State-space models are a statistical framework for modelling temporal phenomena via a hidden state. In this framework, the hidden state is not observed, and instead a series of related observations are obtained. A state-space model is defined by the state dynamics, which is encoded as a distribution. The parameters of this distribution are often unknown, and must be estimated in order to perform inference. In real-world systems, it is common that not all dimensions of the hidden state directly interact, which implies a sparse system. Most parameter estimation methods for state-space models cannot recover sparsity. In this work, we propose PolyGrad, a fully automatic method for obtaining sparse estimates of the state interactions of a non-linear state-space model via a polynomial approximation. This novel versatile methodology allows to infer both the structure and values of a generic parameterisation of a state-space model. The proposed method is computationally efficient and can represent a large class of complex systems.

State-space models are a popular statistical framework for analysing sequential data. Within this framework, particle filters are often used to perform inference on non-linear state-space models. We introduce a new method, StateMixNN, that uses a pair of neural networks to learn the proposal distribution and transition kernel of a particle filter. Both distributions are approximated using multivariate Gaussian mixtures. The component means and covariances of these mixtures are learnt as outputs of learned functions. Our method is trained targeting the log-likelihood, thereby requiring only the observation series, and combines the interpretability of state-space models with the flexibility and approximation power of artificial neural networks . The proposed method significantly improves recovery of the hidden state in comparison with the state-of-the-art, showing greater improvement in highly non-linear scenarios.

We introduce a new method, named PropMixNN, that uses a neural network to learn the proposal distribution of a particle filter. The optimal proposal distribution is approximated as a multivariate Gaussian mixture, so the proposed method aims at learning the means and covariance matrices of the S components that characterise the mixture. This unsupervised method is trained to target the log-likelihood, which does not require knowledge of the hidden state. The performance of the method is assessed in a stochastic Lorenz 96 model, which presents a non-linear chaotic behaviour. The proposed method reduces estimation errors in comparison with the state-of-the-art, showing greater improvement in highly non-linear scenarios.

Unlike other diversity-based approaches, N-variant systems thwart attacks without requiring secrets. Instead, they use redundancy (to require an attacker to simultaneously compromise multiple variants with the same input) and tailored diversity (to make it impossible to compromise all the variants with the same input for given attack classes). In this work, we develop a method for using data diversity in N-variant systems to provide high-assurance arguments against a class of data corruption attacks. Data is transformed in the variants so identical concrete data values have different interpretations. In order to corrupt the data without detection, an attacker would need to alter the corresponding data in each variant in a different way while sending the same inputs to all variants. We demonstrate our approach with a case study using that thwarts attacks that corrupt UID values.