Related papers: Machine learning approach to inverse problem and u…

We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…

In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…

Machine unlearning aims to solve the problem of removing the influence of selected training examples from a learned model. Despite the increasing attention to this problem, it remains an open research question how to evaluate unlearning in…

Machine unlearning, an emerging research topic focusing on compliance with data privacy regulations, enables trained models to remove the information learned from specific data. While many existing methods indirectly address this issue by…

Employing machine learning models in the real world requires collecting large amounts of data, which is both time consuming and costly to collect. A common approach to circumvent this is to leverage existing, similar data-sets with large…

Transfer reinforcement learning (RL) methods leverage on the experience collected on a set of source tasks to speed-up RL algorithms. A simple and effective approach is to transfer samples from source tasks and include them into the…

In real word applications, data generating process for training a machine learning model often differs from what the model encounters in the test stage. Understanding how and whether machine learning models generalize under such…

We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching…

Human inertial thinking schemes can be formed through learning, which are then applied to quickly solve similar problems later. However, when problems are significantly different, inertial thinking generally presents the solutions that are…

Unfolding, in the context of high-energy particle physics, refers to the process of removing detector distortions in experimental data. The resulting unfolded measurements are straightforward to use for direct comparisons between…

Methodologies for training machine learning potentials (MLPs) to quantum-mechanical simulation data have recently seen tremendous progress. Experimental data has a very different character than simulated data, and most MLP training…

We introduce a significant improvement for a relatively new machine learning method called Transformation-Based Learning. By applying a Monte Carlo strategy to randomly sample from the space of rules, rather than exhaustively analyzing all…

Scientific machine learning has become an increasingly important tool in materials science and engineering. It is particularly well suited to tackle material problems involving many variables or to allow rapid construction of surrogates of…

Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo…

Monte-Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve particle size distributions from small-angle scattering patterns of dilute solutions of scatterers. The size sensitivity of…

In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…

The paper describes the practical work for students visually clarifying the mechanism of the Monte Carlo method applying to approximating the value of Pi. Considering a traditional quadrant (circular sector) inscribed in a square, here we…

It is often necessary to make sampling-based statistical inference about many probability distributions in parallel. Given a finite computational resource, this article addresses how to optimally divide sampling effort between the samplers…

Machine unlearning refers to the task of removing a subset of training data, thereby removing its contributions to a trained model. Approximate unlearning are one class of methods for this task which avoid the need to retrain the model from…

Deep neural networks have been applied successfully to a wide variety of inverse problems arising in computational imaging. These networks are typically trained using a forward model that describes the measurement process to be inverted,…