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Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…
We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…
We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
We present an efficient Monte Carlo algorithm for the simulation of the two-dimensional Random Field Ising Model (RFIM). The method combines the event-driven, rejection-free character of the Bortz Kalos-Lebowitz (BKL) algorithm with Glauber…
The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties…
Probabilistic models based on Restricted Boltzmann Machines (RBMs) imply the evaluation of normalized Boltzmann factors, which in turn require from the evaluation of the partition function Z. The exact evaluation of Z, though, becomes a…
Sampling Boltzmann probability distributions plays a key role in machine learning and optimization, motivating the design of hardware accelerators such as Ising machines. While the Ising model can in principle encode arbitrary optimization…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
We propose a novel multi-dimensional integration algorithm using a machine learning (ML) technique. After training a ML regression model to mimic a target integrand, the regression model is used to evaluate an approximation of the integral.…
We present herein a scheme by which to accurately evaluate the error exponents of a lossy data compression problem, which characterize average probabilities over a code ensemble of compression failure and success above or below a critical…
Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the…
This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that…
Uncertainty is ubiquitous in real-world data, and the assumptions underlying classical linear regression models are often violated in practice. Inspired by the theory of sublinear expectation, we consider a linear regression model where the…
We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte…
Concept Bottleneck Models (CBMs) map the black-box visual representations extracted by deep neural networks onto a set of interpretable concepts and use the concepts to make predictions, enhancing the transparency of the decision-making…
Recently, adversarial imitation learning has shown a scalable reward acquisition method for inverse reinforcement learning (IRL) problems. However, estimated reward signals often become uncertain and fail to train a reliable statistical…
The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard…
The restricted Boltzmann machine (RBM) is a flexible tool for modeling complex data, however there have been significant computational difficulties in using RBMs to model high-dimensional multinomial observations. In natural language…