Fortheformer setting, an extensive literature has explored the statistical and computational aspects of learning Booleanfunctions[Angluin,1992,HellersteinandServedio,2007].

The simplest nontrivial geometric concept is perhaps the halfspace.

Online classification is a central problem in optimization, statistical learning and data science. Classical algorithms such as the perceptron offer efficient updates and finite mistake guarantees on linearly separable data, but they do not exploit the underlying geometric structure of the classification problem. We study the offline maximum margin problem through its dual formulation and use the resulting geometric insights to design a principled and efficient algorithm for the online setting. A key feature of our method is its translation invariance, inherited from the offline formulation, which plays a central role in its performance analysis. Our theoretical analysis yields improved mistake and margin bounds that depend only on translation-invariant quantities, offering stronger guarantees than existing algorithms under the same assumptions in favorable settings. In particular, we identify a parameter regime where our algorithm makes at most two mistakes per sequence, whereas the perceptron can be forced to make arbitrarily many mistakes. Our numerical study on real data further demonstrates that our method matches the computational efficiency of existing online algorithms, while significantly outperforming them in accuracy.

Strategic litigation involves bringing a legal case to court with the goal of having a broader impact beyond resolving the case itself: for example, creating precedent which will influence future rulings. In this paper, we explore strategic litigation from the perspective of machine learning theory. We consider an abstract model of a common-law legal system where a lower court decides new cases by applying a decision rule learned from a higher court's past rulings. In this model, we explore the power of a strategic litigator, who strategically brings cases to the higher court to influence the learned decision rule, thereby affecting future cases. We explore questions including: What impact can a strategic litigator have? Which cases should a strategic litigator bring to court? Does it ever make sense for a strategic litigator to bring a case when they are sure the court will rule against them?

We present the first sample compression algorithm for nearest neighbors with nontrivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our bound is nearly optimal. Our result yields new insight into margin-based nearest neighbor classification in metric spaces and allows us to significantly sharpen and simplify existing bounds. Some encouraging empirical results are also presented.

In clinical procedures, precise localization of the target area is an essential step for clinical diagnosis and screening. For many diagnostic applications, lung segmentation of chest X-ray images is an essential first step that significantly reduces the image size to speed up the subsequent analysis. One of the primary difficulties with this task is segmenting the lung regions covered by dense abnormalities also known as opacities due to diseases like pneumonia and tuberculosis. SAM has astonishing generalization capabilities for category agnostic segmentation. In this study we propose an algorithm to improve zero shot performance of SAM on lung region segmentation task by automatic prompt selection. Two separate UNet models were trained, one for predicting lung segments and another for heart segment. Though these predictions lack fine details around the edges, they provide positive and negative points as prompt for SAM. Using proposed prompting method zero shot performance of SAM is evaluated on two benchmark datasets. ViT-l version of the model achieved slightly better performance compared to other two versions, ViTh and ViTb. It yields an average Dice score of 95.5 percent and 94.9 percent on hold out data for two datasets respectively. Though, for most of the images, SAM did outstanding segmentation, its prediction was way off for some of the images. After careful inspection it is found that all of these images either had extreme abnormality or distorted shape. Unlike most of the research performed so far on lung segmentation from CXR images using SAM, this study proposes a fully automated prompt selection process only from the input image. Our finding indicates that using pretrained models for prompt selection can utilize SAM impressive generalization capability to its full extent.

We consider the following problem in computational geometry: given, in the d-dimensional real space, a set of points marked as positive and a set of points marked as negative, such that the convex hull of the positive set does not intersect the negative set, find K hyperplanes that separate, if possible, all the positive points from the negative ones. That is, we search for a convex polyhedron with at most K faces, containing all the positive points and no negative point. The problem is known in the literature for pure convex polyhedral approximation; our interest stems from its possible applications in constraint learning, where points are feasible or infeasible solutions of a Mixed Integer Program, and the K hyperplanes are linear constraints to be found. We cast the problem as an optimization one, minimizing the number of negative points inside the convex polyhedron, whenever exact separation cannot be achieved. We introduce models inspired by support vector machines and we design two mathematical programming formulations with binary variables. We exploit Dantzig-Wolfe decomposition to obtain extended formulations, and we devise column generation algorithms with ad-hoc pricing routines. We compare computing time and separation error values obtained by all our approaches on synthetic datasets, with number of points from hundreds up to a few thousands, showing our approaches to perform better than existing ones from the literature. Furthermore, we observe that key computational differences arise, depending on whether the budget K is sufficient to completely separate the positive points from the negative ones or not. On 8-dimensional instances (and over), existing convex hull algorithms become computational inapplicable, while our algorithms allow to identify good convex hull approximations in minutes of computation.

Treatment of stagnant water bodies that act as a breeding site for malarial vectors is a fundamental step in most malaria elimination campaigns. However, identification of such water bodies over large areas is expensive, labour-intensive and time-consuming and hence, challenging in countries with limited resources. Practical models that can efficiently locate water bodies can target the limited resources by greatly reducing the area that needs to be scanned by the field workers. To this end, we propose a practical topographic model based on easily available, global, high-resolution DEM data to predict locations of potential vector-breeding water sites. We surveyed the Obuasi region of Ghana to assess the impact of various topographic features on different types of water bodies and uncover the features that significantly influence the formation of aquatic habitats. We further evaluate the effectiveness of multiple models. Our best model significantly outperforms earlier attempts that employ topographic variables for detection of small water sites, even the ones that utilize additional satellite imagery data and demonstrates robustness across different settings.

Crowd counting and localization have become increasingly important in computer vision due to their wide-ranging applications. While point-based strategies have been widely used in crowd counting methods, they face a significant challenge, i.e., the lack of an effective learning strategy to guide the matching process. This deficiency leads to instability in matching point proposals to target points, adversely affecting overall performance. To address this issue, we introduce an effective approach to stabilize the proposal-target matching in point-based methods. We propose Auxiliary Point Guidance (APG) to provide clear and effective guidance for proposal selection and optimization, addressing the core issue of matching uncertainty. Additionally, we develop Implicit Feature Interpolation (IFI) to enable adaptive feature extraction in diverse crowd scenarios, further enhancing the model's robustness and accuracy. Extensive experiments demonstrate the effectiveness of our approach, showing significant improvements in crowd counting and localization performance, particularly under challenging conditions. The source codes and trained models will be made publicly available.

The process of clearing areas, namely demining, starts by assessing and prioritizing potential hazardous areas (i.e., desk assessment) to go under thorough investigation of experts, who confirm the risk and proceed with the mines clearance operations. This paper presents Desk-AId that supports the desk assessment phase by estimating landmine risks using geospatial data and socioeconomic information. Desk-AId uses a Geospatial AI approach specialized to landmines. The approach includes mixed data sampling strategies and context-enrichment by historical conflicts and key multi-domain facilities (e.g., buildings, roads, health sites). The proposed system addresses the issue of having only ground-truth for confirmed hazardous areas by implementing a new hard-negative data sampling strategy, where negative points are sampled in the vicinity of hazardous areas. Experiments validate Desk-Aid in two domains for landmine risk assessment: 1) country-wide, and 2) uncharted study areas). The proposed approach increases the estimation accuracies up to 92%, for different classification models such as RandomForest (RF), Feedforward Neural Networks (FNN), and Graph Neural Networks (GNN).