Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Density-sensitive semisupervised inference   Semisupervised methods are techniques for using labeled data
$(X_1,Y_1),\ldots,(X_n,Y_n)$ together with unlabeled data $X_{n+1},\ldots,X_N$
to make predictions. These methods invoke some assumptions that link the
marginal distribution $P_X$ of X to the regression function f(x). For example,
it is common to assume that f is very smooth over high density regions of
$P_X$. Many of the methods are ad-hoc and have been shown to work in specific
examples but are lacking a theoretical foundation. We provide a minimax
framework for analyzing semisupervised methods. In particular, we study methods
based on metrics that are sensitive to the distribution $P_X$. Our model
includes a parameter $\alpha$ that controls the strength of the semisupervised
assumption. We then use the data to adapt to $\alpha$.

25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess