Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Near-Optimal Procedures for Model Discrimination with Non-Disclosure
  Properties   Let $\theta_0,\theta_1 \in \mathbb{R}^d$ be the population risk minimizers
associated to some loss $\ell:\mathbb{R}^d\times \mathcal{Z}\to\mathbb{R}$ and
two distributions $\mathbb{P}_0,\mathbb{P}_1$ on $\mathcal{Z}$. The models
$\theta_0,\theta_1$ are unknown, and $\mathbb{P}_0,\mathbb{P}_1$ can be
accessed by drawing i.i.d samples from them. Our work is motivated by the
following model discrimination question: "What sizes of the samples from
$\mathbb{P}_0$ and $\mathbb{P}_1$ allow to distinguish between the two
hypotheses $\theta^*=\theta_0$ and $\theta^*=\theta_1$ for given
$\theta^*\in\{\theta_0,\theta_1\}$?" Making the first steps towards answering
it in full generality, we first consider the case of a well-specified linear
model with squared loss. Here we provide matching upper and lower bounds on the
sample complexity as given by $\min\{1/\Delta^2,\sqrt{r}/\Delta\}$ up to a
constant factor; here $\Delta$ is a measure of separation between
$\mathbb{P}_0$ and $\mathbb{P}_1$ and $r$ is the rank of the design covariance
matrix. We then extend this result in two directions: (i) for general
parametric models in asymptotic regime; (ii) for generalized linear models in
small samples ($n\le r$) under weak moment assumptions. In both cases we derive
sample complexity bounds of a similar form while allowing for model
misspecification. In fact, our testing procedures only access $\theta^*$ via a
certain functional of empirical risk. In addition, the number of observations
that allows us to reach statistical confidence does not allow to "resolve" the
two models $-$ that is, recover $\theta_0,\theta_1$ up to $O(\Delta)$
prediction accuracy. These two properties allow to use our framework in applied
tasks where one would like to $\textit{identify}$ a prediction model, which can
be proprietary, while guaranteeing that the model cannot be actually
$\textit{inferred}$ by the identifying agent.

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The categories of this paper are: eess
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas