Related papers: Riemannian information gradient methods for the pa…

Bayesian Experimental Design (BED), which aims to find the optimal experimental conditions for Bayesian inference, is usually posed as to optimize the expected information gain (EIG). The gradient information is often needed for efficient…

The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…

In this paper, we propose a probabilistic optimization method, named probabilistic incremental proximal gradient (PIPG) method, by developing a probabilistic interpretation of the incremental proximal gradient algorithm. We explicitly model…

We conducted a reproducibility study on Integrated Gradients (IG) based methods and the Important Direction Gradient Integration (IDGI) framework. IDGI eliminates the explanation noise in each step of the computation of IG-based methods…

Integrated Gradients (IG) is a widely used algorithm for attributing the outputs of a deep neural network to its input features. Due to the absence of closed-form integrals for deep learning models, inaccurate Riemann Sum approximations are…

We study the minimization of smooth, possibly nonconvex functions over the positive orthant, a key setting in Poisson inverse problems, using the exponentiated gradient (EG) method. Interpreting EG as Riemannian gradient descent (RGD) with…

We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the…

Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on Riemannian…

Attribution algorithms are frequently employed to explain the decisions of neural network models. Integrated Gradients (IG) is an influential attribution method due to its strong axiomatic foundation. The algorithm is based on integrating…

Differential equations are pivotal in modeling and understanding the dynamics of various systems, offering insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and…

Computing expected information gain (EIG) from prior to posterior (equivalently, mutual information between candidate observations and model parameters or other quantities of interest) is a fundamental challenge in Bayesian optimal…

Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…

We develop methods for parameter estimation in settings with large-scale data sets, where traditional methods are no longer tenable. Our methods rely on stochastic approximations, which are computationally efficient as they maintain one…

Riemannian geometry has been applied to Brain Computer Interface (BCI) for brain signals classification yielding promising results. Studying electroencephalographic (EEG) signals from their associated covariance matrices allows a mitigation…

This paper considers a type of incremental aggregated gradient (IAG) method for large-scale distributed optimization. The IAG method is well suited for the parameter server architecture as the latter can easily aggregate potentially staled…

Mutual Information (MI) plays an important role in representation learning. However, MI is unfortunately intractable in continuous and high-dimensional settings. Recent advances establish tractable and scalable MI estimators to discover…

Graph-based Cognitive Diagnosis (CD) has attracted much research interest due to its strong ability on inferring students' proficiency levels on knowledge concepts. While graph-based CD models have demonstrated remarkable performance, we…

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…

Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…

Sensors producing 3D point clouds such as 3D laser scanners and RGB-D cameras are widely used in robotics, be it for autonomous driving or manipulation. Aligning point clouds produced by these sensors is a vital component in such…