Interdependent Durations

This paper studies the identification of a simultaneous equation model where the variable of interest is a duration measure. It proposes a game theoretic model in which durations are determined by strategic agents. In the absence of strategic motives, the model delivers a version of the generalized accelerated failure time model. In its most general form, the system resembles a classical simultaneous equation model in which endogenous variables interact with observable and unobservable exogenous components to characterize a certain economic environment. In this paper, the endogenous variables are the individually chosen equilibrium durations. Even though a unique solution to the game is not always attainable in this context, the structural elements of the economic system are shown to be semiparametrically point identified. We also present a brief discussion of estimation ideas and a set of simulation studies on the model.duration, empirical games, identification

ExplaiNE: An Approach for Explaining Network Embedding-based Link Predictions

Networks are powerful data structures, but are challenging to work with for conventional machine learning methods. Network Embedding (NE) methods attempt to resolve this by learning vector representations for the nodes, for subsequent use in downstream machine learning tasks. Link Prediction (LP) is one such downstream machine learning task that is an important use case and popular benchmark for NE methods. Unfortunately, while NE methods perform exceedingly well at this task, they are lacking in transparency as compared to simpler LP approaches. We introduce ExplaiNE, an approach to offer counterfactual explanations for NE-based LP methods, by identifying existing links in the network that explain the predicted links. ExplaiNE is applicable to a broad class of NE algorithms. An extensive empirical evaluation for the NE method `Conditional Network Embedding' in particular demonstrates its accuracy and scalability

Conditional network embeddings

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that 'similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if 'similar' means being 'more likely to be connected') or classification (if 'similar' means 'being more likely to have the same label'). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes. A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties: (approximate) multipartiteness, certain degree distributions, assortativity, etc. To overcome this, we introduce a conceptual innovation to the NE literature and propose to create \emph{Conditional Network Embeddings} (CNEs); embeddings that maximally add information with respect to given structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently. We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization

ALPINE : Active Link Prediction using Network Embedding

Many real-world problems can be formalized as predicting links in a partially observed network. Examples include Facebook friendship suggestions, consumer-product recommendations, and the identification of hidden interactions between actors in a crime network. Several link prediction algorithms, notably those recently introduced using network embedding, are capable of doing this by just relying on the observed part of the network. Often, the link status of a node pair can be queried, which can be used as additional information by the link prediction algorithm. Unfortunately, such queries can be expensive or time-consuming, mandating the careful consideration of which node pairs to query. In this paper we estimate the improvement in link prediction accuracy after querying any particular node pair, to use in an active learning setup. Specifically, we propose ALPINE (Active Link Prediction usIng Network Embedding), the first method to achieve this for link prediction based on network embedding. To this end, we generalized the notion of V-optimality from experimental design to this setting, as well as more basic active learning heuristics originally developed in standard classification settings. Empirical results on real data show that ALPINE is scalable, and boosts link prediction accuracy with far fewer queries

Explainable subgraphs with surprising densities : a subgroup discovery approach

The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between any pair of people depends on a range of attributes, such as their age, residence location, workplace, and hobbies. The high-level structure of a graph can thus possibly be described well by means of patterns of the form `the subgroup of all individuals with a certain properties X are often (or rarely) friends with individuals in another subgroup defined by properties Y', in comparison to what is expected. Such rules present potentially actionable and generalizable insight into the graph. We present a method that finds node subgroup pairs between which the edge density is interestingly high or low, using an information-theoretic definition of interestingness. Additionally, the interestingness is quantified subjectively, to contrast with prior information an analyst may have about the connectivity. This view immediatly enables iterative mining of such patterns. This is the first method aimed at graph connectivity relations between different subgroups. Our method generalizes prior work on dense subgraphs induced by a subgroup description. Although this setting has been studied already, we demonstrate for this special case considerable practical advantages of our subjective interestingness measure with respect to a wide range of (objective) interestingness measures

Informative Data Projections: A Framework and Two Examples

Methods for Projection Pursuit aim to facilitate the visual exploration of high-dimensional data by identifying interesting low-dimensional projections. A major challenge is the design of a suitable quality metric of projections, commonly referred to as the projection index, to be maximized by the Projection Pursuit algorithm. In this paper, we introduce a new information-theoretic strategy for tackling this problem, based on quantifying the amount of information the projection conveys to a user given their prior beliefs about the data. The resulting projection index is a subjective quantity, explicitly dependent on the intended user. As a useful illustration, we developed this idea for two particular kinds of prior beliefs. The first kind leads to PCA (Principal Component Analysis), shining new light on when PCA is (not) appropriate. The second kind leads to a novel projection index, the maximization of which can be regarded as a robust variant of PCA. We show how this projection index, though non-convex, can be effectively maximized using a modified power method as well as using a semidefinite programming relaxation. The usefulness of this new projection index is demonstrated in comparative empirical experiments against PCA and a popular Projection Pursuit method

Tactical fixed job scheduling with spread-time constraints

We address the tactical fixed job scheduling problem with spread-time constraints. In such a problem, there are a fixed number of classes of machines and a fixed number of groups of jobs. Jobs of the same group can only be processed by machines of a given set of classes. All jobs have their fixed start and end times. Each machine is associated with a cost according to its machine class. Machines have spread-time constraints, with which each machine is only available for L consecutive time units from the start time of the earliest job assigned to it. The objective is to minimize the total cost of the machines used to process all the jobs. For this strongly NP-hard problem, we develop a branch-and-price algorithm, which solves instances with up to 300 jobs, as compared with CPLEX, which cannot solve instances of 100 jobs. We further investigate the influence of machine flexibility by computational experiments. Our results show that limited machine flexibility is sufficient in most situations