We analyze the information-theoretic limits for the recovery of node labels in several network models.

Inference in the introduced linear Gaussian SSM is straightforward and can be performed using Kalman prediction and observation updates.

We present a novel approach to probabilistic time series forecasting that combines state space models with deep learning. By parametrizing a per-time-series linear state space model with a jointly-learned recurrent neural network, our method retains desired properties of state space models such as data efficiency and inter-pretability, while making use of the ability to learn complex patterns from raw data offered by deep learning approaches. Our method scales gracefully from regimes where little training data is available to regimes where data from large collection of time series can be leveraged to learn accurate models. We provide qualitative as well as quantitative results with the proposed method, showing that it compares favorably to the state-of-the-art.

Inference in the introduced linear Gaussian SSM is straightforward and can be performed using Kalman prediction and observation updates.

Directly learning to generate audio waveforms in an autoregressive manner is a challenging task, due to the length of the raw sequences and the existence of important structure on many different timescales. Traditional approaches based on recurrent neural networks, as well as causal convolutions and self-attention, have only had limited success on this task. However, recent work has shown that deep state space models, also referred to as linear RNNs, can be highly efficient in this context. In this work, we push the boundaries of linear RNNs applied to raw audio modeling, investigating the effects of different architectural choices and using context-parallelism to enable training on sequences up to one minute (1M tokens) in length. We present a model, HarmonicRNN, which attains state of the art log-likelihoods and perceptual metrics on small-scale datasets.

The state space dynamics representation is the most general approach for nonlinear systems and often chosen for system identification. During training, the state trajectory can deform significantly leading to poor data coverage of the state space. This can cause significant issues for space-oriented training algorithms which e.g. rely on grid structures, tree partitioning, or similar. Besides hindering training, significant state trajectory deformations also deteriorate interpretability and robustness properties. This paper proposes a new type of space-filling regularization that ensures a favorable data distribution in state space via introducing a data-distribution-based penalty. This method is demonstrated in local model network architectures where good interpretability is a major concern. The proposed approach integrates ideas from modeling and design of experiments for state space structures. This is why we present two regularization techniques for the data point distributions of the state trajectories for local affine state space models. Beyond that, we demonstrate the results on a widely known system identification benchmark.

Differential privacy is a well-established framework for safeguarding sensitive information in data. While extensively applied across various domains, its application to network data -- particularly at the node level -- remains underexplored. Existing methods for node-level privacy either focus exclusively on query-based approaches, which restrict output to pre-specified network statistics, or fail to preserve key structural properties of the network. In this work, we propose GRAND (Graph Release with Assured Node Differential privacy), which is, to the best of our knowledge, the first network release mechanism that releases entire networks while ensuring node-level differential privacy and preserving structural properties. Under a broad class of latent space models, we show that the released network asymptotically follows the same distribution as the original network. The effectiveness of the approach is evaluated through extensive experiments on both synthetic and real-world datasets.