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Model Predictive Control (MPC) is an optimal control algorithm with strong stability and robustness guarantees. Despite its popularity in robotics and industrial applications, the main challenge in deploying MPC is its high computation…

In this paper, we propose the Adaptive Physics-Informed Neural Networks (APINNs) for accurate and efficient simulation-free Bayesian parameter estimation via Markov-Chain Monte Carlo (MCMC). We specifically focus on a class of parameter…

Model counting is a fundamental problem that consists of determining the number of satisfying assignments for a given Boolean formula. The weighted variant, which computes the weighted sum of satisfying assignments, has extensive…

Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…

Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning framework based on deterministic number-theoretic sampling…

This survey article is concerned with the application of lattice rules to Deep Neural Networks (DNNs), lattice rules being a family of quasi-Monte Carlo methods. They have demonstrated effectiveness in various contexts for high-dimensional…

In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…

Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…

Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…

Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…

With the rapid advancement in the performance of deep neural networks (DNNs), there has been significant interest in deploying and incorporating artificial intelligence (AI) systems into real-world scenarios. However, many DNNs lack the…

Learning-based model predictive control (MPC) is an approach designed to reduce the computational cost of MPC. In this paper, a constrained deep neural network (DNN) design is proposed to learn MPC policy for nonlinear systems. Using…

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…

Approximate Bayesian Computation (ABC) methods are increasingly used for inference in situations in which the likelihood function is either computationally costly or intractable to evaluate. Extensions of the basic ABC rejection algorithm…

In the following article we consider approximate Bayesian parameter inference for observation driven time series models. Such statistical models appear in a wide variety of applications, including econometrics and applied mathematics. This…

The discovery of causal relationships is a foundational problem in artificial intelligence, statistics, epidemiology, economics, and beyond. While elegant theories exist for accurate causal discovery given infinite data, real-world…

We describe a quantum PAC learning algorithm for DNF formulae under the uniform distribution with a query complexity of $\tilde{O}(s^{3}/\epsilon + s^{2}/\epsilon^{2})$, where $s$ is the size of DNF formula and $\epsilon$ is the PAC error…

Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often…

Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…