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 q q -th moment convergence of SGD and ASGD. 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.
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.
High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states: many problems become exponentially difficult in high dimensions. Recently, the ot…
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.
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.
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.
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.
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.
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.
Deep learning (DL) is a high dimensional data reduction technique for constructing high-dimensional predictors in input-output models. DL is a form of machine learning that uses hierarchical layers of latent features. In this article, we review the state-of-the-art of deep learning from a modeling and algorithmic persp…
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 ( d log d ) O(d \log d) O ( d log d ) steps. 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.
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.
A new algorithm solves high-dimensional nonlinear BSDEs efficiently.
problem Solving high-dimensional nonlinear backward stochastic differential equations (BSDEs).
method Transformed BSDE into a differential deep learning problem using Malliavin calculus. Discretized integrals using Euler-Maruyama method. Approximated solution with three deep neural networks. Optimized parameters using a differential learning loss function.
result Our algorithm is more accurate and faster than other methods.
Method learns low-dim. state vars from noisy high-dim. data.
problem Discovering dynamical models from noisy high-dimensional data.
method Stochastic Variational Deep Kernel Learning with encoder and latent model.
result Effective denoising, compact state representation, and uncertainty quantification.
New method tackles high-dimensional SBL without covariance matrices.
problem Sparse coding problem in high-dimensional settings.
method Parallel solution of multiple linear systems using conjugate gradient algorithm.
result Our method scales better in computation time and memory.
Formalizes concepts as latent variables in hierarchical models for high-dimensional data.
problem Lack of formalization and theoretical insights for learning discrete concepts from high-dimensional data.
method Formalizes concepts as latent causal variables in a hierarchical model, formulates conditions for concept identification.
result Conditions for identifying latent hierarchical models in unsupervised data, handling complex structures and high-dimensional data.
Paper introduces semi-supervised linear extremile regression for high-dimensional data.
problem Challenges in high-dimensional extremile regression due to data sparsity and overfitting.
method Proposes semi-supervised learning for linear extremile regression, achieving n \sqrt{n} n -consistency. result Demonstrates improved estimation efficiency and performance in high-dimensional settings.
A machine learning model manages portfolio risk in high dimensions.
problem Managing risk in high-dimensional financial portfolios.
method A supervised learning approach using replicating martingales and polynomial/neural network bases.
result The model outperforms naive Monte Carlo and least-squares Monte Carlo methods.
Learning a model of dynamics from high-dimensional images can be a core ingredient for success in many applications across different domains, especially in sequential decision making. However, currently prevailing methods based on latent-variable models are limited to working with low resolution images only. In this wo…
Proposes MamBO for efficient high-dimensional large-scale optimization.
problem High-dimensional and large-scale optimization problems in machine learning and simulation.
method Combines subsampling and subspace embeddings with model aggregation to address uncertainty in surrogate models.
result Improves robustness of Bayesian optimization algorithm and achieves superior performance.
Efficient learning of minimax risk classifiers in high dimensions.
problem Efficient learning of classifiers in high-dimensional data.
method Iterative algorithm leveraging constraint generation methods for minimax risk classifiers.
result The algorithm provides efficient learning and feature selection in high-dimensional scenarios.
High-dimensional models become unstable when sample size falls below a critical level, leading to a phase transition.
problem Instability in high-dimensional learning models when sample size is insufficient.
method Proved the necessity of a Fisher eigenvalue threshold for stability, introduced Fisher floor for verification.
result A sharp phase transition between reliable concentration and inevitable failure in high-dimensional learning.
In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijectiv…
Proposes efficient deep causal generative models for high-dimensional causal inference.
problem Inefficient training of deep generative models for high-dimensional data.
method Modular training of deep causal generative models using adversarial training and pre-trained models.
result First algorithm that provably samples from any identifiable causal query in the presence of latent confounders.
Paper tackles high-dimensional quantile regression with distribution shift using transfer learning.
problem Efficiency of knowledge transfer is severely impacted by distribution shift in high-dimensional regression.
method Proposes a novel transferable set and framework for three types of distribution shift: parameter, covariate, and residual.
result Establishes estimation error bounds and source detection consistency for the proposed method.
Paper analyzes GLM-tron for high-dimensional ReLU regression, providing upper and lower bounds.
problem Learning a single ReLU neuron in high-dimensional settings with overparameterization.
method Perceptron-type algorithm GLM-tron, with finite-sample analysis.
result Sharp characterization of high-dimensional ReLU regression problems via GLM-tron, contrasting with SGD.
Deep learning model solves high-dimensional PDEs using Actor-Critic approach.
problem Solving high-dimensional nonlinear PDEs efficiently.
method Reformulated PDE into BSDE system, inspired by Actor-Critic algorithm for deep RL.
result Improved model with fewer parameters, faster convergence, and less hyperparameter tuning.
Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization, and machine learning. Density Estimation is widely adopted in the domain of unsup…