A Fisher kernel represents the distance in likelihood space between pairs ofsamples for a fitted generative model.Fisher kernelAFisher kernelis the inner product of the gradient of the likelihood ofx,x0given the fitted model scaled by inverseFisher information matrix, orthe information contained in observationxabout model parametersθ.Fisher Kernels allow arbitrarily complex generative models to capture thesimilarity between pairs of samples (e.g., Gaussian mixture model).COS 424/SML 302Features and KernelsFebruary 18, 201947 / 49
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Summary: features and kernelsCrafting informative features is essential to data analysisThis is more art than scienceIt is often difficult to identify predictive features of a complex sampleKernel functions and the kernel trick allow similarity between samplesto be used as features in a computationally efficient wayOther approaches: Word2vec, convolutional autoencodersThese automated approaches lack interpretabilityCOS 424/SML 302Features and KernelsFebruary 18, 201948 / 49
Additional ResourcesMLAPA: Chapter 14Gaussian Processes for Machine Learning: Chapter 4Elements of Statistical Learning: Chapter 3(video) Partha Niyogi:Introduction to Kernel Methods(video) Alex Smola:Kernel Methods and Support Vector MachinesMetacademy:The kernel trickThe Kernel Cookbook:∼dduvenaud/cookbook/COS 424/SML 302Features and KernelsFebruary 18, 201949 / 49
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