Abstract: A computer-implemented method of classifying sensor data for use in controlling and/or monitoring a computer-controlled system. The classification model includes an inference model that, based on the sensor data, determines respective concentration parameters of a Dirichlet distribution of class probabilities for the respective multiple classes. The classification model further includes a generative model that, based on the class probabilities, determines parameters of a probability distribution of sensor data according to a training dataset of the classification model. Concentration parameters according to the inference model are used for anomaly detection by determining a probability of the sensor data being generated according to the generative model based on the concentration parameters. The same concentration parameters are used to determine class probabilities.

Abstract: A computer-implemented method of training a model for making time-series predictions of a computer-controlled system. The model uses a stochastic differential equation (SDE) comprising a drift component and a diffusion component. The drift component has a predefined part representing domain knowledge, that is received as an input to the training; and a trainable part. When training the model, values of the set of SDE variables at a current time point are predicted based on their values at a previous time point, and based on this, the model is refined. In order to predict the values of the set of SDE variables, the predefined part of the drift component is evaluated to get a first drift, and the first drift is combined with a second drift obtained by evaluating the trainable part of the drift component.

Abstract: A computer-implemented method for verifying and/or validating whether a technical system fulfills a desired criterion with a predefined probability. The technical system emits output signals based on input signals supplied to the technical system. The method includes: obtaining models for components of the technical system and connections between the models; obtaining test outputs for the models based on test inputs of the models and the connections between the models; determining an upper or lower bound of an output of the technical system; verifying and/or validating whether the technical system fulfills the criterion with the predefined probability based on the determined upper or lower bound of the output.

Abstract: A device and method for reinforcement learning. The method includes providing parameters of a policy for reinforcement learning, determining a behavior policy depending on the policy, sampling a training data set with the behavior polic, and determining an update for the parameters with an objective function, wherein the objective function maps a difference between an estimate for an expected reward when following the policy and an estimate for a distance between the policy and the behavior policy, that depends on the policy and on the behavior policy, to the update. Or, the method includes providing distribution for parameters of a policy for reinforcement learning, determining a behavior policy depending on the policy, sampling a training data set with the behavior policy, and determining an update for the distribution with another objective function.

Abstract: A device, computer program and computer-implemented method for machine learning. The method comprises providing a task comprising an action space of a multi-armed bandit problem or a contextual bandit problem and a distribution over rewards that is conditioned on actions, providing a hyperprior, wherein the hyperprior is a distribution over the action space, determining, depending on the hyperprior, a hyperposterior for that a lower bound for an expected reward on future bandit tasks has as large a value as possible, when using priors sampled from the hyperposterior, and wherein the hyperposterior is a distribution over the action space.

Abstract: A method for training the neural drift network and the neural diffusion network of a neural stochastic differential equation. The method includes drawing a training trajectory from training sensor data, and, starting from the training data point which the training trajectory includes for a starting instant, determining the data-point mean and the data-point covariance at the prediction instant for each prediction instant of the sequence of prediction instants using the neural networks. The method also includes determining a dependency of the probability that the data-point distributions of the prediction instants—which are given by the ascertained data-point means and the ascertained data-point covariances—will supply the training data points at the prediction instants, on the weights of the neural drift network and of the neural diffusion network, and adapting the neural drift network and the neural diffusion network to increase the probability.

Abstract: A method of machine learning a model for mapping a dataset to a solution of a task depending on a first parameter. The method includes determining a second parameter for assigning the second parameter to the first parameter in a first iteration of learning and determining a third parameter for determining a rate for changing the first parameter in at least one iteration of learning depending on the third parameter and depending on a measure for evaluating the solution to the task. The determining of the second or third parameter includes determining a solution of an initial value problem that depends on partial derivatives, and determining the second parameter and/or the third parameter depending on at least one of the partial derivatives.

Abstract: A trained model is described in the form of a Bayesian neural network (BNN) which provides a quantification of its inference uncertainty during use and which is trained using marginal likelihood maximization. A Probably Approximately Correct (PAC) bound may be used in the training to incorporate prior knowledge and to improve training stability even when the network architecture is deep.

Abstract: A generator for converting an input vector from a latent space to one or more records x of measurement data that is realistic with respect to a given application domain. The generator includes: a trained neural network that is configured to map the input vector to a set of distribution parameters that characterize a random distribution of realistic measurement data, where this random distribution is configured such that given said set of distribution parameters and at least one source of randomness, samples of realistic measurement data may be obtained; and a sampling module including a random or pseudo-random number generator as a source of randomness and configured to sample the realistic measurement data from the random distribution.

Abstract: A computer-implemented method of training a model for making time-series predictions of a computer-controlled system. The model uses a stochastic differential equation (SDE) comprising a drift component and a diffusion component. The drift component has a predefined part representing domain knowledge, that is received as an input to the training; and a trainable part. When training the model, values of the set of SDE variables at a current time point are predicted based on their values at a previous time point, and based on this, the model is refined. In order to predict the values of the set of SDE variables, the predefined part of the drift component is evaluated to get a first drift, and the first drift is combined with a second drift obtained by evaluating the trainable part of the drift component.

Abstract: A computer-implemented method for enabling control or monitoring of a computer-controlled entity operating in an environment by predicting a future state of the computer-controlled entity and/or its environment using sensor data which is indicative of a current state of the computer-controlled entity and/or its environment. The method includes using a first neural network for approximating a drift component of a stochastic differential equation and a second neural network for approximating a diffusion component of the stochastic differential equation, and discretizing the stochastic differential equation into time steps, and obtaining time-evolving mean and covariance functions based on the discretization and determining a probability distribution of a second state of the computer-controlled entity and/or its environment therefrom.

Abstract: A method for processing sensor data. The method includes receiving input sensor data, determining, starting from the input sensor data as initial state, a plurality of end states, including determining, for each end state, a sequence of states, wherein determining the sequence of states comprises, for each state of the sequence beginning with the initial state until the end state, a first Bayesian neural network determining a sample of a drift term in response to inputting the respective state, a second Bayesian neural network determining a sample of a diffusion term in response to inputting the respective state and determining a subsequent state by sampling a stochastic differential equation including the sample of the drift term as drift term and the sample of the diffusion term as diffusion term. An end state probability distribution is determined, and a processing result is determined from the end state probability distribution.

Abstract: A device and a method for generating a compressed network from a trained neural network are provided. The method includes: a model generating a compressing map from first training data, the compressing map representing the impact of model components of the model to first output data in response to the first training data; generating a compressed network by compressing the trained neural network in accordance with the compressing map; the trained neural network generating trained network output data in response to second training data; the compressed network generating compressed network output data in response to the second training data; training the model by comparing the trained network output data with the compressed network output data.

Abstract: An event classification is trained by machine learning. An anomaly detection for detecting events in an image data set is thereby performed. Based on the performance of the anomaly detection, a model assumption of the event classification is determined. An image data set may include a plurality of images, and each image may include an array of pixels. Further, an image data set may include volume data and/or a time sequence of images and in this way represent a video sequence.

Abstract: A trained model is described in the form of a Bayesian neural network (BNN) which provides a quantification of its inference uncertainty during use and which is trained using marginal likelihood maximization. A Probably Approximately Correct (PAC) bound may be used in the training to incorporate prior knowledge and to improve training stability even when the network architecture is deep.

Abstract: An event classification is trained by machine learning. An anomaly detection for detecting events in an image data set is thereby performed. Based on the performance of the anomaly detection, a model assumption of the event classification is determined. An image data set may include a plurality of images, and each image may include an array of pixels. Further, an image data set may include volume data and/or a time sequence of images and in this way represent a video sequence.