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Most real-world classification tasks suffer from label noise to some extent. Such noise in the data adversely affects the generalization error of learned models and complicates the evaluation of noise-handling methods, as their performance cannot be accurately measured without clean labels. In label noise research, typically either noisy or incomplex simulated data are accepted as a baseline, into which additional noise with known properties is injected. In this paper, we propose SYNLABEL, a framework that aims to improve upon the aforementioned methodologies. It allows for creating a noiseless dataset informed by real data, by either pre-specifying or learning a function and defining it as the ground truth function from which labels are generated. Furthermore, by resampling a number of values for selected features in the function domain, evaluating the function and aggregating the resulting labels, each data point can be assigned a soft label or label distribution. Such distributions allow for direct injection and quantification of label noise. The generated datasets serve as a clean baseline of adjustable complexity into which different types of noise may be introduced. We illustrate how the framework can be applied, how it enables quantification of label noise and how it improves over existing methodologies.

Spherical polygons used in practice are nice, but the spherical point-in-polygon problem (SPiP) has long eluded solutions based on the winding number (wn). That a punctured sphere is simply connected is to blame. As a workaround, we prove that requiring the boundary of a spherical polygon to never intersect its antipode is sufficient to reduce its SPiP problem to the planar, point-in-polygon (PiP) problem, whose state-of-the-art solution uses wn and does not utilize known interior points (KIP). We refer to such spherical polygons as boundary antipode-excluding (BAE) and show that all spherical polygons fully contained within an open hemisphere is BAE. We document two successful reduction methods, one based on rotation and the other on shearing, and address a common concern. Both reduction algorithms, when combined with a wn-PiP algorithm, solve SPiP correctly and efficiently for BAE spherical polygons. The MATLAB code provided demonstrates scenarios that are problematic for previous work.

This paper presents a method for determining the area explored by a line-sweep sensor during an area-covering mission in a two-dimensional plane. Accurate knowledge of the explored area is crucial for various applications in robotics, such as mapping, surveillance, and coverage optimization. The proposed method leverages the concept of coverage measure of the environment and its relation to the topological degree in the plane, to estimate the extent of the explored region. In addition, we extend the approach to uncertain coverage measure values using interval analysis. This last contribution allows for a guaranteed characterization of the explored area, essential considering the often critical character of area-covering missions. Finally, this paper also proposes a novel algorithm for computing the topological degree in the 2-dimensional plane, for all the points inside an area of interest, which differs from existing solutions that compute the topological degree for single points. The applicability of the method is evaluated through a real-world experiment.

In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only be solved numerically via a time discretization. We develop, based upon the approach in [20], a new particle and multilevel particle filter (MLPF) in order to approximate the filter associated to the discretized ODE. We provide a bound on the mean square error associated to the MLPF which provides guidance on setting the simulation parameter of that algorithm and implies that significant computational gains can be obtained versus using a particle filter. Our theoretical claims are confirmed in several numerical examples.

This paper discusses the geometrical features and wideband performance of the beam with maximal ratio combining coefficients for a generic multi-antenna receiver. In particular, in case the channel is a linear combination of plane waves, we show that such a beam can be decomposed in a linear combination of beams pointed in the direction of each plane wave, and we compute how many directions can be effectively utilized. This highlights that such beam is better exploiting the spatial diversity provided by the channel, and therefore it is expected to be more robust to disruptions. Moreover, we compute the achieved Signal-to-Noise-Ratio for a wideband receiver, showing that it is not significantly worse than for other methods. Finally, we provide some insights on the robustness of the method by simulating the impact of the blockage of one multipath components.

This paper aims for a new generation task: non-stationary multi-texture synthesis, which unifies synthesizing multiple non-stationary textures in a single model. Most non-stationary textures have large scale variance and can hardly be synthesized through one model. To combat this, we propose a multi-scale generator to capture structural patterns of various scales and effectively synthesize textures with a minor cost. However, it is still hard to handle textures of different categories with different texture patterns. Therefore, we present a category-specific training strategy to focus on learning texture pattern of a specific domain. Interestingly, once trained, our model is able to produce multi-pattern generations with dynamic variations without the need to finetune the model for different styles. Moreover, an objective evaluation metric is designed for evaluating the quality of texture expansion and global structure consistency. To our knowledge, ours is the first scheme for this challenging task, including model, training, and evaluation. Experimental results demonstrate the proposed method achieves superior performance and time efficiency. The code will be available after the publication.

This paper proposes a new multilinear projection method for dimension-reduction in modeling high-dimensional matrix-variate time series. It assumes that a $p_1\times p_2$ matrix-variate time series consists of a dynamically dependent, lower-dimensional matrix-variate factor process and a $p_1\times p_2$ matrix white noise series. Covariance matrix of the vectorized white noises assumes a Kronecker structure such that the row and column covariances of the noise all have diverging/spiked eigenvalues to accommodate the case of low signal-to-noise ratio often encountered in applications, such as in finance and economics. We use an iterative projection procedure to {reduce the dimensions and noise effects in estimating} front and back loading matrices and {to} obtain faster convergence rates than those of the traditional methods available in the literature. Furthermore, we introduce a two-way projected Principal Component Analysis to mitigate the diverging noise effects, and implement a high-dimensional white-noise testing procedure to estimate the dimension of the factor matrix. Asymptotic properties of the proposed method are established as the dimensions and sample size go to infinity. Simulated and real examples are used to assess the performance of the proposed method. We also compared the proposed method with some existing ones in the literature concerning the forecasting ability of the identified factors and found that the proposed approach fares well in out-of-sample forecasting.

This paper begins with a description of methods for estimating probability density functions for images that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space - not every pattern of pixels is an image. It is common to say that images lie on a lower-dimensional manifold in the high-dimensional space. However, although images may lie on such lower-dimensional manifolds, it is not the case that all points on the manifold have an equal probability of being images. Images are unevenly distributed on the manifold, and our task is to devise ways to model this distribution as a probability distribution. In pursuing this goal, we consider generative models that are popular in AI and computer vision community. For our purposes, generative/probabilistic models should have the properties of 1) sample generation: it should be possible to sample from this distribution according to the modelled density function, and 2) probability computation: given a previously unseen sample from the dataset of interest, one should be able to compute the probability of the sample, at least up to a normalising constant. To this end, we investigate the use of methods such as normalising flow and diffusion models. We then show that such probabilistic descriptions can be used to construct defences against adversarial attacks. In addition to describing the manifold in terms of density, we also consider how semantic interpretations can be used to describe points on the manifold. To this end, we consider an emergent language framework which makes use of variational encoders to produce a disentangled representation of points that reside on a given manifold. Trajectories between points on a manifold can then be described in terms of evolving semantic descriptions.

The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.