We propose DenseHMM - a modification of Hidden Markov Models (HMMs) that allows to learn dense representations of both the hidden states and the observables. Compared to the standard HMM, transition probabilities are not atomic but composed of these representations via kernelization. Our approach enables constraint-free and gradient-based optimization. We propose two optimization schemes that make use of this: a modification of the Baum-Welch algorithm and a direct co-occurrence optimization. The latter one is highly scalable and comes empirically without loss of performance compared to standard HMMs. We show that the non-linearity of the kernelization is crucial for the expressiveness of the representations. The properties of the DenseHMM like learned co-occurrences and log-likelihoods are studied empirically on synthetic and biomedical datasets.
Artificial intelligence for autonomous driving must meet strict requirements on safety and robustness. We propose to validate machine learning models for self-driving vehicles not only with given ground truth labels, but also with additional a-priori knowledge. In particular, we suggest to validate the drivable area in semantic segmentation masks using given street map data. We present first results, which indicate that prediction errors can be uncovered by map-based validation.
Monte Carlo (MC) dropout is one of the state-of-the-art approaches for uncertainty estimation in neural networks (NNs). It has been interpreted as approximately performing Bayesian inference. Based on previous work on the approximation of Gaussian processes by wide and deep neural networks with random weights, we study the limiting distribution of wide untrained NNs under dropout more rigorously and prove that they as well converge to Gaussian processes for fixed sets of weights and biases. We sketch an argument that this property might also hold for infinitely wide feed-forward networks that are trained with (full-batch) gradient descent. The theory is contrasted by an empirical analysis in which we find correlations and non-Gaussian behaviour for the pre-activations of finite width NNs. We therefore investigate how (strongly) correlated pre-activations can induce non-Gaussian behavior in NNs with strongly correlated weights.
We propose an efficient protocol for decentralized training of deep neural networks from distributed data sources. The proposed protocol allows to handle different phases of model training equally well and to quickly adapt to concept drifts. This leads to a reduction of communication by an order of magnitude compared to periodically communicating state-of-the-art approaches. Moreover, we derive a communication bound that scales well with the hardness of the serialized learning problem. The reduction in communication comes at almost no cost, as the predictive performance remains virtually unchanged. Indeed, the proposed protocol retains loss bounds of periodically averaging schemes. An extensive empirical evaluation validates major improvement of the trade-off between model performance and communication which could be beneficial for numerous decentralized learning applications, such as autonomous driving, or voice recognition and image classification on mobile phones.