Kernel embedding of distributions

In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which a probability distribution is represented as an element of a reproducing kernel Hilbert space (RKHS). A generalization of the individual data-point feature mapping done in classical kernel methods, the embedding of distributions into infinite-dimensional feature spaces can preserve all of the statistical features of arbitrary distributions, while allowing one to compare and manipulate distributions using Hilbert space operations such as inner products, distances, projections, linear transformations, and spectral analysis. This learning framework is very general and can be applied to distributions over any space \Omega on which a sensible kernel function (measuring similarity between elements of \Omega ) may be defined. For example, various kernels have been proposed for learning from data which are:

Image Denoising with Control over Deep Network Hallucination

Majed El Helou, Qiyuan Liang, Sabine Süsstrunk

Deep image denoisers achieve state-of-the-art results but with a hidden cost. As witnessed in recent literature, these deep networks are capable of overfitting their training distributions, causing inaccurate hallucinations to be added to the output and generalizing poorly to varying data. For better control and interpretability over a deep denoiser, we propose a novel framework exploiting a denoising network. We call it controllable confidence-based image denoising (CCID). In this framework, we exploit the outputs of a deep denoising network alongside an image convolved with a reliable filter. Such a filter can be a simple convolution kernel which does not risk adding hallucinated information. We propose to fuse the two components with a frequency-domain approach that takes into account the reliability of the deep network outputs. With our framework, the user can control the fusion of the two components in the frequency domain. We also provide a user-friendly map estimating spatially the confidence in the output that potentially contains network hallucination. Results show that our CCID not only provides more interpretability and control, but can even outperform both the quantitative performance of the deep denoiser and that of the reliable filter, especially when the test data diverge from the training data.

Society for Imaging Science and Technology (IS&T)2022

Reconstruction using approximate message passing methods

Giovanni Cherubini, Paul Hurley, Sanaz Kazemi, Matthieu Martin Jean-André Simeoni

The present invention is notably directed to a computer-implemented method for image reconstruction. The method comprises: accessing elements that respectively correspond to measurement values, which can be respectively mapped to measurement nodes; and performing message passing estimator operations to obtain estimates of random variables associated with variable nodes, according to a message passing method in a bipartite factor graph. In this message passing method: the measurement values are, each, expressed as a term that comprises linear combinations of the random variables; each message exchanged between any of the measurement nodes and any of the variable nodes is parameterized by parameters of a distribution of the random variables; and performing the message passing estimator operations further comprises randomly mapping measurement values to the measurement nodes, at one or more iterations of the message passing method. Finally, image data are obtained from the obtained estimates of the random variables, which image data are adapted to reconstruct an image. The present invention is further directed to related systems and methods using the above image reconstruction method.

2017

Learning to Play Sequential Games versus Unknown Opponents

Ilija Bogunovic, Andreas Krause

We consider a repeated sequential game between a learner, who plays first, and an opponent who responds to the chosen action. We seek to design strategies for the learner to successfully interact with the opponent. While most previous approaches consider known opponent models, we focus on the setting in which the opponent’s model is unknown. To this end, we use kernel-based regularity assumptions to capture and exploit the structure in the opponent’s response. We propose a novel algorithm for the learner when playing against an adversarial sequence of opponents. The algorithm combines ideas from bilevel optimization and online learning to effectively balance between exploration (learning about the opponent’s model) and exploitation (selecting highly rewarding actions for the learner). Our results include algorithm’s regret guarantees that depend on the regularity of the opponent’s response and scale sublinearly with the number of game rounds. Moreover, we specialize our approach to repeated Stackelberg games, and empirically demonstrate its effectiveness in a traffic routing and wildlife conservation task.

Curran Associates, Inc.2020