Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear regression through PAC-Bayesian truncation   We consider the problem of predicting as well as the best linear combination
of d given functions in least squares regression under L^\infty constraints on
the linear combination. When the input distribution is known, there already
exists an algorithm having an expected excess risk of order d/n, where n is the
size of the training data. Without this strong assumption, standard results
often contain a multiplicative log(n) factor, complex constants involving the
conditioning of the Gram matrix of the covariates, kurtosis coefficients or
some geometric quantity characterizing the relation between L^2 and
L^\infty-balls and require some additional assumptions like exponential moments
of the output. This work provides a PAC-Bayesian shrinkage procedure with a
simple excess risk bound of order d/n holding in expectation and in deviations,
under various assumptions. The common surprising factor of these results is
their simplicity and the absence of exponential moment condition on the output
distribution while achieving exponential deviations. The risk bounds are
obtained through a PAC-Bayesian analysis on truncated differences of losses. We
also show that these results can be generalized to other strongly convex loss
functions.

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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn