MPE framework proves universal approximation for quantum data distribution.
problem Challenges in generating quantum data from underlying distributions.
method Many-body Projected Ensemble (MPE) framework for quantum state design.
result MPE can approximate any quantum distribution within 1-Wasserstein distance error.
Study symmetry breaking in quantum mechanics to understand many-body physics.
problem Understanding many-body physics from quantum mechanics.
method Analyzing potentials with unstable critical points and local minima.
result Emergence of many-body physics from spontaneous symmetry breaking.
New MBL hidden Born machine learns various tasks.
problem Learning from quantum many-body systems.
method MBL dynamics and hidden units for training.
result Enhanced trainability and stability in learning.
A new ensemble method using random projections for kNN classification.
problem Improving kNN classification accuracy through ensemble methods.
method Random projection of bootstrap samples into lower dimensions, using extended neighbourhood rule for base learners.
result Enhanced classification accuracy compared to traditional kNN and other ensembles.
Dataset of Bose-Einstein condensates images aids ML in many-body physics.
problem Understanding solitons in Bose-Einstein condensates.
method Machine learning (ML) framework with convolutional neural networks and physics-informed classifiers.
result Automatic labeling of solitonic excitations in experimental images.
New method interprets quantum many-body snapshots for phase detection.
problem Classifying phases of matter from quantum simulations.
method Confusion learning with correlation convolutional neural networks.
result Network detects changes in thermodynamic properties of quantum systems.
Diverse projection ensembles improve distributional reinforcement learning.
problem Learning the distribution of returns in reinforcement learning.
method Combining multiple projection methods to improve model diversity and exploration.
result Diverse projection ensembles lead to significant performance improvements in exploration tasks.
CE improves climate uncertainty quantification using GCM ensembles and observational data.
problem Uncertainty in climate projections due to model inadequacies and variability.
method Conformal ensembles integrating GCM ensembles and observational data.
result CE generates statistically rigorous, easy-to-interpret uncertainty estimates.
K-nearest neighbor (kNN) search has wide applications in many areas, including data mining, machine learning, statistics and many applied domains. Inspired by the success of ensemble methods and the flexibility of tree-based methodology, we propose random projection forests (rpForests), for kNN search. rpForests finds …
The paper analyzes an ensemble of randomly projected linear discriminants for high-dimensional data.
problem Classification issues in small samples of high-dimensional data.
method Asymptotic analysis using random matrix theory.
result The ensemble offers a performance advantage under certain conditions.
A new framework for dimension reduction using ensemble of random projections.
problem High-dimensional regression problems with limited data.
method Aggregating an ensemble of carefully chosen random projections, retaining based on empirical performance, and selecting singular vectors.
result The proposed method stabilizes error as the number of projection groups increases.
Bayesian Neural Networks improve geophysical model ensembles with reduced uncertainty.
problem Improving geophysical model projections and uncertainty quantification.
method Developed a Bayesian Neural Network ensemble strategy for geophysical models.
result Bayesian Neural Network ensemble outperforms existing methods in ozone prediction.
A new method for decomposing non-negative tensors using energy-based modeling.
problem Challenges in traditional tensor decomposition methods, especially global optimization and rank selection.
method Energy-based modeling of tensors, considering interactions between modes for global optimization.
result Demonstrates effectiveness in tensor completion and approximation, revealing a relationship between many-body and low-rank approximations.
The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent that TNs can be used for machine learning. Previous results used one-dimensional T…
Bayesian inference learns free energy landscapes from experimental data.
problem Characterize the free energy landscape of classical many-body systems from experimental data.
method Combines non-parametric Bayesian inference with physically-motivated constraints to automate the construction of approximate free energy functionals.
result Inference algorithms yield a probability distribution over free energy functionals, leading to highly accurate analytic expressions.
We discuss possible relationships between geometric and topological interactions on one side and physical interactions on the other side.
Enhash detects concept drift in data streams quickly and efficiently.
problem Detecting abrupt, gradual, virtual, or recurring events in data streams.
method Uses projection hash to insert incoming samples and detects concept drift.
result Enhash has competitive performance and moderate resource requirements compared to existing ensemble learners.
Tensor network (TN) has recently triggered extensive interests in developing machine-learning models in quantum many-body Hilbert space. Here we purpose a generative TN classification (GTNC) approach for supervised learning. The strategy is to train the generative TN for each class of the samples to construct the class…
The restricted Boltzmann machine (RBM) is one of the fundamental building blocks of deep learning. RBM finds wide applications in dimensional reduction, feature extraction, and recommender systems via modeling the probability distributions of a variety of input data including natural images, speech signals, and custome…
Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are investigated; a representation in terms of Legendre polynomials is found to be superior due…
Defines products for fibered corners manifolds, generalizing resolutions.
problem Resolving fibered corners manifolds.
method Introduces a category of fibered corners manifolds with products and transverse fiber products, defining the 'ordered product' for wedge metrics.
result The 'ordered product' is a natural product for wedge metrics.
TEC combines multiple RPSTMs to classify big tensors efficiently.
problem Tensor classification for big data applications.
method Tensor Ensemble Classifier (TEC) using Random Projection-based Support Tensor Machine (RPSTM).
result TEC provides statistically consistent predictions with reduced computational cost.
New theory shows how multi-head attention reduces variance and decorrelates outputs.
problem Understanding and optimizing multi-head attention in neural networks.
method Developed a statistical theory linking multi-head attention to ensemble Nadaraya-Watson estimators.
result MHA variance reduction depends on head decorrelation, not just head count.
Develops a framework for analyzing multi-agent and many-body systems with feedback loops.
problem Optimal order of multi-agent and general many-body systems
method Derive macroscopic properties and optimal degree of order
result Optimal degree of order balances productivity, stability, and adaptability
Research proposes an ensemble learning model for efficient software defect prediction.
problem Efficient and cost-effective software testing to minimize project resources.
method Machine learning analysis on different datasets using KNN, Decision Tree, SVM, and Naïve Bayes.
result Ensemble learning model outperforms other techniques in accuracy, precision, recall, and F1-score.
Theory and method for reducing prediction variance in noisy feature-subsampled ridge ensembles.
problem Reduction of prediction variance in noisy data with feature bagging.
method Developed analytical learning curves for noisy ridge ensembles, introduced heterogeneous feature ensembling.
result Subsampling shifts the double-descent peak, leading to improved performance over a single linear predictor.
Multi-label classification has attracted an increasing amount of attention in recent years. To this end, many algorithms have been developed to classify multi-label data in an effective manner. However, they usually do not consider the pairwise relations indicated by sample labels, which actually play important roles i…
Improved disability insurance model with collective health claims.
problem Enhance disability insurance model with collective health claims.
method Expand classic semi-Markov model with collective health claims, solve many-body problem using mean-field approach.
result Mean-field approach simplifies complex model into a transparent pricing method.
Computing equilibrium states in condensed-matter many-body systems, such as solvated proteins, is a long-standing challenge. Lacking methods for generating statistically independent equilibrium samples in "one shot", vast computational effort is invested for simulating these system in small steps, e.g., using Molecular…
A new graph model HMG and neural network HMGNN improve molecule property predictions.
problem Predicting quantum mechanical properties of molecules with limited consideration of many-body interactions.
method Introducing heterogeneous molecular graphs (HMG) and building HMGNN on neural message passing scheme.
result HMGNN achieves state-of-the-art performance in 9 out of 12 tasks on the QM9 dataset.
Graph Prolongation Convolutional Networks improve model performance in microtubule bending simulations.
problem Improving prediction accuracy in coarse-grained mechanochemical simulations of microtubule bending.
method Defines a novel ensemble Graph Convolutional Network model using optimized linear projection operators to map between graph scales.
result Graph Prolongation-Convolutional Network outperforms other GCN ensemble models in predicting microtubule bending potential energy.
Recent advances show that deep neural networks are not robust to deliberately crafted adversarial examples which many are generated by adding human imperceptible perturbation to clear input. Consider l2 norms attacks, Project Gradient Descent (PGD) and the Carlini and Wagner (C\&W) attacks are the two main methods, …
Expected centre of mass for random embeddings is constant.
problem Understanding the expected centre of mass for random embeddings.
method Analyzing the Haar measure and Gaussian unitary ensemble on SL(N, C).
result The expectation of the centre of mass is a constant multiple of the identity matrix.
KOD detects outliers in high-dimensional data.
problem Challenges in outlier detection in high-dimensional settings.
method Kernel transformation followed by projection pursuit approach with ensemble of directions and result combination.
result Empirical evaluations show effectiveness on various datasets.
A brief review is given of the minority game, an idealized model stimulated by a market of speculative agents, and its complex many-body behaviour. Particular consideration is given to analytic results for the model rather than discussions of its relevance in real-world situations.
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In classification problems there are two general techniques using random projections. T…
We present a machine learning approach to the inversion of Fredholm integrals of the first kind. The approach provides a natural regularization in cases where the inverse of the Fredholm kernel is ill-conditioned. It also provides an efficient and stable treatment of constraints. The key observation is that the stabili…
Neural network models colloidal particle dynamics in non-equilibrium systems.
problem Analyzing non-equilibrium dynamics of many-body colloidal systems.
method Combining power functional theory and machine learning, training a neural network to predict internal force fields.
result The neural network accurately predicts dynamics in non-equilibrium systems, in good agreement with simulations.
New method uses kernel methods to approximate ground states of quantum Hamiltonians efficiently.
problem Approximating ground states of quantum Hamiltonians using neural networks is computationally expensive.
method Introduces a statistical learning approach using kernel methods to make optimization trivial.
result Ground state properties of arbitrary gapped quantum Hamiltonians can be reached with polynomial resources.
This paper surveys various methods for dimensionality reduction and nearest neighbor search.
problem Efficiently reducing high-dimensional data to lower dimensions while preserving essential information.
method Linear and nonlinear random projections, including sparse random projections, random Fourier Features, and Random Kitchen Sinks.
result Various methods for dimensionality reduction and nearest neighbor search are explained and compared.
Recently, the binary expansion testing framework was introduced to test the independence of two continuous random variables by utilizing symmetry statistics that are complete sufficient statistics for dependence. We develop a new test based on an ensemble approach that uses the sum of squared symmetry statistics and di…
NN-GPR improves climate model predictions by preserving fine-scale spatial information.
problem Dilution of fine-scale spatial information and bias in model averaging.
method Gaussian process regression with an infinitely wide deep neural network.
result NN-GPR produces more accurate and detailed climate projections.
We adapt the idea of random projections applied to the output space, so as to enhance tree-based ensemble methods in the context of multi-label classification. We show how learning time complexity can be reduced without affecting computational complexity and accuracy of predictions. We also show that random output spac…
Equivariant flows generate symmetric distributions for complex systems.
problem Generating symmetric distributions for complex systems with exact likelihood.
method Equivariant normalizing flows that preserve symmetries.
result Equivariant flows generate symmetric distributions that are invariant to symmetries in physical systems.
RBM and DBM are represented as 2D tensor networks, revealing their expressive power and efficiency.
problem Understanding and optimizing RBM and DBM models.
method Representing RBM and DBM as 2D tensor networks and developing an efficient tensor network contraction algorithm.
result The proposed algorithm for computing partition functions is more accurate than state-of-the-art methods.
No free lunch theorem formalized for tensor network models.
problem Understanding limitations of tensor network machine learning models.
method Formalized rigorous no-free-lunch theorem for specific tensor network models.
result Revealed intrinsic limitations of tensor network-based learning models.
Study improves precipitation predictions for High Mountain Asia using machine learning.
problem Uncertainty in future precipitation over High Mountain Asia due to regional climate model biases.
method Probabilistic machine learning framework combining 13 regional climate models via a mixture of experts.
result 32% improvement over equally-weighted average and 254% improvement over single ensemble member.
ControlBurn selects few features from tree ensembles for better model interpretability.
problem Improving model interpretability in machine learning models.
method Sparse tree ensembles with lasso optimization.
result ControlBurn selects feature-sparse subsets for better model interpretability.