55,543 research outputs found
An Algorithmic Approach to Information and Meaning
I will survey some matters of relevance to a philosophical discussion of
information, taking into account developments in algorithmic information theory
(AIT). I will propose that meaning is deep in the sense of Bennett's logical
depth, and that algorithmic probability may provide the stability needed for a
robust algorithmic definition of meaning, one that takes into consideration the
interpretation and the recipient's own knowledge encoded in the story attached
to a message.Comment: preprint reviewed version closer to the version accepted by the
journa
Approximations of Algorithmic and Structural Complexity Validate Cognitive-behavioural Experimental Results
We apply methods for estimating the algorithmic complexity of sequences to
behavioural sequences of three landmark studies of animal behavior each of
increasing sophistication, including foraging communication by ants, flight
patterns of fruit flies, and tactical deception and competition strategies in
rodents. In each case, we demonstrate that approximations of Logical Depth and
Kolmogorv-Chaitin complexity capture and validate previously reported results,
in contrast to other measures such as Shannon Entropy, compression or ad hoc.
Our method is practically useful when dealing with short sequences, such as
those often encountered in cognitive-behavioural research. Our analysis
supports and reveals non-random behavior (LD and K complexity) in flies even in
the absence of external stimuli, and confirms the "stochastic" behaviour of
transgenic rats when faced that they cannot defeat by counter prediction. The
method constitutes a formal approach for testing hypotheses about the
mechanisms underlying animal behaviour.Comment: 28 pages, 7 figures and 2 table
An Algorithmic Argument for Nonadaptive Query Complexity Lower Bounds on Advised Quantum Computation
This paper employs a powerful argument, called an algorithmic argument, to
prove lower bounds of the quantum query complexity of a multiple-block ordered
search problem in which, given a block number i, we are to find a location of a
target keyword in an ordered list of the i-th block. Apart from much studied
polynomial and adversary methods for quantum query complexity lower bounds, our
argument shows that the multiple-block ordered search needs a large number of
nonadaptive oracle queries on a black-box model of quantum computation that is
also supplemented with advice. Our argument is also applied to the notions of
computational complexity theory: quantum truth-table reducibility and quantum
truth-table autoreducibility.Comment: 16 pages. An extended abstract will appear in the Proceedings of the
29th International Symposium on Mathematical Foundations of Computer Science,
Lecture Notes in Computer Science, Springer-Verlag, Prague, August 22-27,
200
Causal Inference by Stochastic Complexity
The algorithmic Markov condition states that the most likely causal direction
between two random variables X and Y can be identified as that direction with
the lowest Kolmogorov complexity. Due to the halting problem, however, this
notion is not computable.
We hence propose to do causal inference by stochastic complexity. That is, we
propose to approximate Kolmogorov complexity via the Minimum Description Length
(MDL) principle, using a score that is mini-max optimal with regard to the
model class under consideration. This means that even in an adversarial
setting, such as when the true distribution is not in this class, we still
obtain the optimal encoding for the data relative to the class.
We instantiate this framework, which we call CISC, for pairs of univariate
discrete variables, using the class of multinomial distributions. Experiments
show that CISC is highly accurate on synthetic, benchmark, as well as
real-world data, outperforming the state of the art by a margin, and scales
extremely well with regard to sample and domain sizes
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