New neural networks learn distribution functions using quantiles and moments.
problem Approximating functions of distributions in probability spaces.
method Quantile and moment neural networks, mixing quantile and moment features.
result Moment neural network outperforms others for bivariate distributions.
New algorithm solves mean-field control problems using actor-critic learning with moment neural networks.
problem Solving mean-field control problems in continuous time reinforcement learning.
method Gradient-based policy and value function learning with moment neural networks on the Wasserstein space.
result Effective solution for diverse mean-field control problems, including multi-dimensional and nonlinear settings.
TGNN combines GNN and SMM for better trading network predictions.
problem Predicting asset prices in trading networks with structural impact factors.
method Combines GNN and SMM for asset price prediction.
result TGNN outperforms existing methods in prediction accuracy.
Empower efficient representation of distributions through moment-preserving methods.
problem Representing high-dimensional probability measures efficiently and accurately.
method Empower efficient representation of distributions through moment-preserving methods.
result Empowers efficient and accurate representation of high-dimensional probability measures.
Machine learning models accurately predict molecular magnetic anisotropy tensors.
problem Accurately modeling molecular magnetic anisotropy tensors.
method Gaussian-moment neural-network approach for machine learning.
result Achieved accuracy of 0.3--0.4 cm−1 for magnetic anisotropy tensor predictions. New method improves estimation of complex models from conditional moment restrictions.
problem Estimation of complex models from conditional moment restrictions.
method Functional Generalized Empirical Likelihood (GEL) with a practical method.
result The method achieves state-of-the-art performance on two problems.
We introduce a novel approach, requiring only mild assumptions, for the characterization of deep neural networks at initialization. Our approach applies both to fully-connected and convolutional networks and easily incorporates batch normalization and skip-connections. Our key insight is to consider the evolution with …
Framework generates causal probabilities from observational data.
problem Generating causal probabilities from observational data.
method Moment-matching graph-networks for causal inference.
result Automated sampling of latent space conditional probability distributions.
Derives moments of PL networks for robust DNNs.
problem Analyzing robustness of DNNs to adversarial attacks.
method Derives exact analytic expressions for moments of PL networks, generalizes variance expression, and constructs sparse and smooth adversarial attacks.
result New variance expressions are tighter and can be efficiently approximated.
GANs learn distributions by matching low-degree moments.
problem Understanding when GANs learn the target distribution efficiently.
method Theoretical analysis and empirical observation of GAN training process.
result GANs can learn notable distributions by matching polynomially many low-degree moments.
Estimates high-dimensional posterior densities by marginal distributions and neural networks.
problem High-dimensional probability density estimation for inference is difficult.
method Direct estimation of lower-dimensional marginal distributions, using Moment Networks for fast computation of moments.
result Demonstrates estimation of gravitational wave time series and applications in cosmology.
New method uses geometric moments for accurate machine learning potentials.
problem Creating high-dimensional potential energy surfaces efficiently.
method Feed-forward neural networks with invariant local molecular descriptors based on geometric moments.
result Accuracy comparable to established models, high efficiency.
Novel neural network predicts electricity prices with higher moments.
problem Probabilistic forecasting of volatile electricity prices.
method Distributional neural network with a probability layer.
result Significantly outperforms benchmarks in forecasting.
Improved neural network models predict molecular and material properties efficiently.
problem Training neural networks for accurate interatomic potentials is computationally expensive.
method Gaussian moment-based neural networks with improved architecture and active learning.
result The new models achieve high accuracy and reduced training times.
New method improves robustness of neural network-based debiasing.
problem Improving robustness of neural network-based debiasing.
method Moment-constrained learning for neural networks.
result Improved performance compared to state-of-the-art benchmarks.
We propose a method of moments (MoM) algorithm for training large-scale implicit generative models. Moment estimation in this setting encounters two problems: it is often difficult to define the millions of moments needed to learn the model parameters, and it is hard to determine which properties are useful when specif…
A new framework for lightweight BNNs learns heteroscedastic uncertainties efficiently.
problem Learning heteroscedastic uncertainties from BNNs for lightweight networks.
method Embedding heteroscedastic variances into BNN parameters and using moment propagation for inference.
result Improves predictive performance for lightweight BNNs without increasing parameter count.
A new method for uncertainty estimation in neural networks using existing optimization steps.
problem Uncertainty quantification in deep neural networks.
method L2M: Practical posterior Laplace approximation with optimization-driven second moment estimation.
result L2M method yields reasonable results without requiring changes in models or extra computational steps.
A new neural network initialization method is proposed for faster and more accurate training.
problem Efficient initialization for training multi-layer feedforward neural networks.
method Initialization based on Stein's identity, using eigenvectors of cross-moment matrix.
result The SteinGLM method is faster and more accurate than other initialization methods.
We tackle causal inference under conditional moment restrictions using importance weighting.
problem Challenges in causal inference under conditional moment restrictions, especially in high-dimensional settings.
method Transform conditional moment restrictions to unconditional moment restrictions through importance weighting.
result Successfully estimate nonparametric functions defined under conditional moment restrictions.
New methods for uncertainty in neural networks with leaky ReLU activations.
problem Uncertainty in feed-forward neural networks with random input perturbations.
method Analytical expressions for PDF and moments of neural network output, linearization of leaky ReLU, Gaussian copula surrogate models.
result Accurate statistical results for large input perturbations, excellent agreement with Monte Carlo simulations.
Study how neural networks learn from non-Gaussian data models.
problem Understanding neural network learning dynamics with non-Gaussian data.
method Developed a two-layer neural network with Hermite polynomial activations to control high-order cumulants.
result Neural networks progressively learn high-order cumulants after capturing low-order statistics.
New bounds for neural networks without loss boundedness assumption.
problem Generalization error bounds for two-layer neural networks.
method Wasserstein distance estimates and moment bounds for stochastic gradient method.
result Dimension-free rate of order O(n−1/2) for independent test data. Paper provides unbiased spectral moment estimates from finite data.
problem Challenges in estimating spectral moments from limited data.
method Dynamic programming approach to estimate spectral moments of kernel integral operator.
result Demonstrates consistency with theoretical spectra and practical utility in neural networks.
To deepen our understanding of graph neural networks, we investigate the representation power of Graph Convolutional Networks (GCN) through the looking glass of graph moments, a key property of graph topology encoding path of various lengths. We find that GCNs are rather restrictive in learning graph moments. Without c…
The paper examines how the angle between inputs in ReLU networks decreases with depth, impacting training.
problem Depth degeneracy in neural networks, leading to constant function behavior on initialization.
method Combinatorial expansions and Monte Carlo experiments to analyze the angle between inputs in ReLU networks of increasing depth.
result The angle between inputs in ReLU networks decreases exponentially with depth, leading to constant function behavior on initialization.
The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature representations directly in the hidden activation space. Although some standard distributi…
A2-SBNN models spatial data with copulas for non-Gaussian dependencies.
problem Capturing complex spatial relationships and extreme dependencies in non-Gaussian data.
method Embedding A2 copula into a Bayesian neural network, trained with Wasserstein loss and moment matching.
result A2-SBNN consistently delivers high accuracy across various dependency strengths.
Paper develops methods for inference on time series data using neural networks and sieves.
problem Inference on time series data with nonparametric conditional moment restrictions.
method GN-QLR based inference using general nonlinear sieves and multilayer neural networks.
result Optimally weighted GN-QLR statistic is asymptotically Chi-square distributed.
Deep neural networks predict earthquake locations with high accuracy.
problem Predicting the location of earthquakes with high precision.
method Recurrent Convolutional Neural Networks (R-CNN) model that accounts for spatio-temporal dependencies.
result Neural networks model outperforms baseline models in predicting earthquakes with ROC AUC 0.975 and PR AUC 0.0890.
This paper examines how noise affects deep neural networks and improves their performance.
problem The impact of noise on the stability of deep ReLU neural networks for nonparametric regression.
method Investigates the optimal rate of convergence for deep ReLU neural networks under Huber loss, considering the p-th moment of noise and the smoothness of the function.
result The optimal rate of convergence cannot be achieved by ordinary least squares but can be by Huber loss with a properly chosen parameter.
Rotationally equivariant convolutions improve molecular property prediction.
problem Predicting molecular properties using graph neural networks.
method Ablation study with rotationally equivariant and invariant convolutions on QM9 data set.
result Rotationally equivariant layers decrease test error by an average of 23%.
New initialization schemes preserve fractional moments of weights in deep networks, improving training and test performance.
problem Heavy-tailed distribution of stochastic gradients in DNNs during training.
method Developed initialization schemes that preserve any given fractional moment of order s < 2 over layers for various activations.
result The network output admits a heavy-tailed distribution with finite moments, improving training and test performance.
Wide neural networks learn features under μP, identifying weights and decomposing support.
problem Feature learning in wide neural networks under μP. method Proving mean-field limit, characterizing identifiability, sparse-dictionary decomposition, and feature-learning-error decomposition.
result The triple (w∗,Dorb∗,S∗) identifies the natural learning cell of the architecture-data pair (σ,ρ). Paper presents a method to accurately quantify neural network uncertainty without sampling.
problem Uncertainty quantification in neural networks for reliability and robustness.
method Sample-free moment propagation technique for mean vectors and covariance matrices.
result Analytic solution for covariance of nonlinear activation functions.
We provide an approach for learning deep neural net representations of models described via conditional moment restrictions. Conditional moment restrictions are widely used, as they are the language by which social scientists describe the assumptions they make to enable causal inference. We formulate the problem of est…
The study finds dense clusters of solutions in a simple neural network model, providing bounds for their existence.
problem Exploring the existence of minimizers in a simple neural network model with binary weights.
method Formulating the learning problem as a constraint satisfaction problem and computing moment bounds for the existence of solutions.
result First rigorous steps toward proving the existence of dense clusters of solutions in certain parameter regimes.
Adaptive gradient methods such as Adam have been shown to be very effective for training deep neural networks (DNNs) by tracking the second moment of gradients to compute the individual learning rates. Differently from existing methods, we make use of the most recent first moment of gradients to compute the individual …
DML-CMR estimator reduces bias in CMR problems using deep neural networks.
problem Solving conditional moment restrictions with deep neural networks.
method Double/debiased machine learning framework for unbiased estimation.
result Achieves minimax optimal convergence rate of O(N−1/2). Optimal stock price prediction model using recurrent neural networks with RMSprop optimizer.
problem Stock price prediction using neural networks.
method Comparison of fully connected, convolutional, and recurrent architectures; inclusion of three optimization techniques.
result Single layer recurrent neural network with RMSprop optimizer produces optimal results with validation and test MAE of 0.0150 and 0.0148 respectively.
New algorithm recovers sparse measures in polynomial time.
problem Recovering sparse measures from Fourier moments.
method Polynomial-time recovery method inspired by mean-field theory.
result Improves upon convex relaxation methods in specific parameter regime.
GraphMoE generates random graphs using neural networks and graphlets.
problem Learning generative models for random graphs.
method GraphMoE uses a neural network trained with graphlets and subgraph counts to match the distribution of random graphs.
result GraphMoE can generate graphs that mimic various real-world datasets and fool graph classifiers.
A new method for estimating causal parameters from observables reduces the need for finite moment conditions.
problem Estimating causal parameters from observational data with unknown or infinite moment conditions.
method Variational Method of Moments (VMM) for a general class of estimators, including kernel and neural net-based methods.
result VMM estimators are consistent, asymptotically normal, and semiparametrically efficient.
We provide novel guaranteed approaches for training feedforward neural networks with sparse connectivity. We leverage on the techniques developed previously for learning linear networks and show that they can also be effectively adopted to learn non-linear networks. We operate on the moments involving label and the sco…
Training deep neural networks requires intricate initialization and careful selection of learning rates. The emergence of stochastic gradient optimization methods that use adaptive learning rates based on squared past gradients, e.g., AdaGrad, AdaDelta, and Adam, eases the job slightly. However, such methods have also …
SPIDER uses deep neural networks for streaming tensor factorization.
problem Lack of effective approach for deep tensor factorization of streaming data.
method Bayesian neural networks with spike-and-slab prior, Taylor expansions, moment matching, and EPI framework.
result Effective incremental updates for latent factors and NN weights.
Study heavy-tailed weights' impact on neural network's spectral distribution.
problem Analyzing spectral distribution of conjugate kernel matrices with heavy-tailed weights.
method Computed limiting eigenvalue distribution through moments, considering heavy-tailed distributions and nonlinear activation functions.
result Heavy-tailed weights induce strong correlations, leading to fundamentally different spectral behavior.
Improves Bayesian optimization for multi-fidelity functions.
problem Inefficient estimation of black-box functions due to ignored or oversimplified correlations between fidelities.
method Proposes DNN-MFBO using deep neural networks to capture complex relationships between fidelities.
result Shows significant improvement in optimization performance on synthetic and real-world datasets.