David Stein

David Stein, Silvia Di Gregorio, Bjoern Andres

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.

David Stein, Bjoern Andres

Bird sound classification is the task of relating any sound recording to those species of bird that can be heard in the recording. Here, we study bird sound clustering, the task of deciding for any pair of sound recordings whether the same species of bird can be heard in both. We address this problem by first learning, from a training set, probabilities of pairs of recordings being related in this way, and then inferring a maximally probable partition of a test set by correlation clustering. We address the following questions: How accurate is this clustering, compared to a classification of the test set? How do the clusters thus inferred relate to the clusters obtained by classification? How accurate is this clustering when applied to recordings of bird species not heard during training? How effective is this clustering in separating, from bird sounds, environmental noise not heard during training?

David Stein, Jannik Irmai, Bjoern Andres

Preordering is a generalization of clustering and partial ordering with applications in bioinformatics and social network analysis. Given a finite set $V$ and a value $c_{ab} \in \mathbb{R}$ for every ordered pair $ab$ of elements of $V$, the preordering problem asks for a preorder $\lesssim$ on $V$ that maximizes the sum of the values of those pairs $ab$ for which $a \lesssim b$. Building on the state of the art in solving this NP-hard problem partially, we contribute new partial optimality conditions and efficient algorithms for deciding these conditions. In experiments with real and synthetic data, these new conditions increase, in particular, the fraction of pairs $ab$ for which it is decided efficiently that $a \not\lesssim b$ in an optimal preorder.

Fedor Borisyuk, Shihai He, Yunbo Ouyang et al.

In this paper, we present LiGNN, a deployed large-scale Graph Neural Networks (GNNs) Framework. We share our insight on developing and deployment of GNNs at large scale at LinkedIn. We present a set of algorithmic improvements to the quality of GNN representation learning including temporal graph architectures with long term losses, effective cold start solutions via graph densification, ID embeddings and multi-hop neighbor sampling. We explain how we built and sped up by 7x our large-scale training on LinkedIn graphs with adaptive sampling of neighbors, grouping and slicing of training data batches, specialized shared-memory queue and local gradient optimization. We summarize our deployment lessons and learnings gathered from A/B test experiments. The techniques presented in this work have contributed to an approximate relative improvements of 1% of Job application hearing back rate, 2% Ads CTR lift, 0.5% of Feed engaged daily active users, 0.2% session lift and 0.1% weekly active user lift from people recommendation. We believe that this work can provide practical solutions and insights for engineers who are interested in applying Graph neural networks at large scale.

Jannik Presberger, Rashmiparvathi Keshara, David Stein et al.

In biological and medical research, scientists now routinely acquire microscopy images of hundreds of morphologically heterogeneous organoids and are then faced with the task of finding patterns in the image collection, i.e., subsets of organoids that appear similar and potentially represent the same morphological class. We adopt models and algorithms for correlating organoid images, i.e., for quantifying the similarity in appearance and geometry of the organoids they depict, and for clustering organoid images by consolidating conflicting correlations. For correlating organoid images, we adopt and compare two alternatives, a partial quadratic assignment problem and a twin network. For clustering organoid images, we employ the correlation clustering problem. Empirically, we learn the parameters of these models, infer a clustering of organoid images, and quantify the accuracy of the inferred clusters, with respect to a training set and a test set we contribute of state-of-the-art light microscopy images of organoids clustered manually by biologists.

David Stein, Bjoern Andres, Silvia Di Gregorio

The higher-order correlation clustering problem for a graph $G$ and costs associated with cliques of $G$ consists in finding a clustering of $G$ so as to minimize the sum of the costs of those cliques whose nodes all belong to the same cluster. To tackle this NP-hard problem in practice, local search heuristics have been proposed and studied in the context of applications. Here, we establish partial optimality conditions for cubic correlation clustering, i.e., for the special case of at most 3-cliques. We define and implement algorithms for deciding these conditions and examine their effectiveness numerically, on two data sets.

Paul Swoboda, Bjoern Andres, Andrea Hornakova et al.

Structured prediction problems are one of the fundamental tools in machine learning. In order to facilitate algorithm development for their numerical solution, we collect in one place a large number of datasets in easy to read formats for a diverse set of problem classes. We provide archival links to datasets, description of the considered problems and problem formats, and a short summary of problem characteristics including size, number of instances etc. For reference we also give a non-exhaustive selection of algorithms proposed in the literature for their solution. We hope that this central repository will make benchmarking and comparison to established works easier. We welcome submission of interesting new datasets and algorithms for inclusion in our archive.

David Stein, Bjoern Andres

We consider the problem of jointly minimizing forms of two Boolean functions $f, g \colon \{0,1\}^J \to \{0,1\}$ such that $f + g \leq 1$ and so as to separate disjoint sets $A \cup B \subseteq \{0,1\}^J$ such that $f(A) = \{1\}$ and $g(B) = \{1\}$. We hypothesize that this problem is easier to solve or approximate than the well-understood problem of minimizing the form of one Boolean function $h: \{0,1\}^J \to \{0,1\}$ such that $h(A) = \{1\}$ and $h(B) = \{0\}$. For a large class of forms, including binary decision trees and ordered binary decision diagrams, we refute this hypothesis. For disjunctive normal forms, we show that the problem is at least as hard as MIN-SET-COVER. For all these forms, we establish that no $o(\ln (|A| + |B| -1))$-approximation algorithm exists unless P$=$NP.