35,700 research outputs found
Error Bounds for Piecewise Smooth and Switching Regression
The paper deals with regression problems, in which the nonsmooth target is
assumed to switch between different operating modes. Specifically, piecewise
smooth (PWS) regression considers target functions switching deterministically
via a partition of the input space, while switching regression considers
arbitrary switching laws. The paper derives generalization error bounds in
these two settings by following the approach based on Rademacher complexities.
For PWS regression, our derivation involves a chaining argument and a
decomposition of the covering numbers of PWS classes in terms of the ones of
their component functions and the capacity of the classifier partitioning the
input space. This yields error bounds with a radical dependency on the number
of modes. For switching regression, the decomposition can be performed directly
at the level of the Rademacher complexities, which yields bounds with a linear
dependency on the number of modes. By using once more chaining and a
decomposition at the level of covering numbers, we show how to recover a
radical dependency. Examples of applications are given in particular for PWS
and swichting regression with linear and kernel-based component functions.Comment: This work has been submitted to the IEEE for possible publication.
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Logic in Opposition
It is claimed hereby that, against a current view of logic as a theory of consequence, opposition is a basic logical concept that can be used to define consequence itself. This requires some substantial changes in the underlying framework, including: a non-Fregean semantics of questions and answers, instead of the usual truth-conditional semantics; an extension of opposition as a relation between any structured objects; a definition of oppositions in terms of basic negation. Objections to this claim will be reviewed
Heterogeneity in Distributed Live Streaming: Blessing or Curse?
Distributed live streaming has brought a lot of interest in the past few
years. In the homogeneous case (all nodes having the same capacity), many
algorithms have been proposed, which have been proven almost optimal or
optimal. On the other hand, the performance of heterogeneous systems is not
completely understood yet. In this paper, we investigate the impact of
heterogeneity on the achievable delay of chunk-based live streaming systems. We
propose several models for taking the atomicity of a chunk into account. For
all these models, when considering the transmission of a single chunk,
heterogeneity is indeed a ``blessing'', in the sense that the achievable delay
is always faster than an equivalent homogeneous system. But for a stream of
chunks, we show that it can be a ``curse'': there is systems where the
achievable delay can be arbitrary greater compared to equivalent homogeneous
systems. However, if the system is slightly bandwidth-overprovisioned, optimal
single chunk diffusion schemes can be adapted to a stream of chunks, leading to
near-optimal, faster than homogeneous systems, heterogeneous live streaming
systems
Non-Epicurean Desires
In this paper, it is argued that there can be necessary and non-natural desires. After a discussion about what seems wrong with such desires, Epicurus’ classification of desires is treated similarly to Kripke’s treatment of the Kantian table of judgments. A sample of three cases is suggested to make this point
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