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.

Ex Input:
Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are detrimental to machine learning. We also study the behavior of the shortest path distance in weighted kNN graphs.

Ex Output:
Shortest path distance in random k-nearest neighbor graphs


Ex Input:
This paper proposes and experimentally validates a Bayesian network model of a range finder adapted to dynamic environments. All modeling assumptions are rigorously explained, and all model parameters have a physical interpretation. This approach results in a transparent and intuitive model. With respect to the state of the art beam model this paper: (i) proposes a different functional form for the probability of range measurements caused by unmodeled objects, (ii) intuitively explains the discontinuity encountered in the state of the art beam model, and (iii) reduces the number of model parameters, while maintaining the same representational power for experimental data. The proposed beam model is called RBBM, short for Rigorously Bayesian Beam Model. A maximum likelihood and a variational Bayesian estimator (both based on expectation-maximization) are proposed to learn the model parameters. Furthermore, the RBBM is extended to a full scan model in two steps: first, to a full scan model for static environments and next, to a full scan model for general, dynamic environments. The full scan model accounts for the dependency between beams and adapts to the local sample density when using a particle filter. In contrast to Gaussian-based state of the art models, the proposed full scan model uses a sample-based approximation. This sample-based approximation enables handling dynamic environments and capturing multimodality, which occurs even in simple static environments.

Ex Output:
A Rigorously Bayesian Beam Model and an Adaptive Full Scan Model for Range Finders in Dynamic Environments


Ex Input:
An RNN-based forecasting approach is used to early detect anomalies in industrial multivariate time series data from a simulated Tennessee Eastman Process (TEP) with many cyberattacks. This work continues a previously proposed LSTM-based approach to the fault detection in simpler data. It is considered necessary to adapt the RNN network to deal with data containing stochastic, stationary, transitive and a rich variety of anomalous behaviours. There is particular focus on early detection with special NABmetric. A comparison with the DPCA approach is provided. The generated data set is made publicly available.

Ex Output:

RNN-based Early Cyber-Attack Detection for the Tennessee Eastman Process