Related papers: Embedding stochastic differential equations into n…
Stochastic differential equations are widely used in various fields; in particular, the usefulness of duality relations has been demonstrated in some models such as population models and Brownian momentum processes. In this study, a…
Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…
We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…
Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood…
In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in…
Neural processes (NPs) constitute a family of variational approximate models for stochastic processes with promising properties in computational efficiency and uncertainty quantification. These processes use neural networks with latent…
Ensemble weather predictions require statistical post-processing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian belief networks. By imposing additional assumptions about the nature of the probabilistic models represented in the belief networks, we derive…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural…
We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…
In neural networks with binary activations and or binary weights the training by gradient descent is complicated as the model has piecewise constant response. We consider stochastic binary networks, obtained by adding noises in front of…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are…
Probabilistic neural networks are typically modeled with independent weight priors, which do not capture weight correlations in the prior and do not provide a parsimonious interface to express properties in function space. A desirable class…
We propose a novel deep neural network (DNN) based approximation architecture to learn estimates of measurements. We detail an algorithm that enables training of the DNN. The DNN estimator only uses measurements, if and when they are…
Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality.…
Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…
To model time series accurately is important within a wide range of fields. As the world is generally too complex to be modelled exactly, it is often meaningful to assess the probability of a dynamical system to be in a specific state. This…
Dynamic DNN optimization techniques such as layer-skipping offer increased adaptability and efficiency gains but can lead to i) a larger memory footprint as in decision gates, ii) increased training complexity (e.g., with non-differentiable…