The paper provides statistical guarantees for SGD and ASGD in high-dimensional settings.
problem Theoretical understanding of SGD and ASGD in high-dimensional settings.
method Transfer of tools from high-dimensional time series to online learning, using coupling techniques.
result Established geometric-moment contraction and q-th moment convergence of SGD and ASGD. High-dimensional data simplifies problems, contrary to the curse of dimensionality.
problem Exponential difficulty in high-dimensional problems.
method Analysis of high-dimensional datasets and their geometric properties.
result Generic high-dimensional datasets exhibit simple geometric properties.
Machine learning improves high-dimensional matrix estimation.
problem Efficient estimation of high-dimensional matrices.
method Integrates machine learning with classical optimization algorithms for high-dimensional matrix estimation.
result The reparameterized LADMM achieves faster convergence and higher accuracy.
FSGD uses latent factors to scale SGD for high-dimensional learning.
problem Scalable optimization in high-dimensional machine learning.
method Factor-Augmented SGD (FSGD) that operates on streaming data.
result Established theoretical framework for latent factor estimation error in SGD.
A new machine learning method solves high-dimensional Kolmogorov PDEs efficiently.
problem Solving high-dimensional Kolmogorov PDEs and SDEs.
method Stochastic weighted minimization and stochastic gradient descent with Malliavin weights.
result Accurate approximation of high-dimensional Kolmogorov PDEs and SDEs without curse of dimensionality.
Solves high-dimensional observation learning for control models.
problem Learning dynamics from high-dimensional images is challenging.
method Proposes a Beta DVBF approach to handle latent and observable space discrepancies.
result Demonstrates improved model learning from high-dimensional observations.
Deep learning reduces complex data to simpler predictors.
problem High-dimensional data reduction in input-output models.
method Hierarchical layers of latent features for constructing predictors.
result Deep learning is a black-box method for high-dimensional function estimation.
Overview of high-dimensional time series regression methods.
problem Estimation and inference with high-dimensional time series data.
method Limit theory for high-dimensional dependent data, asymptotic theory for time series regression, statistical learning methods.
result Main limit theory results and asymptotic theory for high-dimensional time series regression.
i-flow uses normalizing flows for high-dimensional integration and sampling.
problem High-dimensional integration in science and statistics.
method Normalizing flows for bijective mappings between distributions.
result i-flow outperforms other algorithms for high-dimensional correlated integrals.
A new distributed learning method for high-dimensional linear classification.
problem Efficiently performing linear classification on large-scale, high-dimensional data.
method Feature-distributed stochastic variance reduced gradient (FD-SVRG) for high-dimensional linear classification.
result FD-SVRG outperforms other distributed methods in terms of communication cost and wall-clock time.
A new method uses Gaussian processes and deep kernel learning to price high-dimensional American options efficiently.
problem Challenges in pricing high-dimensional American options, especially with excessive computational costs.
method Modified Gaussian process regression with deep kernel learning and sparse variational Gaussian processes.
result The method outperforms least squares Monte Carlo in high-dimensional scenarios, especially with Merton's jump diffusion model.
Study on meta-reinforcement learning generalization in high-dimensional tasks.
problem Generalization performance of meta-reinforcement learning algorithms in high-dimensional tasks.
method High-dimensional, procedurally generated environments.
result Meta-reinforcement learning algorithms exhibit strong overfitting on challenging tasks.
The paper optimizes bandwidth for detecting circular structures in high-dimensional data.
problem Detecting circular structures in high-dimensional data.
method Optimal bandwidth estimation for fast manifold learning.
result Minimization of functions of bandwidth for optimal detection.
Human engineered features don't outperform XGBoost on high dimensional data.
problem Comparing human engineered features to machine learning models trained directly on data.
method Training XGBoost on human engineered features and comparing to direct data training.
result Human engineered features are comparable to XGBoost trained directly on data.
New deep learning solver for high-dimensional derivative pricing.
problem High-dimensional derivatives pricing problems.
method Combines deep learning with least square regression for backward SDE solving.
result Accurate and efficient pricing of complex derivatives.
A new method improves graph-based learning for high-dimensional data.
problem Inconsistent high-dimensional learning efficiency of semi-supervised graph regularization.
method Introducing a novel regularization approach involving centering operation.
result Empirical results show improved performance over spectral clustering.
This paper reviews nonparametric density estimation methods for high-dimensional data.
problem Challenges in analyzing high-dimensional data with many features.
method Review of nonparametric density estimation algorithms for high-dimensional data.
result Discussion of algorithms and their applications in modal clustering.
Study dynamic batch learning in high-dimensional sparse linear bandits.
problem Dynamic batch learning in high-dimensional sparse linear contextual bandits under batch constraints.
method Characterized fundamental learning limits via regret lower bound and provided matching upper bound.
result Prescribed an optimal scheme for dynamic batch learning in high-dimensional sparse linear contextual bandits.
Derives a method to optimize high-dimensional functions on low-dimensional manifolds.
problem High-dimensional derivative-free optimization with high sample complexity.
method Online learning approach that learns the manifold while optimizing the function.
result Significantly reduces sample complexity compared to existing methods.
Proposes a transfer learning method for high-dimensional quantile regression.
problem Inadequate handling of heterogeneity and heavy tails in transfer learning.
method High-dimensional quantile regression framework with double transfer learning estimator.
result Established error bounds and valid confidence intervals for high-dimensional quantile regression coefficients.
E&E uses contrastive learning to speed up SBI for high-dimensional systems.
problem Challenges in training high-dimensional emulators for complex systems.
method Contrastive learning for low-dimensional latent embedding and fast emulator.
result Superior performance in non-identifiable parameter estimation tasks.
AD-EnKFs use machine learning to improve data assimilation in high-dimensional systems.
problem Data assimilation in high-dimensional, unknown dynamics systems.
method Auto-differentiable ensemble Kalman filters blending machine learning and ensemble Kalman filters.
result AD-EnKFs outperform existing methods in the Lorenz-96 model.
IBPF algorithm tackles high-dimensional parameter learning for complex systems.
problem Learning high-dimensional parameters in complex, partially observed, and nonlinear systems.
method Iterated Block Particle Filter (IBPF) for graphical state space models.
result IBPF algorithm consistently beats the curse of dimensionality across various experiments.
Improves joint distribution learning for high-dimensional datasets with complex correlations.
problem Conditional independence assumption limitations in VAE decoders for high-dimensional datasets.
method Cramer-Wold distance regularization and two-step learning method for flexible prior modeling.
result Effective joint distributional learning for high-dimensional datasets with multiple categorical variables.
Proposes MscaleDNN for solving high-dimensional PDEs efficiently.
problem Solving high-dimensional PDEs efficiently.
method Radial scaling in frequency domain and compact support activation functions.
result Increased power in multi-scale resolution and high frequency capturing.
The paper explores high-dimensional learning in finance, proving key aspects and setting lower bounds.
problem Understanding when and how large, over-parameterized models achieve predictive success in finance.
method Theoretical foundations and empirical validation of two key aspects: standardization and information-theoretic lower bounds.
result Empirical validation shows that high-dimensional learning in finance often relies on lower-complexity artefacts rather than the intended mechanism.
Deep learning method uses asymptotic expansion to solve high-dimensional BSDEs faster.
problem Solving high-dimensional BSDEs efficiently.
method Asymptotic expansion as prior knowledge in deep learning for BSDEs.
result Significantly reduces loss function and accelerates convergence.
SILBO optimizes high-dimensional Bayesian optimization using semi-supervised embedding learning.
problem Bayesian optimization struggles with high-dimensional search spaces.
method SILBO uses semi-supervised dimension reduction to find a low-dimensional space for iterative optimization.
result SILBO outperforms existing methods on high-dimensional Bayesian optimization tasks.
Geometric framework detects outliers in high-dimensional data.
problem Detecting outliers in high-dimensional data.
method Geometric framework exploiting manifold structure.
result Significant improvement in outlier detection in high-dimensional data.
HashReward improves imitation learning in high-dimensional environments by balancing reward generation and dimensionality reduction.
problem Making policies generalize well in high-dimensional state-action spaces, especially in game playing with raw pixel inputs.
method HashReward uses supervised hashing to balance reward generation and dimensionality reduction.
result HashReward outperforms state-of-the-art methods in high-dimensional environments.
Pairwise methods outperform pseudo-likelihood in high-dimensional Markov network structure learning.
problem Learning the structure of high-dimensional binary pairwise Markov networks.
method Comparison of pseudo-likelihood and pairwise methods on binary pairwise Markov networks.
result Pairwise methods can be more accurate than pseudo-likelihood methods in high-dimensional settings.
PDE-DKL combines NNs and GPs for high-dimensional PDE problems.
problem High-dimensional PDE problems with scarce data.
method PDE-constrained Deep Kernel Learning (PDE-DKL) framework.
result High accuracy with reduced data requirements.
Learning rate needs to decrease with higher data moments for effective ICA in high dimensions.
problem Slower convergence of ICA in high-dimensional data with high-order moments.
method High-dimensional ODE analysis of ICA algorithm under controlled moment structure.
result Critical learning rate threshold for effective ICA when moments are high.
Deep learning approximates high-dimensional stochastic control problems.
problem High-dimensional stochastic control problems with the curse of dimensionality.
method Approximates time-dependent controls as neural networks and trains them through model dynamics.
result Achieves satisfactory accuracy in high-dimensional problems.
Paper explores differential privacy in high-dimensional federated learning, tackling server trustworthiness and estimation.
problem Maintaining privacy in distributed environments with high-dimensional data.
method Investigates scenarios with untrusted and trusted central servers, introduces novel federated estimation algorithms for linear regression models.
result Tight minimax rates depend on high-dimensionality even with sparsity assumptions, and novel algorithms handle slight variations among distributed models.
Paper tackles attribute pattern learning in high-dimensional SLAMs.
problem Learning significant attribute patterns from high-dimensional SLAMs.
method Proposes a penalized likelihood method for selecting attribute patterns.
result Establishes selection consistency in overfitted SLAMs.
This paper tackles high-dimensional Bayesian optimization using supervised dimension reduction.
problem Challenges in extending Bayesian optimization to high dimensions.
method Introduces Sliced Inverse Regression (SIR) for high-dimensional Bayesian optimization.
result Demonstrates computational benefits and theoretical regret bounds for high-dimensional Bayesian optimization.
Proposes Causal-Batle for estimating treatment effects in small high-dimensional datasets.
problem Estimating treatment effects with small high-dimensional datasets.
method Adopts transfer learning techniques for causal inference.
result Improves treatment effect estimates in small high-dimensional datasets.
A new benchmark task for evaluating policy learning in complex, high-dimensional action spaces.
problem Lack of a commonly accepted benchmark for evaluating policy learning in hierarchical tasks with high-dimensional action spaces.
method Proposed DinerDash Gym benchmark and Decomposed Policy Graph Modelling (DPGM) algorithm.
result DPGM achieves significant improvement over baselines and effectively injects domain knowledge.
Deep networks learn hierarchical functions more efficiently than shallow ones.
problem Understanding the advantage of deep neural networks over shallow models.
method Analytical study of learning dynamics and generalization performance of deep networks compared to shallow ones.
result Deep networks reduce effective dimensionality, enabling learning with fewer samples.
Efficient algorithms learn high-dimensional distributions robustly, independent of dimensionality.
problem Learning high-dimensional distributions in the presence of adversarial corruption.
method Developed computationally efficient algorithms with dimension-independent error guarantees.
result Achieved error independent of dimension and nearly-linear in corrupted samples fraction.
This thesis explores optimization methods for high-dimensional machine learning problems.
problem High-dimensional optimization challenges in machine learning.
method Intuition and convergence proofs for stochastic gradient descent and momentum methods.
result Explanation of why common machine learning optimization methods are successful.
Data repetition improves SGD's learning of high-dimensional functions.
problem Learning pertinent features in multi-index models with high-dimensional noisy data.
method Investigation of two-layer shallow neural networks trained with gradient-based algorithms, focusing on data repetition.
result Data repetition significantly improves the computational efficiency of SGD, learning all directions with at most O(dlogd) steps. Active learning improves GP regression on complex, high-dimensional data.
problem Improving Gaussian Process regression in high-dimensional spaces with discontinuous functions.
method Combines manifold learning with active learning to optimize data selection and reduce dimensionality.
result Superior performance over random learning in synthetic data experiments.
DMLreg uses expert knowledge to improve model performance in high-dimensional settings.
problem Improving model performance in high-dimensional prediction problems.
method Learning a Mahalanobis distance metric from expert comparisons and integrating it into a regularized linear model.
result DMLreg leads to improvements in model performance when expert knowledge is relevant.
New method learns unbiased treatment representations from structured high-dimensional data.
problem Estimating causal effects from high-dimensional, structured treatments.
method Contrastive learning approach to learn unbiased treatment representations.
result The method identifies causal factors and discards non-causal ones, leading to unbiased causal effect estimates.
Boosting ridge regression for high-dimensional data classification reduces computational cost and improves learning time.
problem High computational demand of inverting regularised covariance matrix in ridge regression for high-dimensional problems.
method Train an ensemble of ridge regressors in randomly projected subspaces, then combine them using adaptive boosting.
result Effective in terms of learning time and improved predictive performance in some cases.
PCENet reduces uncertainty in high-dimensional data efficiently.
problem Uncertainty quantification in high-dimensional data is computationally expensive.
method Two-stage learning process: variational autoencoder for low-dimensional representation, polynomial chaos expansion for mapping.
result Model captures system dynamics, learns under uncertainty, estimates high-dimensional data uncertainty, matches output distribution moments.