**Low-Level, First-Order Probabilistic Programming Language (LF-PPL)**

We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density function is discontinuous with respect to, while further providing runtime checks for boundary crossings. This enables the introduction of new inference engines that are able to exploit gradient information, while remaining efficient for models which are not everywhere differentiable. We demonstrate this ability by incorporating a discontinuous Hamiltonian Monte Carlo (DHMC) inference engine that is able to deliver automated and efficient inference for non-differentiable models. Our system is backed up by a mathematical formalism that ensures that any model expressed in this language has a density with measure zero discontinuities to maintain the validity of the inference engine. … **Frequency-Based Kernel Kalman Filter (FKKF)**

One main challenge for the design of networks is that traffic load is not generally known in advance. This makes it hard to adequately devote resources such as to best prevent or mitigate bottlenecks. While several authors have shown how to predict traffic in a coarse grained manner by aggregating flows, fine grained prediction of traffic at the level of individual flows, including bursty traffic, is widely considered to be impossible. This paper shows, to the best of our knowledge, the first approach to fine grained per flow traffic prediction. In short, we introduce the Frequency-based Kernel Kalman Filter (FKKF), which predicts individual flows’ behavior based on measurements. Our FKKF relies on the well known Kalman Filter in combination with a kernel to support the prediction of non linear functions. Furthermore we change the operating space from time to frequency space. In this space, into which we transform the input data via a Short-Time Fourier Transform (STFT), the peak structures of flows can be predicted after gleaning their key characteristics, with a Principal Component Analysis (PCA), from past and ongoing flows that stem from the same socket-to-socket connection. We demonstrate the effectiveness of our approach on popular benchmark traces from a university data center. Our approach predicts traffic on average across 17 out of 20 groups of flows with an average prediction error of 6.43% around 0.49 (average) seconds in advance, whilst existing coarse grained approaches exhibit prediction errors of 77% at best. … **Gaussian image entropy and piecewise stationary time series analysis (SPEV)**

Vision-based methods for visibility estimation can play a critical role in reducing traffic accidents caused by fog and haze. To overcome the disadvantages of current visibility estimation methods, we present a novel data-driven approach based on Gaussian image entropy and piecewise stationary time series analysis (SPEV). This is the first time that Gaussian image entropy is used for estimating atmospheric visibility. To lessen the impact of landscape and sunshine illuminance on visibility estimation, we used region of interest (ROI) analysis and took into account relative ratios of image entropy, to improve estimation accuracy. We assume fog and haze cause blurred images and that fog and haze can be considered as a piecewise stationary signal. We used piecewise stationary time series analysis to construct the piecewise causal relationship between image entropy and visibility. To obtain a real-world visibility measure during fog and haze, a subjective assessment was established through a study with 36 subjects who performed visibility observations. Finally, a total of two million videos were used for training the SPEV model and validate its effectiveness. The videos were collected from the constantly foggy and hazy Tongqi expressway in Jiangsu, China. The contrast model of visibility estimation was used for algorithm performance comparison, and the validation results of the SPEV model were encouraging as 99.14% of the relative errors were less than 10%. … **Gromov-Wasserstein Distance**

Modeling datasets as metric spaces seems to be natural for some applications and concepts revolving around the Gromov-Hausdorff distance – a notion of distance between compact metric spaces – provide a useful language for expressing properties of data and shape analysis methods. In many situations, however, this is not enough, and one must incorporate other sources of information into the model, with ‘weights’ attached to each point being one of them. This gives rise to the idea of representing data as metric measure spaces, which are metric spaces endowed with a probability measure. In terms of a distance, the Gromov-Hausdorff metric is replaced with the Gromov-Wasserstein metric. …

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