4,205 research outputs found
New Ideas for Brain Modelling
This paper describes some biologically-inspired processes that could be used
to build the sort of networks that we associate with the human brain. New to
this paper, a 'refined' neuron will be proposed. This is a group of neurons
that by joining together can produce a more analogue system, but with the same
level of control and reliability that a binary neuron would have. With this new
structure, it will be possible to think of an essentially binary system in
terms of a more variable set of values. The paper also shows how recent
research associated with the new model, can be combined with established
theories, to produce a more complete picture. The propositions are largely in
line with conventional thinking, but possibly with one or two more radical
suggestions. An earlier cognitive model can be filled in with more specific
details, based on the new research results, where the components appear to fit
together almost seamlessly. The intention of the research has been to describe
plausible 'mechanical' processes that can produce the appropriate brain
structures and mechanisms, but that could be used without the magical
'intelligence' part that is still not fully understood. There are also some
important updates from an earlier version of this paper
Replica theory for learning curves for Gaussian processes on random graphs
Statistical physics approaches can be used to derive accurate predictions for
the performance of inference methods learning from potentially noisy data, as
quantified by the learning curve defined as the average error versus number of
training examples. We analyse a challenging problem in the area of
non-parametric inference where an effectively infinite number of parameters has
to be learned, specifically Gaussian process regression. When the inputs are
vertices on a random graph and the outputs noisy function values, we show that
replica techniques can be used to obtain exact performance predictions in the
limit of large graphs. The covariance of the Gaussian process prior is defined
by a random walk kernel, the discrete analogue of squared exponential kernels
on continuous spaces. Conventionally this kernel is normalised only globally,
so that the prior variance can differ between vertices; as a more principled
alternative we consider local normalisation, where the prior variance is
uniform
Multivariate Granger Causality and Generalized Variance
Granger causality analysis is a popular method for inference on directed
interactions in complex systems of many variables. A shortcoming of the
standard framework for Granger causality is that it only allows for examination
of interactions between single (univariate) variables within a system, perhaps
conditioned on other variables. However, interactions do not necessarily take
place between single variables, but may occur among groups, or "ensembles", of
variables. In this study we establish a principled framework for Granger
causality in the context of causal interactions among two or more multivariate
sets of variables. Building on Geweke's seminal 1982 work, we offer new
justifications for one particular form of multivariate Granger causality based
on the generalized variances of residual errors. Taken together, our results
support a comprehensive and theoretically consistent extension of Granger
causality to the multivariate case. Treated individually, they highlight
several specific advantages of the generalized variance measure, which we
illustrate using applications in neuroscience as an example. We further show
how the measure can be used to define "partial" Granger causality in the
multivariate context and we also motivate reformulations of "causal density"
and "Granger autonomy". Our results are directly applicable to experimental
data and promise to reveal new types of functional relations in complex
systems, neural and otherwise.Comment: added 1 reference, minor change to discussion, typos corrected; 28
pages, 3 figures, 1 table, LaTe
Robustness Verification for Classifier Ensembles
We give a formal verification procedure that decides whether a classifier
ensemble is robust against arbitrary randomized attacks. Such attacks consist
of a set of deterministic attacks and a distribution over this set. The
robustness-checking problem consists of assessing, given a set of classifiers
and a labelled data set, whether there exists a randomized attack that induces
a certain expected loss against all classifiers. We show the NP-hardness of the
problem and provide an upper bound on the number of attacks that is sufficient
to form an optimal randomized attack. These results provide an effective way to
reason about the robustness of a classifier ensemble. We provide SMT and MILP
encodings to compute optimal randomized attacks or prove that there is no
attack inducing a certain expected loss. In the latter case, the classifier
ensemble is provably robust. Our prototype implementation verifies multiple
neural-network ensembles trained for image-classification tasks. The
experimental results using the MILP encoding are promising both in terms of
scalability and the general applicability of our verification procedure
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