. Using the Dirichlet process as the building block, our model constructs a product base-m…
We apply multilevel Monte Carlo for option pricing problems using exponential Lévy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate the computational efficiency of this approach. We derive estimates of the convergen…