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Lottery ticket hypothesis for deep neural networks emphasizes the importance of initialization used to re-train the sparser networks obtained using the iterative magnitude pruning process. An explanation for why the specific initialization proposed by the lottery ticket hypothesis tends to work better in terms of generalization (and training) performance has been lacking. Moreover, the underlying principles in iterative magnitude pruning, like the pruning of smaller magnitude weights and the role of the iterative process, lack full understanding and explanation. In this work, we attempt to provide insights into these phenomena by empirically studying the volume/geometry and loss landscape characteristics of the solutions obtained at various stages of the iterative magnitude pruning process.

Accurate estimation of queuing delays is crucial for designing and optimizing communication networks, particularly in the context of Deterministic Networking (DetNet) scenarios. This study investigates the approximation of Internet queuing delays using an M/M/1 envelope model, which provides a simple methodology to find tight upper bounds of real delay percentiles. Real traffic statistics collected at large Internet Exchange Points (like Amsterdam and San Francisco) have been used to fit polynomial regression models for transforming packet queuing delays into the M/M/1 envelope models. We finally propose a methodology for providing delay percentiles in DetNet scenarios where tight latency guarantees need to be assured.

The non-life insurance sector operates within a highly competitive and tightly regulated framework, confronting a pivotal juncture in the formulation of pricing strategies. Insurers are compelled to harness a range of statistical methodologies and available data to construct optimal pricing structures that align with the overarching corporate strategy while accommodating the dynamics of market competition. Given the fundamental societal role played by insurance, premium rates are subject to rigorous scrutiny by regulatory authorities. These rates must conform to principles of transparency, explainability, and ethical considerations. Consequently, the act of pricing transcends mere statistical calculations and carries the weight of strategic and societal factors. These multifaceted concerns may drive insurers to establish equitable premiums, taking into account various variables. For instance, regulations mandate the provision of equitable premiums, considering factors such as policyholder gender or mutualist group dynamics in accordance with respective corporate strategies. Age-based premium fairness is also mandated. In certain insurance domains, variables such as the presence of serious illnesses or disabilities are emerging as new dimensions for evaluating fairness. Regardless of the motivating factor prompting an insurer to adopt fairer pricing strategies for a specific variable, the insurer must possess the capability to define, measure, and ultimately mitigate any ethical biases inherent in its pricing practices while upholding standards of consistency and performance. This study seeks to provide a comprehensive set of tools for these endeavors and assess their effectiveness through practical application in the context of automobile insurance.

We leverage the duality between risk-averse and distributionally robust optimization (DRO) to devise a distributionally robust estimator that strictly outperforms the empirical average for all probability distributions with negative excess kurtosis. The aforesaid estimator solves the $\chi^{2}-$robust mean squared error problem in closed form.

Shape-constrained functional data encompass a wide array of application fields especially in the life sciences, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are subject to inherent shape constraints, while some specialized techniques rely on strict distributional assumptions. We propose an approach for modeling such data that harnesses the intrinsic geometry of functional trajectories by decomposing them into size and shape components. We focus on the two most prevalent shape constraints, positivity and monotonicity, and develop individual-level estimators for the size and shape components. Furthermore, we demonstrate the applicability of our approach by conducting subsequent analyses involving Fr\'{e}chet mean and Fr\'{e}chet regression and establish rates of convergence for the empirical estimators. Illustrative examples include simulations and data applications for activity profiles for Mediterranean fruit flies during their entire lifespan and for data from the Z\"{u}rich longitudinal growth study.

Significant pattern mining is a fundamental task in mining transactional data, requiring to identify patterns significantly associated with the value of a given feature, the target. In several applications, such as biomedicine, basket market analysis, and social networks, the goal is to discover patterns whose association with the target is defined with respect to an underlying population, or process, of which the dataset represents only a collection of observations, or samples. A natural way to capture the association of a pattern with the target is to consider its statistical significance, assessing its deviation from the (null) hypothesis of independence between the pattern and the target. While several algorithms have been proposed to find statistically significant patterns, it remains a computationally demanding task, and for complex patterns such as subgroups, no efficient solution exists. We present FSR, an efficient algorithm to identify statistically significant patterns with rigorous guarantees on the probability of false discoveries. FSR builds on a novel general framework for mining significant patterns that captures some of the most commonly considered patterns, including itemsets, sequential patterns, and subgroups. FSR uses a small number of resampled datasets, obtained by assigning i.i.d. labels to each transaction, to rigorously bound the supremum deviation of a quality statistic measuring the significance of patterns. FSR builds on novel tight bounds on the supremum deviation that require to mine a small number of resampled datasets, while providing a high effectiveness in discovering significant patterns. As a test case, we consider significant subgroup mining, and our evaluation on several real datasets shows that FSR is effective in discovering significant subgroups, while requiring a small number of resampled datasets.

Segmentation models for brain lesions in MRI are commonly developed for a specific disease and trained on data with a predefined set of MRI modalities. Each such model cannot segment the disease using data with a different set of MRI modalities, nor can it segment any other type of disease. Moreover, this training paradigm does not allow a model to benefit from learning from heterogeneous databases that may contain scans and segmentation labels for different types of brain pathologies and diverse sets of MRI modalities. Is it feasible to use Federated Learning (FL) for training a single model on client databases that contain scans and labels of different brain pathologies and diverse sets of MRI modalities? We demonstrate promising results by combining appropriate, simple, and practical modifications to the model and training strategy: Designing a model with input channels that cover the whole set of modalities available across clients, training with random modality drop, and exploring the effects of feature normalization methods. Evaluation on 7 brain MRI databases with 5 different diseases shows that such FL framework can train a single model that is shown to be very promising in segmenting all disease types seen during training. Importantly, it is able to segment these diseases in new databases that contain sets of modalities different from those in training clients. These results demonstrate, for the first time, feasibility and effectiveness of using FL to train a single segmentation model on decentralised data with diverse brain diseases and MRI modalities, a necessary step towards leveraging heterogeneous real-world databases. Code will be made available at: //github.com/FelixWag/FL-MultiDisease-MRI

Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based algorithms that can solve bilevel optimization problems with provable guarantees. However, the existing literature mainly focuses on bilevel problems either without constraints, or featuring only simple constraints that do not couple variables across the upper and lower levels, excluding a range of complex applications. Our paper studies this challenging but less explored scenario and develops a (fully) first-order algorithm, which we term BLOCC, to tackle BiLevel Optimization problems with Coupled Constraints. We establish rigorous convergence theory for the proposed algorithm and demonstrate its effectiveness on two well-known real-world applications - hyperparameter selection in support vector machine (SVM) and infrastructure planning in transportation networks using the real data from the city of Seville.

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.

Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results. Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses. We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly. Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge.