
On Tractable Computation of Expected Predictions
Computing expected predictions has many interesting applications in area...
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Kernel Mean Embedding of Distributions: A Review and Beyond
A Hilbert space embedding of a distributionin short, a kernel mean em...
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Generalized support vector regression: duality and tensorkernel representation
In this paper we study the variational problem associated to support vec...
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A Compositional Atlas of Tractable Circuit Operations: From Simple Transformations to Complex InformationTheoretic Queries
Circuit representations are becoming the lingua franca to express and re...
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The Random Forest Kernel and other kernels for big data from random partitions
We present Random Partition Kernels, a new class of kernels derived by d...
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Characteristic Kernels and Infinitely Divisible Distributions
We connect shiftinvariant characteristic kernels to infinitely divisibl...
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AnalogyBased Preference Learning with Kernels
Building on a specific formalization of analogical relationships of the ...
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Tractable Computation of Expected Kernels by Circuits
Computing the expectation of some kernel function is ubiquitous in machine learning, from the classical theory of support vector machines, to exploiting kernel embeddings of distributions in applications ranging from probabilistic modeling, statistical inference, casual discovery, and deep learning. In all these scenarios, we tend to resort to Monte Carlo estimates as expectations of kernels are intractable in general. In this work, we characterize the conditions under which we can compute expected kernels exactly and efficiently, by leveraging recent advances in probabilistic circuit representations. We first construct a circuit representation for kernels and propose an approach to such tractable computation. We then demonstrate possible advancements for kernel embedding frameworks by exploiting tractable expected kernels to derive new algorithms for two challenging scenarios: 1) reasoning under missing data with kernel support vector regressors; 2) devising a collapsed blackbox importance sampling scheme. Finally, we empirically evaluate both algorithms and show that they outperform standard baselines on a variety of datasets.
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