A Fisher kernel represents the distance in likelihood space between pairs of

A fisher kernel represents the distance in likelihood

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A Fisher kernel represents the distance in likelihood space between pairs of samples for a fitted generative model. Fisher kernel A Fisher kernel is the inner product of the gradient of the likelihood of x , x 0 given the fitted model scaled by inverse Fisher information matrix , or the information contained in observation x about model parameters θ . Fisher Kernels allow arbitrarily complex generative models to capture the similarity between pairs of samples (e.g., Gaussian mixture model). COS 424/SML 302 Features and Kernels February 18, 2019 47 / 49
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Summary: features and kernels Crafting informative features is essential to data analysis This is more art than science It is often difficult to identify predictive features of a complex sample Kernel functions and the kernel trick allow similarity between samples to be used as features in a computationally efficient way Other approaches: Word2vec, convolutional autoencoders These automated approaches lack interpretability COS 424/SML 302 Features and Kernels February 18, 2019 48 / 49
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Additional Resources MLAPA : Chapter 14 Gaussian Processes for Machine Learning : Chapter 4 Elements of Statistical Learning : Chapter 3 (video) Partha Niyogi: Introduction to Kernel Methods (video) Alex Smola: Kernel Methods and Support Vector Machines Metacademy: The kernel trick The Kernel Cookbook : dduvenaud/cookbook/ COS 424/SML 302 Features and Kernels February 18, 2019 49 / 49
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