211 research outputs found
The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy
The principle of maximum entropy (Maxent) is often used to obtain prior
probability distributions as a method to obtain a Gibbs measure under some
restriction giving the probability that a system will be in a certain state
compared to the rest of the elements in the distribution. Because classical
entropy-based Maxent collapses cases confounding all distinct degrees of
randomness and pseudo-randomness, here we take into consideration the
generative mechanism of the systems considered in the ensemble to separate
objects that may comply with the principle under some restriction and whose
entropy is maximal but may be generated recursively from those that are
actually algorithmically random offering a refinement to classical Maxent. We
take advantage of a causal algorithmic calculus to derive a thermodynamic-like
result based on how difficult it is to reprogram a computer code. Using the
distinction between computable and algorithmic randomness we quantify the cost
in information loss associated with reprogramming. To illustrate this we apply
the algorithmic refinement to Maxent on graphs and introduce a Maximal
Algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a
generalisation over previous approaches. We discuss practical implications of
evaluation of network randomness. Our analysis provides insight in that the
reprogrammability asymmetry appears to originate from a non-monotonic
relationship to algorithmic probability. Our analysis motivates further
analysis of the origin and consequences of the aforementioned asymmetries,
reprogrammability, and computation.Comment: 30 page
Is there any real substance to the claims for a 'new computationalism'?
'Computationalism' is a relatively vague term used to describe attempts to apply Turing's model of computation to phenomena outside its original purview: in modelling the human mind, in physics, mathematics, etc. Early versions of computationalism faced strong objections from many (and varied) quarters, from philosophers to practitioners of the aforementioned disciplines. Here we will not address the fundamental question of whether computational models are appropriate for describing some or all of the wide range of processes that they have been applied to, but will focus instead on whether `renovated' versions of the \textit{new computationalism} shed any new light on or resolve previous tensions between proponents and skeptics. We find this, however, not to be the case, because the 'new computationalism' falls short by using limited versions of "traditional computation", or proposing computational models that easily fall within the scope of Turing's original model, or else proffering versions of hypercomputation with its many pitfalls
Minimal Algorithmic Information Loss Methods for Dimension Reduction, Feature Selection and Network Sparsification
We introduce a family of unsupervised, domain-free, and (asymptotically)
model-independent algorithms based on the principles of algorithmic probability
and information theory designed to minimize the loss of algorithmic
information, including a lossless-compression-based lossy compression
algorithm. The methods can select and coarse-grain data in an
algorithmic-complexity fashion (without the use of popular compression
algorithms) by collapsing regions that may procedurally be regenerated from a
computable candidate model. We show that the method can preserve the salient
properties of objects and perform dimension reduction, denoising, feature
selection, and network sparsification. As validation case, we demonstrate that
the method preserves all the graph-theoretic indices measured on a well-known
set of synthetic and real-world networks of very different nature, ranging from
degree distribution and clustering coefficient to edge betweenness and degree
and eigenvector centralities, achieving equal or significantly better results
than other data reduction and some of the leading network sparsification
methods. The methods (InfoRank, MILS) can also be applied to applications such
as image segmentation based on algorithmic probability.Comment: 23 pages in double column including Appendix, online implementation
at http://complexitycalculator.com/MILS
Approximate and Situated Causality in Deep Learning
Altres ajuts: ICREA Academia 2019, and "AppPhil: Applied Philosophy for the Value-Design of Social Networks Apps" project, funded by Caixabank in Recercaixa2017.Causality is the most important topic in the history of western science, and since the beginning of the statistical paradigm, its meaning has been reconceptualized many times. Causality entered into the realm of multi-causal and statistical scenarios some centuries ago. Despite widespread critics, today deep learning and machine learning advances are not weakening causality but are creating a new way of finding correlations between indirect factors. This process makes it possible for us to talk about approximate causality, as well as about a situated causality
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