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.
ResiliNet improves distributed neural network inference resilience.
problem Physical node failures in distributed neural networks cause performance drops.
method Skip hyperconnection and failout technique.
result ResiliNet provides inference resiliency for distributed neural networks.
Paper develops neural network for distribution regression.
problem Regression with probability measures.
method Develops a novel fully connected neural network (FNN) for distribution inputs.
result Almost optimal learning rates for distribution regression derived.
VAEs and GANs use simple distributions and neural networks to implicitly approximate complex data distributions.
problem Approximating high-dimensional complex distributions explicitly is often intractable.
method VAEs and GANs use simple base distributions and neural networks to implicitly approximate complex distributions.
result Implicit approximation of complex distributions is crucial but introduces limitations, especially in VAEs with fixed Gaussian priors.
Introduces NQ network for non-crossing quantile learning.
problem Quantile crossing issue in distributional learning.
method Non-negative activation functions ensure monotonic distributions.
result Effective for distributional reinforcement learning and causal effect estimation.
Deep networks can approximate high-dimensional distributions from low-dimensional ones.
problem Approximating high-dimensional distributions from low-dimensional ones.
method Proved neural networks can transform low-dimensional distributions to high-dimensional ones with arbitrary closeness measured by Wasserstein distances and maximum mean discrepancy.
result Upper bounds of the approximation error are obtained in terms of the width and depth of neural network.
We investigate the wealth evolution in a system of agents that exchange wealth through a disordered network in presence of an additive stochastic Gaussian noise. We show that the resulting wealth distribution is shaped by the degree distribution of the underlying network and in particular we verify that scale free netw…
Deep neural networks can generate any 2D distribution with high accuracy.
problem Generating accurate high-dimensional distributions from random noise.
method A deep neural network with a space-filling property of sawtooth functions.
result The network can approximate any 2D Lipschitz-continuous distribution arbitrarily closely.
A distributed algorithm for training graph convolutional networks.
problem Training graph convolutional networks with sparse network topology and distributed agents.
method Formulate inference and optimization in a distributed scenario, propose a gradient descent procedure, and design communication topology.
result Convergence to stationary solutions of the GCN training problem under mild conditions.
Method learns conditional distributions using neural entropic optimal transport.
problem Challenges in learning multiple conditional distributions.
method Neural entropic optimal transport method with two networks and regularization.
result Effective learning of conditional distributions with limited samples.
HyperVAE encodes distributions of distributions using variational inference.
problem Modeling distributions of distributions efficiently and preserving information.
method Variational inference with Gaussian mixture models and matrix-network decoders.
result HyperVAE encodes parameters of a VAE in a low-dimensional Gaussian distribution, preserving more information.
TDistNNs improve prediction intervals for neural networks by using t-distributions.
problem Traditional neural networks provide only point estimates, lacking predictive uncertainty.
method TDistNNs generate t-distributed outputs with adjustable degrees of freedom, enhancing robustness to non-Gaussian data.
result TDistNNs produce narrower prediction intervals with proper coverage compared to Gaussian-based PNNs.
This paper investigates the ability of generative networks to convert their input noise distributions into other distributions. Firstly, we demonstrate a construction that allows ReLU networks to increase the dimensionality of their noise distribution by implementing a "space-filling" function based on iterated tent ma…
We show, analytically and numerically, that wealth distribution in the Bouchaud-Mézard network model of the economy is described by a three-parameter generalized inverse gamma distribution. In the mean-field limit of a network with any two agents linked, it reduces to the inverse gamma distribution.
Analyzes geodesic lengths in sparse networks, deriving a distribution.
problem Understanding connectivity and robustness in networked systems.
method Analytic derivation of geodesic length distribution in sparse networks.
result Simple closed-form expression for geodesic length distribution.
Hardness proven for neural networks with natural weights.
problem Difficulty in learning neural networks with weights from natural distributions.
method Proved hardness for depth-2 networks with natural weights distributions.
result Most networks are hard to learn with natural weights.
Modern neural networks are very powerful predictive models, but they are often incapable of recognizing when their predictions may be wrong. Closely related to this is the task of out-of-distribution detection, where a network must determine whether or not an input is outside of the set on which it is expected to safel…
DRN improves actuarial distributional forecasting with interpretable neural networks.
problem Challenges in modeling loss distributional properties with classic methods.
method Combines GLMs with a modified DDR method to flexibly refine baseline distribution.
result DRN improves predictive performance while maintaining interpretability.
Stable processes emerge as limits of deep neural networks with symmetric stable distributions.
problem Understanding the behavior of deep neural networks as they become infinitely wide.
method Analyzing fully connected feed-forward deep neural networks with symmetric stable distributions and showing the limit as a stable process.
result The infinite wide limit of the network is a stable process with multivariate stable distributions.
We study the mixtures of factorizing probability distributions represented as visible marginal distributions in stochastic layered networks. We take the perspective of kernel transitions of distributions, which gives a unified picture of distributed representations arising from Deep Belief Networks (DBN) and other netw…
We study the wealth distribution of the Bouchaud--Mézard (BM) model on complex networks. It has been known that this distribution depends on the topology of network by numerical simulations, however, no one have succeeded to explain it. Using "adiabatic" and "independent" assumptions along with the central-limit theore…
MEP-Net uses MEP to generate solutions from limited data.
problem Generating solutions to scientific problems with incomplete information.
method Combines MEP with neural networks to learn complex distributions from moment constraints.
result Demonstrates MEP-Net's effectiveness in modeling biochemical reaction networks and generating complex distributions.
New method uses extreme value theory to estimate neural network errors.
problem Quantifying the error of neural networks, especially for large values.
method Applying extreme value theory to approximate the distribution of error.
result Developed a new estimator for the shape parameter of the Pareto distribution.
This work develops secure distributed algorithms for machine learning to protect against data poisoning and network attacks.
problem Vulnerability of distributed machine learning algorithms to cyber threats.
method Game-theoretic framework to capture conflicting goals of a learner and an attacker, iterative distributed algorithm.
result Distributed SVM is prone to fail in different types of attacks, with impact depending on network structure and attack capabilities.
FDN improves probabilistic regressors' adaptability to distribution shifts.
problem Overconfidence in modern probabilistic regressors under distribution shift.
method FDN uses input-conditioned distributions over network weights, trained with a Monte Carlo beta-ELBO objective.
result FDN produces predictive mixtures whose dispersion adapts to the input, providing shift-aware uncertainty.
A new distributed method for convex optimization over networks with fast convergence.
problem Large-scale convex optimization over networks with limited communication.
method Distributed cubic-regularized Newton method.
result Convergence rate of O(k−3) for convex functions with Lipschitz gradient and Hessian. New model for detecting communities in weighted bipartite networks.
problem No model for community detection in overlapping bipartite weighted networks.
method Introduces BiMMDF model allowing any distribution with block structure.
result Efficient algorithm with theoretical guarantee of consistent estimation.
Deep neural networks forecast financial return distributions accurately.
problem Forecasting probability distributions of financial returns.
method Used 1D CNN and LSTM architectures with custom loss functions to optimize distribution parameters.
result LSTM with skewed Student's t distribution outperformed classical models in multiple evaluation metrics.
There is emerging interest in performing regression between distributions. In contrast to prediction on single instances, these machine learning methods can be useful for population-based studies or on problems that are inherently statistical in nature. The recently proposed distribution regression network (DRN) has sh…
Paper finds how many neurons are needed to approximate histogram distributions.
problem How many neurons are needed to approximate a target probability distribution?
method Examined for uniform input distribution and histogram target distributions, using efficient neural net construction.
result Obtained a new upper bound on the number of required neurons, strictly better than previous bounds.
New findings show learning deeper neural networks is hard even with Gaussian inputs and non-degenerate weights.
problem The computational complexity of learning neural networks, especially deeper ones.
method Smoothed analysis framework and local pseudorandom generators.
result Learning depth-3 ReLU networks under Gaussian input distribution is hard even if weight matrices are non-degenerate.
Deep neural networks converge to Gaussian mixtures as layer width increases.
problem Understanding the distribution of outputs from deep neural networks.
method Proof and experiments with a simple model showing the convergence of neural network outputs to Gaussian mixtures.
result Neural networks converge to Gaussian mixtures as the width of the last hidden layer increases.
Forecast stock return distributions using neural networks.
problem Accurately modeling non-Gaussian stock return features.
method Two-stage quantile neural network with spline interpolation.
result Improved mean and variance forecasts compared to standard models.
We propose a new \cu{class-optimal} algorithm for the distributed computation of Wasserstein Barycenters over networks. Assuming that each node in a graph has a probability distribution, we prove that every node can reach the barycenter of all distributions held in the network by using local interactions compliant with…
Neural network MCMC sampler maximizes proposal entropy for efficient sampling.
problem Inefficient sampling from complex probability distributions.
method Proposes a neural network MCMC sampler that maximizes proposal entropy.
result Significantly higher efficiency in various sampling tasks.
This paper improves dependency networks using information geometry.
problem Technical disadvantage in dependency networks' learned distribution.
method Interpret pseudo-Gibbs sampling as iterative m-projections onto manifolds.
result Dependency networks can learn faster and have similar performance to Bayesian networks.
GANs learn distributions well from samples, with rates depending on intrinsic dimension.
problem Learning distributions from samples using GANs.
method Oracle inequality, Hölder functions approximation, neural network approximation, integral probability metrics.
result Convergence rates of GANs depend on intrinsic dimension, not ambient dimension.
Deep neural networks can approximate any target probability distribution given certain conditions.
problem Approximating complex probability distributions with deep neural networks.
method Proving the existence of a deep neural network mapping that approximates a target distribution under various integral probability metrics.
result Upper bounds on the size of the neural network in terms of dimension and approximation error for different metrics.
SFSVI uses Gaussian mixtures to approximate neural network outputs for continual learning.
problem Learning new tasks without forgetting old ones in neural networks.
method Sequential function-space variational inference with Gaussian mixture approximation.
result Gaussian mixture SFSVI outperforms other methods in continual learning.
The paper proposes a neural network architecture inspired by Langevin Monte Carlo for sampling from target distributions.
problem Sampling from complex target distributions efficiently.
method A neural network architecture inspired by Langevin Monte Carlo is proposed to map samples from a simple reference distribution to samples from the target.
result The proposed neural network architecture achieves approximation rates in the Wasserstein-2 distance for smooth, log-concave target distributions.
The paper develops a learning algorithm for distributed training and inference in wireless networks.
problem Challenges of leveraging machine learning in highly distributed wireless networks.
method Developed a learning algorithm and architecture for distributed training and inference.
result Inference propagates and fuses across a network, with benefits over state-of-the-art techniques.
New neural network captures spatial correlations in wind speed predictions.
problem Uncertainty quantification in neural network predictions for high-dimensional, correlated data.
method Training neural networks with multidimensional Gaussian loss, preserving spatial correlation and computational tractability.
result Demonstrated super-resolution of surface wind speed with explicit correlation modeling.
Extends uncertainty detection in neural networks to finer distinctions.
problem Detecting finer distinctions between certain, uncertain, and out-of-distribution points.
method Two-step approach: first builds class distribution using Kernel Activation Vectors, second determines test point confidence.
result Corrects overconfident NN decisions and learns to say 'I don't know' when uncertain.
Fog learning distributes ML model training across heterogeneous devices and networks.
problem Challenges with conventional federated learning in heterogeneous networks.
method Intelligent distribution of ML model training across nodes from edge devices to cloud servers.
result Enhanced federated learning with multi-layer hybrid framework considering network, heterogeneity, and proximity.
Precise estimation of uncertainty in predictions for AI systems is a critical factor in ensuring trust and safety. Deep neural networks trained with a conventional method are prone to over-confident predictions. In contrast to Bayesian neural networks that learn approximate distributions on weights to infer prediction …
Paper tackles distribution matching by partially matching distributions, achieving robust results.
problem Robustly aligning two probability distributions.
method Developed a partial Wasserstein adversarial network (PWAN) to efficiently approximate the partial Wasserstein-1 (PW) discrepancy.
result The PWAN effectively produces highly robust matching results, outperforming state-of-the-art methods.
Ensemble approaches for uncertainty estimation have recently been applied to the tasks of misclassification detection, out-of-distribution input detection and adversarial attack detection. Prior Networks have been proposed as an approach to efficiently \emph{emulate} an ensemble of models for classification by paramete…
The increasing quantity of PV generation connected to distribution networks is creating challenges in maintaining and controlling voltages in those distribution networks. Determining the maximum hosting capacity for new PV installations based on the historical data is an essential task for distribution networks. Analyz…