377 research outputs found
Vertex-pursuit in random directed acyclic graphs
We examine a dynamic model for the disruption of information flow in
hierarchical social networks by considering the vertex-pursuit game Seepage
played in directed acyclic graphs (DAGs). In Seepage, agents attempt to block
the movement of an intruder who moves downward from the source node to a sink.
The minimum number of such agents required to block the intruder is called the
green number. We propose a generalized stochastic model for DAGs with given
expected total degree sequence. Seepage and the green number is analyzed in
stochastic DAGs in both the cases of a regular and power law degree sequence.
For each such sequence, we give asymptotic bounds (and in certain instances,
precise values) for the green number
Quantitative Games under Failures
We study a generalisation of sabotage games, a model of dynamic network games
introduced by van Benthem. The original definition of the game is inherently
finite and therefore does not allow one to model infinite processes. We propose
an extension of the sabotage games in which the first player (Runner) traverses
an arena with dynamic weights determined by the second player (Saboteur). In
our model of quantitative sabotage games, Saboteur is now given a budget that
he can distribute amongst the edges of the graph, whilst Runner attempts to
minimise the quantity of budget witnessed while completing his task. We show
that, on the one hand, for most of the classical cost functions considered in
the literature, the problem of determining if Runner has a strategy to ensure a
cost below some threshold is EXPTIME-complete. On the other hand, if the budget
of Saboteur is fixed a priori, then the problem is in PTIME for most cost
functions. Finally, we show that restricting the dynamics of the game also
leads to better complexity
D'ya like DAGs? A Survey on Structure Learning and Causal Discovery
Causal reasoning is a crucial part of science and human intelligence. In
order to discover causal relationships from data, we need structure discovery
methods. We provide a review of background theory and a survey of methods for
structure discovery. We primarily focus on modern, continuous optimization
methods, and provide reference to further resources such as benchmark datasets
and software packages. Finally, we discuss the assumptive leap required to take
us from structure to causality.Comment: 35 page
Supervised Feature Selection in Graphs with Path Coding Penalties and Network Flows
We consider supervised learning problems where the features are embedded in a
graph, such as gene expressions in a gene network. In this context, it is of
much interest to automatically select a subgraph with few connected components;
by exploiting prior knowledge, one can indeed improve the prediction
performance or obtain results that are easier to interpret. Regularization or
penalty functions for selecting features in graphs have recently been proposed,
but they raise new algorithmic challenges. For example, they typically require
solving a combinatorially hard selection problem among all connected subgraphs.
In this paper, we propose computationally feasible strategies to select a
sparse and well-connected subset of features sitting on a directed acyclic
graph (DAG). We introduce structured sparsity penalties over paths on a DAG
called "path coding" penalties. Unlike existing regularization functions that
model long-range interactions between features in a graph, path coding
penalties are tractable. The penalties and their proximal operators involve
path selection problems, which we efficiently solve by leveraging network flow
optimization. We experimentally show on synthetic, image, and genomic data that
our approach is scalable and leads to more connected subgraphs than other
regularization functions for graphs.Comment: 37 pages; to appear in the Journal of Machine Learning Research
(JMLR
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