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The effect of network topology on optimal exploration strategies and the evolution of cooperation in a mobile population
We model a mobile population interacting over an underlying spatial structure using a Markov movement model. Interactions take the form of public goods games, and can feature an arbitrary group size. Individuals choose strategically to remain at their current location or to move to a neighbouring location, depending upon their exploration strategy and the current composition of their group. This builds upon previous work where the underlying structure was a complete graph (i.e. there was effectively no structure). Here, we consider alternative network structures and a wider variety of, mainly larger, populations. Previously, we had found when cooperation could evolve, depending upon the values of a range of population parameters. In our current work, we see that the complete graph considered before promotes stability, with populations of cooperators or defectors being relatively hard to replace. By contrast, the star graph promotes instability, and often neither type of population can resist replacement. We discuss potential reasons for this in terms of network topology
Interpretable statistics for complex modelling: quantile and topological learning
As the complexity of our data increased exponentially in the last decades, so has our
need for interpretable features. This thesis revolves around two paradigms to approach
this quest for insights.
In the first part we focus on parametric models, where the problem of interpretability
can be seen as a “parametrization selection”. We introduce a quantile-centric
parametrization and we show the advantages of our proposal in the context of regression,
where it allows to bridge the gap between classical generalized linear (mixed)
models and increasingly popular quantile methods.
The second part of the thesis, concerned with topological learning, tackles the
problem from a non-parametric perspective. As topology can be thought of as a way
of characterizing data in terms of their connectivity structure, it allows to represent
complex and possibly high dimensional through few features, such as the number of
connected components, loops and voids. We illustrate how the emerging branch of
statistics devoted to recovering topological structures in the data, Topological Data
Analysis, can be exploited both for exploratory and inferential purposes with a special
emphasis on kernels that preserve the topological information in the data.
Finally, we show with an application how these two approaches can borrow strength
from one another in the identification and description of brain activity through fMRI
data from the ABIDE project
Learning Multiple Visual Tasks while Discovering their Structure
Multi-task learning is a natural approach for computer vision applications
that require the simultaneous solution of several distinct but related
problems, e.g. object detection, classification, tracking of multiple agents,
or denoising, to name a few. The key idea is that exploring task relatedness
(structure) can lead to improved performances.
In this paper, we propose and study a novel sparse, non-parametric approach
exploiting the theory of Reproducing Kernel Hilbert Spaces for vector-valued
functions. We develop a suitable regularization framework which can be
formulated as a convex optimization problem, and is provably solvable using an
alternating minimization approach. Empirical tests show that the proposed
method compares favorably to state of the art techniques and further allows to
recover interpretable structures, a problem of interest in its own right.Comment: 19 pages, 3 figures, 3 table
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