4,619 research outputs found
Optimal sequential fingerprinting: Wald vs. Tardos
We study sequential collusion-resistant fingerprinting, where the
fingerprinting code is generated in advance but accusations may be made between
rounds, and show that in this setting both the dynamic Tardos scheme and
schemes building upon Wald's sequential probability ratio test (SPRT) are
asymptotically optimal. We further compare these two approaches to sequential
fingerprinting, highlighting differences between the two schemes. Based on
these differences, we argue that Wald's scheme should in general be preferred
over the dynamic Tardos scheme, even though both schemes have their merits. As
a side result, we derive an optimal sequential group testing method for the
classical model, which can easily be generalized to different group testing
models.Comment: 12 pages, 10 figure
The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction
Stimulus dimensionality-reduction methods in neuroscience seek to identify a
low-dimensional space of stimulus features that affect a neuron's probability
of spiking. One popular method, known as maximally informative dimensions
(MID), uses an information-theoretic quantity known as "single-spike
information" to identify this space. Here we examine MID from a model-based
perspective. We show that MID is a maximum-likelihood estimator for the
parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical
single-spike information corresponds to the normalized log-likelihood under a
Poisson model. This equivalence implies that MID does not necessarily find
maximally informative stimulus dimensions when spiking is not well described as
Poisson. We provide several examples to illustrate this shortcoming, and derive
a lower bound on the information lost when spiking is Bernoulli in discrete
time bins. To overcome this limitation, we introduce model-based dimensionality
reduction methods for neurons with non-Poisson firing statistics, and show that
they can be framed equivalently in likelihood-based or information-theoretic
terms. Finally, we show how to overcome practical limitations on the number of
stimulus dimensions that MID can estimate by constraining the form of the
non-parametric nonlinearity in an LNP model. We illustrate these methods with
simulations and data from primate visual cortex
Algebraic and algorithmic frameworks for optimized quantum measurements
Von Neumann projections are the main operations by which information can be
extracted from the quantum to the classical realm. They are however static
processes that do not adapt to the states they measure. Advances in the field
of adaptive measurement have shown that this limitation can be overcome by
"wrapping" the von Neumann projectors in a higher-dimensional circuit which
exploits the interplay between measurement outcomes and measurement settings.
Unfortunately, the design of adaptive measurement has often been ad hoc and
setup-specific. We shall here develop a unified framework for designing
optimized measurements. Our approach is two-fold: The first is algebraic and
formulates the problem of measurement as a simple matrix diagonalization
problem. The second is algorithmic and models the optimal interaction between
measurement outcomes and measurement settings as a cascaded network of
conditional probabilities. Finally, we demonstrate that several figures of
merit, such as Bell factors, can be improved by optimized measurements. This
leads us to the promising observation that measurement detectors which---taken
individually---have a low quantum efficiency can be be arranged into circuits
where, collectively, the limitations of inefficiency are compensated for
- …