708 research outputs found
Extracting the Kolmogorov Complexity of Strings and Sequences from Sources with Limited Independence
An infinite binary sequence has randomness rate at least if, for
almost every , the Kolmogorov complexity of its prefix of length is at
least . It is known that for every rational , on
one hand, there exists sequences with randomness rate that can not be
effectively transformed into a sequence with randomness rate higher than
and, on the other hand, any two independent sequences with randomness
rate can be transformed into a sequence with randomness rate higher
than . We show that the latter result holds even if the two input
sequences have linear dependency (which, informally speaking, means that all
prefixes of length of the two sequences have in common a constant fraction
of their information). The similar problem is studied for finite strings. It is
shown that from any two strings with sufficiently large Kolmogorov complexity
and sufficiently small dependence, one can effectively construct a string that
is random even conditioned by any one of the input strings
06051 Abstracts Collection -- Kolmogorov Complexity and Applications
From 29.01.06 to 03.02.06, the Dagstuhl Seminar 06051 ``Kolmogorov Complexity and Applications\u27\u27 was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl. During the seminar, several participants presented
their current research, and ongoing work and open problems were
discussed. Abstracts of the presentations given during the seminar
as well as abstracts of seminar results and ideas are put together
in this paper. The first section describes the seminar topics and
goals in general. Links to extended abstracts or full papers are
provided, if available
Counting dependent and independent strings
The paper gives estimations for the sizes of the the following sets: (1) the
set of strings that have a given dependency with a fixed string, (2) the set of
strings that are pairwise \alpha independent, (3) the set of strings that are
mutually \alpha independent. The relevant definitions are as follows: C(x) is
the Kolmogorov complexity of the string x. A string y has \alpha -dependency
with a string x if C(y) - C(y|x) \geq \alpha. A set of strings {x_1, \ldots,
x_t} is pairwise \alpha-independent if for all i different from j, C(x_i) -
C(x_i | x_j) \leq \alpha. A tuple of strings (x_1, \ldots, x_t) is mutually
\alpha-independent if C(x_{\pi(1)} \ldots x_{\pi(t)}) \geq C(x_1) + \ldots +
C(x_t) - \alpha, for every permutation \pi of [t]
FLEA: Provably Fair Multisource Learning from Unreliable Training Data
Fairness-aware learning aims at constructing classifiers that not only make
accurate predictions, but do not discriminate against specific groups. It is a
fast-growing area of machine learning with far-reaching societal impact.
However, existing fair learning methods are vulnerable to accidental or
malicious artifacts in the training data, which can cause them to unknowingly
produce unfair classifiers. In this work we address the problem of fair
learning from unreliable training data in the robust multisource setting, where
the available training data comes from multiple sources, a fraction of which
might be not representative of the true data distribution. We introduce FLEA, a
filtering-based algorithm that allows the learning system to identify and
suppress those data sources that would have a negative impact on fairness or
accuracy if they were used for training. We show the effectiveness of our
approach by a diverse range of experiments on multiple datasets. Additionally
we prove formally that, given enough data, FLEA protects the learner against
unreliable data as long as the fraction of affected data sources is less than
half
Designing fuzzy rule based classifier using self-organizing feature map for analysis of multispectral satellite images
We propose a novel scheme for designing fuzzy rule based classifier. An SOFM
based method is used for generating a set of prototypes which is used to
generate a set of fuzzy rules. Each rule represents a region in the feature
space that we call the context of the rule. The rules are tuned with respect to
their context. We justified that the reasoning scheme may be different in
different context leading to context sensitive inferencing. To realize context
sensitive inferencing we used a softmin operator with a tunable parameter. The
proposed scheme is tested on several multispectral satellite image data sets
and the performance is found to be much better than the results reported in the
literature.Comment: 23 pages, 7 figure
Impossibility of independence amplification in Kolmogorov complexity theory
The paper studies randomness extraction from sources with bounded
independence and the issue of independence amplification of sources, using the
framework of Kolmogorov complexity. The dependency of strings and is
, where
denotes the Kolmogorov complexity. It is shown that there exists a
computable Kolmogorov extractor such that, for any two -bit strings with
complexity and dependency , it outputs a string of length
with complexity conditioned by any one of the input
strings. It is proven that the above are the optimal parameters a Kolmogorov
extractor can achieve. It is shown that independence amplification cannot be
effectively realized. Specifically, if (after excluding a trivial case) there
exist computable functions and such that for all -bit strings and with , then
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