In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: The preimage of the activities of all the nodes at a certain level of a deep network is the set of inputs that result in the same node activity. For fully connected multi layer rectifier networks we demonstrate how to compute the preimages of activities at arbitrary levels from knowledge of the parameters in a deep rectifying network by disregarding the effects of max-pooling. If the preimage set of a certain activity in the network contains elements from more than one class it means that these classes are irreversibly mixed. This implies that preimage sets which are piecewise linear manifolds are building blocks for describing the input manifolds specific classes, i.e. all preimages should ideally be from the same class. We believe that the knowledge of how to compute preimages will be valuable in understanding the efficiency displayed by deep learning networks and could potentially be used in designing more efficient training algorithms

A: THE PREIMAGE OF RECTIFIER NETWORK ACTIVITIES
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Q: Modern distributed cyber-physical systems encounter a large variety of anomalies and in many cases, they are vulnerable to catastrophic fault propagation scenarios due to strong connectivity among the sub-systems. In this regard, root-cause analysis becomes highly intractable due to complex fault propagation mechanisms in combination with diverse operating modes. This paper presents a new data-driven framework for root-cause analysis for addressing such issues. The framework is based on a spatiotemporal feature extraction scheme for multivariate time series built on the concept of symbolic dynamics for discovering and representing causal interactions among subsystems of a complex system. We propose sequential state switching (S) and artificial anomaly association (A) methods to implement rootcause analysis in an unsupervised and semi-supervised manner respectively. Synthetic data from cases with failed pattern(s) and anomalous node are simulated to validate the proposed approaches, then compared with the performance of vector autoregressive (VAR) model-based root-cause analysis. The results show that: (1) S andA approaches can obtain high accuracy in root-cause analysis and successfully handle multiple nominal operation modes, and (2) the proposed tool-chain is shown to be scalable while maintaining high accuracy.

A: Root-cause analysis for time-series anomalies via spatiotemporal causal graphical modeling
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Q: A decision tree is a classification (and regression) model that, based on the characteristics of a given object, and applying a series of rules, is able to classify it (or return a continuous value in the case of regression). The induction of decision trees from a set of previously classified objects is one of the most popular machine learning models due, among other things, to the low computational demand in their training and the interpretability of their results, so it is a representative white box model. ID3 algorithm presented by R. Quinlan in 1983 for the automatic construction of decision trees from a training set of objects described through a collection of properties. Each object in the training set belongs to a class (usually represented by the value of its target attribute) of a set of mutually exclusive classes. ID3 has been one of the most used techniques in machine learning with applications to tasks as diverse as epidemics prediction, robot control, and automatic classification of clients in banks or insurance entities [19, 18, 7]. The main goal of this work is to offer a methodology that allows to carry out machine learning tasks using decision trees on multi-relational graph data. In this context, the number of possible properties of each object goes far beyond those that it has directly associated, since the properties of the elements that are related to it can also be considered attributes of the object, and even the topological structure formed by the objects in their environment and the various measures that can be taken from the graph structure could be considered as additional attributes. With this objective, we will analyse different techniques that allow automatic induction of decision trees from graph data and we will present our proposal, GGQ-ID3, that aims to provide a framework to classify substructures in a graph, from simple nodes and edges, to larger paths and subgraphs, making use of Generalized Graph Query (GGQ) [1]. This paper is structured as follows: we will start reviewing different techniques of induction of relational decision trees; then, we present our proposal based on the use of Generalized Graph Queries as evaluation tool; once our proposal is presented, we will show some examples of its application; and finally we present some conclusions and future work lines.

A:
Induction of Decision Trees based on Generalized Graph Queries
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