Knowledge is at the Edge! How to Search in Distributed Machine Learning Models

With the advent of the Internet of Things and Industry 4.0 an enormous amount of data is produced at the edge of the network. Due to a lack of computing power, this data is currently send to the cloud where centralized machine learning models are trained to derive higher level knowledge. With the recent development of specialized machine learning hardware for mobile devices, a new era of distributed learning is about to begin that raises a new research question: How can we search in distributed machine learning models? Machine learning at the edge of the network has many benefits, such as low-latency inference and increased privacy. Such distributed machine learning models can also learn personalized for a human user, a specific context, or application scenario. As training data stays on the devices, control over possibly sensitive data is preserved as it is not shared with a third party. This new form of distributed learning leads to the partitioning of knowledge between many devices which makes access difficult. In this paper we tackle the problem of finding specific knowledge by forwarding a search request (query) to a device that can answer it best. To that end, we use a entropy based quality metric that takes the context of a query and the learning quality of a device into account. We show that our forwarding strategy can achieve over 95% accuracy in a urban mobility scenario where we use data from 30 000 people commuting in the city of Trento, Italy.Comment: Published in CoopIS 201

Optimal model-free prediction from multivariate time series

Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal pre-selection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used sub-optimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Ni\~no Southern Oscillation.Comment: 14 pages, 9 figure

Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data based on conditional mutual information combined with a local permutation scheme is presented. Through a nearest neighbor approach, the test efficiently adapts also to non-smooth distributions due to strongly nonlinear dependencies. Numerical experiments demonstrate that the test reliably simulates the null distribution even for small sample sizes and with high-dimensional conditioning sets. The test is better calibrated than kernel-based tests utilizing an analytical approximation of the null distribution, especially for non-smooth densities, and reaches the same or higher power levels. Combining the local permutation scheme with the kernel tests leads to better calibration, but suffers in power. For smaller sample sizes and lower dimensions, the test is faster than random fourier feature-based kernel tests if the permutation scheme is (embarrassingly) parallelized, but the runtime increases more sharply with sample size and dimensionality. Thus, more theoretical research to analytically approximate the null distribution and speed up the estimation for larger sample sizes is desirable.Comment: 17 pages, 12 figures, 1 tabl