In this contribution, we focus on invariances to symmetric additive noise on each of the data generating distributions.

It appears that individuals experience different numbers of small and large growth spurts that differ in magnitude and timing.

When employing underwater vehicles for the autonomous inspection of assets, it is crucial to consider and assess the water conditions. Indeed, they have a significant impact on the visibility, which also affects robotic operations. Turbidity can jeopardise the whole mission as it may prevent correct visual documentation of the inspected structures. Previous works have introduced methods to adapt to turbidity and backscattering, however, they also include manoeuvring and setup constraints. We propose a simple yet efficient approach to enable high-quality image acquisition of assets in a broad range of water conditions. This active perception framework includes a multi-layer perceptron (MLP) trained to predict image quality given a distance to a target and artificial light intensity. We generated a large synthetic dataset including ten water types with different levels of turbidity and backscattering. For this, we modified the modelling software Blender to better account for the underwater light propagation properties. We validated the approach in simulation and showed significant improvements in visual coverage and quality of imagery compared to traditional approaches. The project code is available on our project page at https://roboticimaging.org/Projects/ActiveUW/.

The reliable recovery and uncertainty quantification of a fixed effect function $\mu$ in a functional mixed model, for modelling population- and object-level variability in noisily observed functional data, is a notoriously challenging task: variations along the $x$ and $y$ axes are confounded with additive measurement error, and cannot in general be disentangled. The question then as to what properties of $\mu$ may be reliably recovered becomes important. We demonstrate that it is possible to recover the size-and-shape of a square-integrable $\mu$ under a Bayesian functional mixed model. The size-and-shape of $\mu$ is a geometric property invariant to a family of space-time unitary transformations, viewed as rotations of the Hilbert space, that jointly transform the $x$ and $y$ axes. A random object-level unitary transformation then captures size-and-shape \emph{preserving} deviations of $\mu$ from an individual function, while a random linear term and measurement error capture size-and-shape \emph{altering} deviations. The model is regularized by appropriate priors on the unitary transformations, posterior summaries of which may then be suitably interpreted as optimal data-driven rotations of a fixed orthonormal basis for the Hilbert space. Our numerical experiments demonstrate utility of the proposed model, and superiority over the current state-of-the-art.

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rare that all possible differences between samples are of interest - discovered differences can be due to different types of measurement noise, data collection artefacts or other irrelevant sources of variability. We propose distances between distributions which encode invariance to additive symmetric noise, aimed at testing whether the assumed true underlying processes differ. Moreover, we construct invariant features of distributions, leading to learning algorithms robust to the impairment of the input distributions with symmetric additive noise.

We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly represent the asymptotic phase of the oscillator. The trained autoencoder can perform two functions without relying on the mathematical model of the oscillator: first, it can evaluate the asymptotic phase and phase sensitivity function of the oscillator; second, it can reconstruct the oscillator state on the limit cycle in the original space from the phase value as an input. Using several examples of limit-cycle oscillators, we demonstrate that the asymptotic phase and phase sensitivity function can be estimated only from time-series data by the trained autoencoder. We also present a simple method for globally synchronizing two oscillators as an application of the trained autoencoder.

Physically based rendering of complex scenes can be prohibitively costly with a potentially unbounded and uneven distribution of complexity across the rendered image. The goal of an ideal level of detail (LoD) method is to make rendering costs independent of the 3D scene complexity, while preserving the appearance of the scene. However, current prefiltering LoD methods are limited in the appearances they can support due to their reliance of approximate models and other heuristics. We propose the first comprehensive multi-scale LoD framework for prefiltering 3D environments with complex geometry and materials (e.g., the Disney BRDF), while maintaining the appearance with respect to the ray-traced reference. Using a multi-scale hierarchy of the scene, we perform a data-driven prefiltering step to obtain an appearance phase function and directional coverage mask at each scale. At the heart of our approach is a novel neural representation that encodes this information into a compact latent form that is easy to decode inside a physically based renderer. Once a scene is baked out, our method requires no original geometry, materials, or textures at render time. We demonstrate that our approach compares favorably to state-of-the-art prefiltering methods and achieves considerable savings in memory for complex scenes.

This paper proposes a novel non-oscillatory pattern (NOP) learning scheme for several oscillatory data analysis problems including signal decomposition, super-resolution, and signal sub-sampling. To the best of our knowledge, the proposed NOP is the first algorithm for these problems with fully non-stationary oscillatory data with close and crossover frequencies, and general oscillatory patterns. NOP is capable of handling complicated situations while existing algorithms fail; even in simple cases, e.g., stationary cases with trigonometric patterns, numerical examples show that NOP admits competitive or better performance in terms of accuracy and robustness than several state-of-the-art algorithms.

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that all possible differences between samples are of interest -- discovered differences can be due to different types of measurement noise, data collection artefacts or other irrelevant sources of variability. We propose distances between distributions which encode invariance to additive symmetric noise, aimed at testing whether the assumed true underlying processes differ. Moreover, we construct invariant features of distributions, leading to learning algorithms robust to the impairment of the input distributions with symmetric additive noise.