11,297 research outputs found
Information Cascades on Arbitrary Topologies
In this paper, we study information cascades on graphs. In this setting, each
node in the graph represents a person. One after another, each person has to
take a decision based on a private signal as well as the decisions made by
earlier neighboring nodes. Such information cascades commonly occur in practice
and have been studied in complete graphs where everyone can overhear the
decisions of every other player. It is known that information cascades can be
fragile and based on very little information, and that they have a high
likelihood of being wrong.
Generalizing the problem to arbitrary graphs reveals interesting insights. In
particular, we show that in a random graph , for the right value of
, the number of nodes making a wrong decision is logarithmic in . That
is, in the limit for large , the fraction of players that make a wrong
decision tends to zero. This is intriguing because it contrasts to the two
natural corner cases: empty graph (everyone decides independently based on his
private signal) and complete graph (all decisions are heard by all nodes). In
both of these cases a constant fraction of nodes make a wrong decision in
expectation. Thus, our result shows that while both too little and too much
information sharing causes nodes to take wrong decisions, for exactly the right
amount of information sharing, asymptotically everyone can be right. We further
show that this result in random graphs is asymptotically optimal for any
topology, even if nodes follow a globally optimal algorithmic strategy. Based
on the analysis of random graphs, we explore how topology impacts global
performance and construct an optimal deterministic topology among layer graphs
A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process
We prove that the first passage time density for an
Ornstein-Uhlenbeck process obeying to reach
a fixed threshold from a suprathreshold initial condition
has a lower bound of the form for positive constants and for times exceeding some
positive value . We obtain explicit expressions for and in terms
of , , and , and discuss application of the
results to the synchronization of periodically forced stochastic leaky
integrate-and-fire model neurons.Comment: 15 pages, 1 figur
Deep Learning on Lie Groups for Skeleton-based Action Recognition
In recent years, skeleton-based action recognition has become a popular 3D
classification problem. State-of-the-art methods typically first represent each
motion sequence as a high-dimensional trajectory on a Lie group with an
additional dynamic time warping, and then shallowly learn favorable Lie group
features. In this paper we incorporate the Lie group structure into a deep
network architecture to learn more appropriate Lie group features for 3D action
recognition. Within the network structure, we design rotation mapping layers to
transform the input Lie group features into desirable ones, which are aligned
better in the temporal domain. To reduce the high feature dimensionality, the
architecture is equipped with rotation pooling layers for the elements on the
Lie group. Furthermore, we propose a logarithm mapping layer to map the
resulting manifold data into a tangent space that facilitates the application
of regular output layers for the final classification. Evaluations of the
proposed network for standard 3D human action recognition datasets clearly
demonstrate its superiority over existing shallow Lie group feature learning
methods as well as most conventional deep learning methods.Comment: Accepted to CVPR 201
- …