Related papers: IoU is not submodular
Training a robust classifier and an accurate box regressor are difficult for occluded pedestrian detection. Traditionally adopted Intersection over Union (IoU) measurement does not consider the occluded region of the object and leads to…
Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been…
It has been hypothesized that some form of "modular" structure in artificial neural networks should be useful for learning, compositionality, and generalization. However, defining and quantifying modularity remains an open problem. We cast…
An alternative foundation for 2-categories is explored by studying graph-theoretically a partial operation on 2-cells named juncture, which can replace vertical and horizontal composition. Juncture is a generalized vertical composition of…
In this paper, we investigate a class of submodular problems which in general are very hard. These include minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., optimizing a…
In this paper, we study the submodularity of the covolume function in global function fields. The submodular property is often needed in the study of homogeneous dynamics, especially to define a Margulis function. We proved that the…
As scene segmentation systems reach visually accurate results, many recent papers focus on making these network architectures faster, smaller and more efficient. In particular, studies often aim at designingreal-time'systems. Achieving this…
In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…
In medicine, visualizing chromosomes is important for medical diagnostics, drug development, and biomedical research. Unfortunately, chromosomes often overlap and it is necessary to identify and distinguish between the overlapping…
We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…
Federated learning is an emerging distributed machine learning framework for privacy preservation. However, models trained in federated learning usually have worse performance than those trained in the standard centralized learning mode,…
With the rapid growth of data, it is becoming increasingly difficult to train or improve deep learning models with the right subset of data. We show that this problem can be effectively solved at an additional labeling cost by targeted data…
Transfer learning has recently become the dominant paradigm of machine learning. Pre-trained models fine-tuned for downstream tasks achieve better performance with fewer labelled examples. Nonetheless, it remains unclear how to develop…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
Machine learning (ML) has become a go-to solution for improving how we use, experience, and interact with technology (and the world around us). Unfortunately, studies have repeatedly shown that machine learning technologies may not provide…
We describe a new measure for the evaluation of region level segmentation of objects, as applied to evaluating the accuracy of leaf-level segmentation of plant images. The proposed approach enforces the rule that a region (e.g. a leaf) in…
Submodularity is an important concept in integer and combinatorial optimization. A classical submodular set function models the utility of selecting homogenous items from a single ground set, and such selections can be represented by binary…
Decomposing the domain of a function into parts has many uses in mathematics. A domain may naturally be a union of pieces, a function may be defined by cases, or different boundary conditions may hold on different regions. For any…
Clustering with submodular functions has been of interest over the last few years. Symmetric submodular functions are of particular interest as minimizing them is significantly more efficient and they include many commonly used functions in…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…