Generative normalizing flows are able to model multimodal spatial distributions, and they have been shown to model temporal correlations successfully as well. These models provide several benefits over other types of generative models due to their training stability, invertibility and efficiency in sampling and inference. This makes them a suitable candidate for stochastic spatio-temporal prediction problems, which are omnipresent in many fields of sciences, such as earth sciences, astrophysics or molecular sciences. In this paper, we present a conditional normalizing flow for stochastic spatio-temporal modelling. The method is evaluated on the task of daily temperature map prediction from an ERA5 dataset. Experiments show that our method is able to capture spatio-temporal correlations and extrapolates well beyond the time horizon used during training.
Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of variables formula. Such behavior is desirable in multivariate structured prediction tasks, where handcrafted per-pixel loss-based methods inadequately capture strong correlations between output dimensions. We present a study of conditional normalizing flows (CNFs), a class of NFs where the base density to output space mapping is conditioned on an input x, to model conditional densities p(y|x). CNFs are efficient in sampling and inference, they can be trained with a likelihood-based objective, and CNFs, being generative flows, do not suffer from mode collapse or training instabilities. We provide an effective method to train continuous CNFs for binary problems and in particular, we apply these CNFs to super-resolution and vessel segmentation tasks demonstrating competitive performance on standard benchmark datasets in terms of likelihood and conventional metrics. (Supervised by Emiel Hoogeboom, Rianne van den Berg and Daniel Worrall @ University of Amsterdam, 2019) Pre-print
In Reinforcement Learning the Q-learning algorithm is known to overestimate state-action values under certain conditions. A positive bias is introduced as Q-learning uses the same function to select actions and evaluate a state-action pair. Hence, overoptimistic values are more likely to be used in updates. Hasselt (2016) showed that this can indeed be harmful for performance using Deep Neural Networks and proposed the Double Deep Q Networks algorithm. We apply both algorithms and compare their performance on different environments provided by Open AI Gym (Brockman et al., 2016). Poster
Deep Learning is used to solve a wide range of problems by providing samples of input data along with the expected output from the neural networks. The learning is driven by concrete mathematical rules used systematically to adjust weights of the network — think of these as a collection of numerical knobs adjusted to produce the desired output. What the network actually learns are these numbers which transform an input question into an output answer. What do these numbers signify? Do they represent knowledge which can be interpreted and understood by humans? (Project as part of the Artificial Intelligence Master under supervision of Prof. Zeynep Akata @ University of Amsterdam, 2018) PDF 📝 Blogpost
In this Bachelor thesis we apply a boosting approach for models with sparse network structure on stationary gaussian time series data components. Based on the resulting parameter estimates the concept of Granger-causality graphs can be applied to study the causal relationships among the time series. A sensitivity analysis of the algorithm is conducted by only altering the time dimension and the edge strength and keeping the other parameters fixed. The performance of the boosting method is compared to the conventional Vectore Auto Regression (VAR) where the number of cross sections is relatively small. We show that the algorithm achieves better results when edge weights are strong. In the event where the number of available observations is equal to the number of predictor variables the algorithm still performs better than random guessing. Estimating a VAR model is a favorable approach over the boosting method when the cross-section dimension N is not too large such that consistent estimation is ensured. (Bachelor Thesis written under supervision of Prof. Michael Eichler @ Maastricht University, 2017)