Related papers: Bayes-optimal Hierarchical Classification over Asy…

Thin spanning trees lie at the intersection of graph theory, approximation algorithms, and combinatorial optimization. They are central to the long-standing \emph{thin tree conjecture}, which asks whether every $k$-edge-connected graph…

The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…

When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be…

Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can…

Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function…

Failing to distinguish between a sheepdog and a skyscraper should be worse and penalized more than failing to distinguish between a sheepdog and a poodle; after all, sheepdogs and poodles are both breeds of dogs. However, existing metrics…

This paper deals with the representation and solution of asymmetric Bayesian decision problems. We present a formal framework, termed asymmetric influence diagrams, that is based on the influence diagram and allows an efficient…

When introducing physics-constrained deep learning solutions to the volumetric super-resolution of scientific data, the training is challenging to converge and always time-consuming. We propose a new hierarchical sampling method based on…

While globally optimal empirical risk minimization (ERM) decision trees have become computationally feasible and empirically successful, rigorous theoretical guarantees for their statistical performance remain limited. In this work, we…

Hierarchical classification aims to sort the object into a hierarchical structure of categories. For example, a bird can be categorized according to a three-level hierarchy of order, family, and species. Existing methods commonly address…

Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…

In data centers, data replication is the primary method used to ensure availability of customer data. To avoid correlated failure, cloud storage infrastructure providers model hierarchical failure domains using a tree, and avoid placing a…

We propose a hierarchical training algorithm for standard feed-forward neural networks that adaptively extends the network architecture as soon as the optimization reaches a stationary point. By solving small (low-dimensional) optimization…

Attempts of learning from hierarchical taxonomies in computer vision have been mostly focusing on image classification. Though ways of best harvesting learning improvements from hierarchies in classification are far from being solved, there…

It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…

We explore the role of group symmetries in binary classification tasks, presenting a novel framework that leverages the principles of Neyman-Pearson optimality. Contrary to the common intuition that larger symmetry groups lead to improved…

Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the problem of counting inversions in arrays originated in mathematical…

In this article, we propose a novel approach for plant hierarchical taxonomy classification by posing the problem as an open class problem. It is observed that existing methods for medicinal plant classification often fail to perform…

Single-level density-based approach has long been widely acknowledged to be a conceptually and mathematically convincing clustering method. In this paper, we propose an algorithm called "best-scored clustering forest" that can obtain the…

The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…