Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notes on Computational Hardness of Hypothesis Testing: Predictions using
  the Low-Degree Likelihood Ratio   These notes survey and explore an emerging method, which we call the
low-degree method, for predicting and understanding
statistical-versus-computational tradeoffs in high-dimensional inference
problems. In short, the method posits that a certain quantity -- the second
moment of the low-degree likelihood ratio -- gives insight into how much
computational time is required to solve a given hypothesis testing problem,
which can in turn be used to predict the computational hardness of a variety of
statistical inference tasks. While this method originated in the study of the
sum-of-squares (SoS) hierarchy of convex programs, we present a self-contained
introduction that does not require knowledge of SoS. In addition to showing how
to carry out predictions using the method, we include a discussion
investigating both rigorous and conjectural consequences of these predictions.
  These notes include some new results, simplified proofs, and refined
conjectures. For instance, we point out a formal connection between spectral
methods and the low-degree likelihood ratio, and we give a sharp low-degree
lower bound against subexponential-time algorithms for tensor PCA.

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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
30
The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics