Abstract: Techniques, systems, and devices are described for providing a computational frame for estimating high-dimensional stochastic behaviors. In one exemplary aspect, a method for performing numerical estimation includes receiving a set of measurements of a stochastic behavior. The set of correlated measurements follows a non-standard probability distribution and is non-linearly correlated. Also, a non-linear relationship exists between a set of system variables that describes the stochastic behavior and a corresponding set of measurements. The method includes determining, based on the set of measurements, a numerical model of the stochastic behavior. The numerical model comprises a feature space comprising non-correlated features corresponding to the stochastic behavior. The non-correlated features have a dimensionality of M and the set of measurements has a dimensionality of N, M being smaller than N.

Abstract: Techniques, systems, and devices are described for providing a computational frame for estimating high-dimensional stochastic behaviors. In one exemplary aspect, a method for performing numerical estimation includes receiving a set of measurements of a stochastic behavior. The set of correlated measurements follows a non-standard probability distribution and is non-linearly correlated. Also, a non-linear relationship exists between a set of system variables that describes the stochastic behavior and a corresponding set of measurements. The method includes determining, based on the set of measurements, a numerical model of the stochastic behavior. The numerical model comprises a feature space comprising non-correlated features corresponding to the stochastic behavior. The non-correlated features have a dimensionality of M and the set of measurements has a dimensionality of N, M being smaller than N.

Abstract: Techniques, systems, and devices are described for providing a computational frame for estimating high-dimensional stochastic behaviors. In one exemplary aspect, a method for performing numerical estimation includes receiving a set of measurements of a stochastic behavior. The set of correlated measurements follows a non-standard probability distribution and is non-linearly correlated. Also, a non-linear relationship exists between a set of system variables that describes the stochastic behavior and a corresponding set of measurements. The method includes determining, based on the set of measurements, a numerical model of the stochastic behavior. The numerical model comprises a feature space comprising non-correlated features corresponding to the stochastic behavior. The non-correlated features have a dimensionality of M and the set of measurements has a dimensionality of N, M being smaller than N.

Abstract: A system generates vector representations of entries of traffic logs generated by a firewall. A first model learns contexts of values recorded in the logs during training, and the system extracts vector representations of the values from the trained model. For each log entry, vectors created for the corresponding values are combined to create a vector representing the entry. Cluster analysis of the vector representations can be performed to determine clusters of similar traffic and outliers indicative of potentially anomalous traffic. The system also generates a formal model representing firewall behavior which comprises formulas generated from the firewall rules. Proposed traffic scenarios not recorded in the logs can be evaluated based on the formulas to determine actions which the firewall would take in the scenarios. The combination of models which implement machine learning and formal techniques facilitates evaluation of both observed and hypothetical network traffic based on the firewall rules.

Abstract: Techniques, systems, and devices are described for providing a computational frame for estimating high-dimensional stochastic behaviors. In one exemplary aspect, a method for performing numerical estimation includes receiving a set of measurements of a stochastic behavior. The set of correlated measurements follows a non-standard probability distribution and is non-linearly correlated. Also, a non-linear relationship exists between a set of system variables that describes the stochastic behavior and a corresponding set of measurements. The method includes determining, based on the set of measurements, a numerical model of the stochastic behavior. The numerical model comprises a feature space comprising non-correlated features corresponding to the stochastic behavior. The non-correlated features have a dimensionality of M and the set of measurements has a dimensionality of N, M being smaller than N.