Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The linear conditional expectation in Hilbert space   The linear conditional expectation (LCE) provides a best linear (or rather,
affine) estimate of the conditional expectation and hence plays an important
r\^ole in approximate Bayesian inference, especially the Bayes linear approach.
This article establishes the analytical properties of the LCE in an
infinite-dimensional Hilbert space context. In addition, working in the space
of affine Hilbert--Schmidt operators, we establish a regularisation procedure
for this LCE. As an important application, we obtain a simple alternative
derivation and intuitive justification of the conditional mean embedding
formula, a concept widely used in machine learning to perform the conditioning
of random variables by embedding them into reproducing kernel Hilbert spaces.

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The categories of this paper are: solv-int
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin