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Real-world image de-weathering aims at removing various undesirable weather-related artifacts. Owing to the impossibility of capturing image pairs concurrently, existing real-world de-weathering datasets often exhibit inconsistent illumination, position, and textures between the ground-truth images and the input degraded images, resulting in imperfect supervision. Such non-ideal supervision negatively affects the training process of learning-based de-weathering methods. In this work, we attempt to address the problem with a unified solution for various inconsistencies. Specifically, inspired by information bottleneck theory, we first develop a Consistent Label Constructor (CLC) to generate a pseudo-label as consistent as possible with the input degraded image while removing most weather-related degradations. In particular, multiple adjacent frames of the current input are also fed into CLC to enhance the pseudo-label. Then we combine the original imperfect labels and pseudo-labels to jointly supervise the de-weathering model by the proposed Information Allocation Strategy (IAS). During testing, only the de-weathering model is used for inference. Experiments on two real-world de-weathering datasets show that our method helps existing de-weathering models achieve better performance. Codes are available at //github.com/1180300419/imperfect-deweathering.

Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a simple discretization of a Lippmann-Schwinger style volume integral equation for time-harmonic Maxwell equations, we analyze an analogous discretization of convolution operators with strongly singular kernels. For a class of kernel functions that includes the finite Hilbert transformation in 1D and the principal part of the Maxwell volume integral operator used for DDA in dimensions 2 and 3, we show that the method, which does not fit into known frameworks of projection methods, can nevertheless be considered as a finite section method for an infinite block Toeplitz matrix. The symbol of this matrix is given by a Fourier series that does not converge absolutely. We use Ewald's method to obtain an exponentially fast convergent series representation of this symbol and show that it is a bounded function, thereby allowing to describe the spectrum and the numerical range of the matrix. It turns out that this numerical range includes the numerical range of the integral operator, but that it is in some cases strictly larger. In these cases the discretization method does not provide a spectrally correct approximation, and while it is stable for a large range of the spectral parameter $\lambda$, there are values of $\lambda$ for which the singular integral equation is well posed, but the discretization method is unstable.

When vehicle routing decisions are intertwined with higher-level decisions, the resulting optimization problems pose significant challenges for computation. Examples are the multi-depot vehicle routing problem (MDVRP), where customers are assigned to depots before delivery, and the capacitated location routing problem (CLRP), where the locations of depots should be determined first. A simple and straightforward approach for such hierarchical problems would be to separate the higher-level decisions from the complicated vehicle routing decisions. For each higher-level decision candidate, we may evaluate the underlying vehicle routing problems to assess the candidate. As this approach requires solving vehicle routing problems multiple times, it has been regarded as impractical in most cases. We propose a novel deep-learning-based approach called Genetic Algorithm with Neural Cost Predictor (GANCP) to tackle the challenge and simplify algorithm developments. For each higher-level decision candidate, we predict the objective function values of the underlying vehicle routing problems using a pre-trained graph neural network without actually solving the routing problems. In particular, our proposed neural network learns the objective values of the HGS-CVRP open-source package that solves capacitated vehicle routing problems. Our numerical experiments show that this simplified approach is effective and efficient in generating high-quality solutions for both MDVRP and CLRP and has the potential to expedite algorithm developments for complicated hierarchical problems. We provide computational results evaluated in the standard benchmark instances used in the literature.

Membership inference attacks (MIA) can reveal whether a particular data point was part of the training dataset, potentially exposing sensitive information about individuals. This article explores the fundamental statistical limitations associated with MIAs on machine learning models. More precisely, we first derive the statistical quantity that governs the effectiveness and success of such attacks. Then, we investigate several situations for which we provide bounds on this quantity of interest. This allows us to infer the accuracy of potential attacks as a function of the number of samples and other structural parameters of learning models, which in some cases can be directly estimated from the dataset.

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy's partial differential equation (PDE) for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the PDE for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical PDE solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O(n log n) instead of the typical O(n^3) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy's equation and the numerical solution. Although our method is derived for building a surrogate for the solution of Darcy's equation with a random permeability field, the framework broadly applies to solutions of other PDE with random coefficients.

We aim to maximize the energy efficiency, gauged as average energy cost per job, in a large-scale server farm with various storage or/and computing components modeled as parallel abstracted servers. Each server operates in multiple power modes characterized by potentially different service and energy consumption rates. The heterogeneity of servers and multiple power modes complicate the maximization problem, where optimal solutions are generally intractable. Relying on the Whittle relaxation technique, we resort to a near-optimal, scalable job-assignment policy. Under a mild condition related to the service and energy consumption rates of the servers, we prove that our proposed policy approaches optimality as the size of the entire system tends to infinity; that is, it is asymptotically optimal. For the non-asymptotic regime, we show the effectiveness of the proposed policy through numerical simulations, where the policy outperforms all the tested baselines, and we numerically demonstrate its robustness against heavy-tailed job-size distributions.

Clinically deployed segmentation models are known to fail on data outside of their training distribution. As these models perform well on most cases, it is imperative to detect out-of-distribution (OOD) images at inference to protect against automation bias. This work applies the Mahalanobis distance post hoc to the bottleneck features of a Swin UNETR model that segments the liver on T1-weighted magnetic resonance imaging. By reducing the dimensions of the bottleneck features with principal component analysis, OOD images were detected with high performance and minimal computational load.

Multidimensional constellation shaping of up to 32 dimensions with different spectral efficiencies are compared through AWGN and fiber-optic simulations. The results show that no constellation is universal and the balance of required and effective SNRs should be jointly considered for the specific optical transmission scenario.

When applying deep learning to remote sensing data in archaeological research, a notable obstacle is the limited availability of suitable datasets for training models. The application of transfer learning is frequently employed to mitigate this drawback. However, there is still a need to explore its effectiveness when applied across different archaeological datasets. This paper compares the performance of various transfer learning configurations using two semantic segmentation deep neural networks on two LiDAR datasets. The experimental results indicate that transfer learning-based approaches in archaeology can lead to performance improvements, although a systematic enhancement has not yet been observed. We provide specific insights about the validity of such techniques that can serve as a baseline for future works.

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.