The words "science" and "Church" are here understood in the following sense: Science is not taken in the restricted meaning of natural sciences, but in the general one given to the word by Aristotle and St. Aristotle defines science as a sure and evident knowledge obtained from demonstrations.
They can be used for non-linear regression, time-series modelling, classification, and many other problems. Streaming sparse Gaussian process approximations. Sparse approximations for Gaussian process models provide a suite of methods that enable these models to be deployed in large data regime and enable analytic intractabilities to be sidestepped.
However, the field lacks a principled method to handle streaming data in which the posterior distribution over function values and the hyperparameters are updated in an online fashion. The small number of existing approaches either use suboptimal hand-crafted heuristics for hyperparameter learning, or suffer from catastrophic forgetting or slow updating when new data arrive.
This paper develops a new principled framework for deploying Gaussian process probabilistic models in the streaming setting, providing principled methods for learning hyperparameters and optimising pseudo-input locations.
The proposed framework is experimentally validated using synthetic and real-world datasets. The first two authors contributed equally. The unreasonable effectiveness of structured random orthogonal embeddings.
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation.
We introduce matrices with complex entries which give significant further accuracy improvement. We provide geometric and Markov chain-based perspectives to help understand the benefits, and empirical results which suggest that the approach is helpful in a wider range of applications.
We present a data-efficient reinforcement learning method for continuous state-action systems under significant observation noise.
Data-efficient solutions under small noise exist, such as PILCO which learns the cartpole swing-up task in 30s. PILCO evaluates policies by planning state-trajectories using a dynamics model.
This enables data-efficient learning under significant observation noise, outperforming more naive methods such as post-hoc application of a filter to policies optimised by the original unfiltered PILCO algorithm.
We test our method on the cartpole swing-up task, which involves nonlinear dynamics and requires nonlinear control. Skoglund, Zoran Sjanic, and Manon Kok.
On orientation estimation using iterative methods in Euclidean space. This paper presents three iterative methods for orientation estimation. The third method is based on nonlinear least squares NLS estimation of the angular velocity which is used to parametrise the orientation.
The Multivariate Generalised von Mises distribution: Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community.Dec 25, · The Bernoulli's Principle was a physics principle formulated by Daniel Bernoulli that an increase in the speed of a fluid produces a decrease in pressure and that a decrease in the speed of a fluid produces an increase in pressure.
The Infinite. Working with the infinite is tricky business. Zeno’s paradoxes first alerted philosophers to this in B.C.E. when he argued that a fast runner such as Achilles has an infinite number of places to reach during the pursuit of a slower runner.
So, given that there is a pressure gradient normal to the surface, Bernoulli's principle can then explain whether the air along some streamline is speeding up or slowing down relative to regions of the fluid where there is no surface. Gaussian Processes and Kernel Methods Gaussian processes are non-parametric distributions useful for doing Bayesian inference and learning on unknown functions.
They can be used for non-linear regression, time-series modelling, classification, and many other problems. Bernoulli's principle actually relates pressure to two separate phenomena. One is the idea that if a fluid moves faster, the individual particles will spread out more, decreasing the pressure on the surroundings.
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