136,139 research outputs found
On the Power of Conditional Samples in Distribution Testing
In this paper we define and examine the power of the {\em
conditional-sampling} oracle in the context of distribution-property testing.
The conditional-sampling oracle for a discrete distribution takes as
input a subset of the domain, and outputs a random sample drawn according to , conditioned on (and independently of all
prior samples). The conditional-sampling oracle is a natural generalization of
the ordinary sampling oracle in which always equals .
We show that with the conditional-sampling oracle, testing uniformity,
testing identity to a known distribution, and testing any label-invariant
property of distributions is easier than with the ordinary sampling oracle. On
the other hand, we also show that for some distribution properties the
sample-complexity remains near-maximal even with conditional sampling
Testing Properties of Multiple Distributions with Few Samples
We propose a new setting for testing properties of distributions while
receiving samples from several distributions, but few samples per distribution.
Given samples from distributions, , we design
testers for the following problems: (1) Uniformity Testing: Testing whether all
the 's are uniform or -far from being uniform in
-distance (2) Identity Testing: Testing whether all the 's are
equal to an explicitly given distribution or -far from in
-distance, and (3) Closeness Testing: Testing whether all the 's
are equal to a distribution which we have sample access to, or
-far from in -distance. By assuming an additional natural
condition about the source distributions, we provide sample optimal testers for
all of these problems.Comment: ITCS 202
Approximate reasoning for real-time probabilistic processes
We develop a pseudo-metric analogue of bisimulation for generalized
semi-Markov processes. The kernel of this pseudo-metric corresponds to
bisimulation; thus we have extended bisimulation for continuous-time
probabilistic processes to a much broader class of distributions than
exponential distributions. This pseudo-metric gives a useful handle on
approximate reasoning in the presence of numerical information -- such as
probabilities and time -- in the model. We give a fixed point characterization
of the pseudo-metric. This makes available coinductive reasoning principles for
reasoning about distances. We demonstrate that our approach is insensitive to
potentially ad hoc articulations of distance by showing that it is intrinsic to
an underlying uniformity. We provide a logical characterization of this
uniformity using a real-valued modal logic. We show that several quantitative
properties of interest are continuous with respect to the pseudo-metric. Thus,
if two processes are metrically close, then observable quantitative properties
of interest are indeed close.Comment: Preliminary version appeared in QEST 0
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