Stochastic neural networks can approximate any function, even with correlated outputs.
problem Approximating functions with stochastic outputs and correlations.
method Investigating deep sigmoid belief networks to approximate any stochastic mapping.
result Minimal number of layers and units needed for approximation.
A new method quantifies input model uncertainty in streaming data.
problem Quantifying input model uncertainty in streaming data.
method Two-layer importance sampling framework for online uncertainty quantification.
result Consistency and asymptotic convergence rate of the proposed algorithms.
ISAAC Newton uses input-based curvature for efficient training.
problem Efficient training in small-batch stochastic regimes.
method ISAAC Newton conditions gradients using selected second-order information based on input.
result Effective training even in small-batch stochastic regimes, competitive to first-order and second-order methods.
Paper derives an error bound for stochastic LTI systems.
problem Stochastic LTI systems with inputs in control engineering and econometrics.
method PAC-Bayesian-Like error bound derivation.
result Derived an error bound for stochastic LTI systems.
MF-GLaM models improve stochastic simulator emulation with multifidelity data.
problem Challenging to emulate stochastic simulators' full conditional probability distribution.
method Proposes MF-GLaMs to efficiently emulate HF stochastic simulators using LF data.
result MF-GLaMs achieve improved accuracy or comparable performance at reduced cost.
A method constructs a stochastic surrogate from dimensionality reduction results for high-dimensional uncertainty quantification.
problem High-dimensional uncertainty quantification with physics-based models.
method Constructs a stochastic surrogate model from dimensionality reduction results.
result Preserves convenience of sequential dimensionality reduction and Gaussian process regression while overcoming limitations.
Develops a new approach to optimal control of stochastic systems.
problem Optimal control of stochastic nonlinear dynamical systems is challenging.
method Formulates optimal control as input estimation, using probabilistic inference and Expectation Maximization.
result Extracts time-varying linear Gaussian feedback controllers from the joint state-action distribution.
The paper develops methods to analyze sensitivity in stochastic models using surrogate models.
problem Quantifying the impact of input variability on stochastic simulators with randomness.
method The authors propose using generalized lambda models to emulate response distributions of stochastic simulators and estimate sensitivity indices.
result The proposed method can estimate sensitivity indices even with strong heteroskedasticity and small signal-to-noise ratio.
Generative adversarial networks improve stochastic input parametrization in subsurface flow simulations.
problem Effective parametrization of high-dimensional, correlated stochastic inputs in subsurface flow simulations.
method Training a generative adversarial network to emulate the data generating process of stochastic inputs.
result Generative adversarial networks preserve both visual realism and high-order statistics of flow responses, achieving a significant dimensionality reduction.
When simulating a complex stochastic system, the behavior of output response depends on input parameters estimated from finite real-world data, and the finiteness of data brings input uncertainty into the system. The quantification of the impact of input uncertainty on output response has been extensively studied. Most…
Stochastic gradient descent based algorithms are typically used as the general optimization tools for most deep learning models. A Restricted Boltzmann Machine (RBM) is a probabilistic generative model that can be stacked to construct deep architectures. For RBM with Bernoulli inputs, non-Euclidean algorithm such as st…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input variables of the model. When the statistics of the output event are known, these input …
We introduce and analyze stochastic optimization methods where the input to each gradient update is perturbed by bounded noise. We show that this framework forms the basis of a unified approach to analyze asynchronous implementations of stochastic optimization algorithms.In this framework, asynchronous stochastic optim…
Proposes a new method to selectively access privileged information in reinforcement learning.
problem Selective compression of privileged information in reinforcement learning.
method Formulates a variational bandwidth bottleneck to decide stochastically whether to access privileged information.
result Improves generalization and reduces access to costly information in reinforcement learning experiments.
Deep learning models converge to Gaussian dynamics with mixed structured inputs.
problem Understanding neural network dynamics with complex input distributions.
method Extended hidden manifold model to Gaussian mixtures, analyzed via SGD.
result Learning dynamics with mixed inputs converge to Gaussian behavior.
We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a statistical inference framework that enables the end-to-end training of surrogat…
Paper introduces a new model to handle multi-task learning across different input domains.
problem Learning correlated tasks across varying input domains.
method Develops a novel heterogeneous stochastic variational linear model of coregionalization (HSVLMC) for multi-task learning.
result The proposed model outperforms existing models in diverse multi-task scenarios.
Paper proposes using generalized lambda distributions for stochastic simulators.
problem Uncertainty quantification with complex stochastic models is computationally challenging.
method Flexible generalized lambda distribution approximates response PDF, parameters are sparse polynomial chaos expansions.
result Local inference of response PDF at each point of experimental design using replicated model evaluations.
We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only use the definition of ReLU, in contrast with previous works that …
Stochastic gradient descent is the method of choice for large-scale machine learning problems, by virtue of its light complexity per iteration. However, it lags behind its non-stochastic counterparts with respect to the convergence rate, due to high variance introduced by the stochastic updates. The popular Stochastic …
Bayesian optimization improves performance with common random numbers.
problem Optimizing expensive stochastic functions with common random numbers.
method Proposes a novel Gaussian process model and Knowledge Gradient for Common Random Numbers.
result Significant performance improvements with moderate computational cost.
Neural network based generative models with discriminative components are a powerful approach for semi-supervised learning. However, these techniques a) cannot account for model uncertainty in the estimation of the model's discriminative component and b) lack flexibility to capture complex stochastic patterns in the la…
We present a probabilistic modeling framework and adaptive sampling algorithm wherein unsupervised generative models are combined with black box predictive models to tackle the problem of input design. In input design, one is given one or more stochastic "oracle" predictive functions, each of which maps from the input …
A novel method uses GPLFMs for joint input-state estimation in linear structural systems.
problem Combined state and input estimation of linear structural systems.
method Gaussian process latent force models (GPLFMs) combined with Kalman filters.
result GPLFMs outperform conventional Kalman filters in state and input estimation.
Nonlinear RNNs' memory capacity varies widely, making it impractical.
problem The usefulness of memory capacity as a metric for linear RNNs is questioned.
method Analysis of random nonlinear RNNs with varying input scales.
result Memory capacity of nonlinear RNNs is arbitrary and impractical.
Study robust control for systems with continuous states using adversarial perturbations.
problem Fragile policies in Markov control models under internal or external perturbations.
method Distributionally robust stochastic control with adaptive adversarial perturbations.
result Optimal robust policies for continuous state systems with uniform learning guarantees.
New framework models neural systems with random architecture on manifolds.
problem Complex, uncertain systems with non-Gaussian outputs.
method Latent random field on compact manifold generates neural architecture and weights.
result Synthetic neural systems can produce stochastic outputs for deterministic inputs.
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning scenarios. In this paper, we provide dynamic programming algorithms for the comput…
Proposes a new method to learn operators for stochastic problems using DeepONet with autoencoder.
problem Efficiently solve forward and inverse stochastic problems with limited data.
method MultiAuto-DeepONet, a multi-resolution autoencoder DeepONet model.
result The model effectively handles high-dimensional stochastic inputs and reduces the number of trainable parameters.
Neural networks learn faster with correlated latent variables.
problem Efficiently learning from higher-order correlations in neural networks.
method Analytical derivation and simulations of two-layer neural networks.
result Correlations between latent variables speed up learning from higher-order correlations.
A new method lifts training of input-convex neural networks to avoid dead weights and plateaued loss.
problem Training input-convex neural networks with non-negative weights.
method Introduces a hypernetwork that emits non-negative weights from a summary of the input batch, adding stochasticity to soften the loss landscape.
result The lift method achieves lower test loss than projected gradient descent and direct softplus reparametrization.
Vanilla SGD learns SIM from anisotropic data without explicit covariance estimation.
problem Learning SIM from anisotropic Gaussian inputs.
method Vanilla Stochastic Gradient Descent (SGD) trained on SIM with anisotropic input.
result Vanilla SGD adapts to anisotropic data's covariance structure.
Expands learning paradigm to stochastic orders using Choquet-Toland distance and Variational Dominance Criterion.
problem Learning high-dimensional distributions with stochastic orders.
method Introduces Choquet-Toland distance and Variational Dominance Criterion, uses input convex maxout networks (ICMNs).
result Proposes surrogates for Choquet-Toland distance and Variational Dominance Criterion with parametric rates.
We present a method to quantify uncertainty in the predictions made by simulations of mathematical models that can be applied to a broad class of stochastic, discrete, and differential equation models. Quantifying uncertainty is crucial for determining how accurate the model predictions are and identifying which input …
We consider reinforcement learning in input-driven environments, where an exogenous, stochastic input process affects the dynamics of the system. Input processes arise in many applications, including queuing systems, robotics control with disturbances, and object tracking. Since the state dynamics and rewards depend on…
Paper studies t-SNE convergence with generalized kernels.
problem Understanding convergence of t-SNE with generalized kernels.
method Concrete formulation of generalized kernels, proving convergence to an equilibrium distribution.
result t-SNE converges to an equilibrium distribution under certain conditions for generalized kernels.
Study on estimating unstable open-loop matrices from state trajectories.
problem System identification for stochastic continuous-time dynamics.
method Employing randomized control inputs to estimate unstable open-loop matrix.
result Estimation error decays with trajectory length, signal-to-noise ratio, and excitability.
Paper tackles active labeling for partial supervision.
problem Accessing stochastic gradients with partial supervision.
method Streaming technique to minimize generalization error.
result Proves minimization of generalization error ratio.
GANs improve stochastic parameterization of the Lorenz '96 model.
problem Improving stochastic parameterizations for sub-grid processes.
method Developed a GAN-based stochastic parameterization for the Lorenz '96 model.
result GAN configurations outperform a bespoke parameterization in skillful forecasts and climate simulations.
A new method for high-dimensional RBDO using stochastic emulators.
problem Efficient RBDO in high-dimensional settings.
method Unified stochastic representation, stochastic emulators, deterministic mapping.
result Significant computational gains in high-dimensional settings.
We introduce a new model of stochastic bandits with adversarial corruptions which aims to capture settings where most of the input follows a stochastic pattern but some fraction of it can be adversarially changed to trick the algorithm, e.g., click fraud, fake reviews and email spam. The goal of this model is to encour…
The paper quantifies and attributes uncertainty in complex system simulations.
problem Uncertainty in complex system simulations due to unknown or approximated subprocesses.
method Developed a framework for quantifying and attributing submodel uncertainty using bootstrapping, Bayesian model averaging, and tree-based methods.
result Individual submodels contribute to overall uncertainty, and their importance can be quantified.
In this article, we consider a stochastic numerical simulator to assess the impact of some factors on a phenomenon. The simulator is seen as a black box with inputs and outputs. The quality of a simulation, hereafter referred to as fidelity, is assumed to be tunable by means of an additional input of the simulator (e.g…
Noise in RNNs promotes flatter minima and more stable dynamics.
problem Understanding and optimizing the training of RNNs with noise.
method Formalizing RNNs as stochastic differential equations and analyzing the effect of noise in the hidden states.
result Noise injection in RNNs leads to flatter minima, more stable dynamics, and improved robustness.
State-space systems generate probabilistic dependencies between inputs and outputs.
problem Understanding probabilistic dependencies in state-space systems.
method Introducing a probabilistic framework and proving sufficient conditions for output existence and uniqueness.
result State-space systems can generate probabilistic dependencies, even without functional relations.
This paper tackles reliability analysis for stochastic systems using surrogate models.
problem Traditional reliability analysis relies on deterministic models, which are not suitable for stochastic systems with non-repeatable outcomes.
method The paper introduces reliability analysis for stochastic models by using generalized lambda models and stochastic polynomial chaos expansions as surrogate models to lower computational cost.
result The surrogate models enable efficient uncertainty quantification at a lower cost than traditional Monte Carlo simulation.
This thesis investigates unsupervised time series representation learning for sequence prediction problems, i.e. generating nice-looking input samples given a previous history, for high dimensional input sequences by decoupling the static input representation from the recurrent sequence representation. We introduce thr…
Conditional Leibniz Derivative Estimation reduces variance in stochastic models.
problem Estimating derivatives in stochastic models with discontinuous sample performance.
method Combining push-out likelihood ratio method with Leibniz integral rules.
result Conditional Leibniz estimator reduces variance and is easy to implement.