774 research outputs found
Network Inference with Hidden Units
We derive learning rules for finding the connections between units in
stochastic dynamical networks from the recorded history of a ``visible'' subset
of the units. We consider two models. In both of them, the visible units are
binary and stochastic. In one model the ``hidden'' units are continuous-valued,
with sigmoidal activation functions, and in the other they are binary and
stochastic like the visible ones. We derive exact learning rules for both
cases. For the stochastic case, performing the exact calculation requires, in
general, repeated summations over an number of configurations that grows
exponentially with the size of the system and the data length, which is not
feasible for large systems. We derive a mean field theory, based on a
factorized ansatz for the distribution of hidden-unit states, which offers an
attractive alternative for large systems. We present the results of some
numerical calculations that illustrate key features of the two models and, for
the stochastic case, the exact and approximate calculations
Mean Field Theory For Non-Equilibrium Network Reconstruction
There has been recent progress on the problem of inferring the structure of
interactions in complex networks when they are in stationary states satisfying
detailed balance, but little has been done for non-equilibrium systems. Here we
introduce an approach to this problem, considering, as an example, the question
of recovering the interactions in an asymmetrically-coupled,
synchronously-updated Sherrington-Kirkpatrick model. We derive an exact
iterative inversion algorithm and develop efficient approximations based on
dynamical mean-field and Thouless-Anderson-Palmer equations that express the
interactions in terms of equal-time and one time step-delayed correlation
functions.Comment: new version, accepted in PRL. For the Supp. Mat. (ref. 11), please
contact the author
Cumulants of Hawkes point processes
We derive explicit, closed-form expressions for the cumulant densities of a
multivariate, self-exciting Hawkes point process, generalizing a result of
Hawkes in his earlier work on the covariance density and Bartlett spectrum of
such processes. To do this, we represent the Hawkes process in terms of a
Poisson cluster process and show how the cumulant density formulas can be
derived by enumerating all possible "family trees", representing complex
interactions between point events. We also consider the problem of computing
the integrated cumulants, characterizing the average measure of correlated
activity between events of different types, and derive the relevant equations.Comment: 11 pages, 4 figure
Ising Models for Inferring Network Structure From Spike Data
Now that spike trains from many neurons can be recorded simultaneously, there
is a need for methods to decode these data to learn about the networks that
these neurons are part of. One approach to this problem is to adjust the
parameters of a simple model network to make its spike trains resemble the data
as much as possible. The connections in the model network can then give us an
idea of how the real neurons that generated the data are connected and how they
influence each other. In this chapter we describe how to do this for the
simplest kind of model: an Ising network. We derive algorithms for finding the
best model connection strengths for fitting a given data set, as well as faster
approximate algorithms based on mean field theory. We test the performance of
these algorithms on data from model networks and experiments.Comment: To appear in "Principles of Neural Coding", edited by Stefano Panzeri
and Rodrigo Quian Quirog
âThe Heighe Worthynesse of Loveâ: Visions of Perception, Convention, and Contradiction in Chaucerâs Troilus and Criseyde
This thesis examines three images associated with the manuscripts and early printed editions of Chaucerâs Troilus and Criseyde which I have dubbed âProstrate Troilus,â âPandarus as Messenger,â and âCriseyde in the Garden.â These images are artifacts of contemporary textual interpretation that âreadâ Chaucerâs text and the tale of Troilus. They each illustrate the way in which Troilus, Pandarus, and Criseyde âreadâ images, gestures, symbols, and speeches within the narrative, and they show how these characters are constrained and influenced by their individual primary modes of perception. Troilus reads but does not analyze. Pandarus actively reads his own meanings into messages. Criseydeâs reading is reflective. Ultimately, the different interpretive strategies that Chaucer explores in Troilus mirror those of Chaucerâs readers
Statistical physics of pairwise probability models
Statistical models for describing the probability distribution over the
states of biological systems are commonly used for dimensional reduction. Among
these models, pairwise models are very attractive in part because they can be
fit using a reasonable amount of data: knowledge of the means and correlations
between pairs of elements in the system is sufficient. Not surprisingly, then,
using pairwise models for studying neural data has been the focus of many
studies in recent years. In this paper, we describe how tools from statistical
physics can be employed for studying and using pairwise models. We build on our
previous work on the subject and study the relation between different methods
for fitting these models and evaluating their quality. In particular, using
data from simulated cortical networks we study how the quality of various
approximate methods for inferring the parameters in a pairwise model depends on
the time bin chosen for binning the data. We also study the effect of the size
of the time bin on the model quality itself, again using simulated data. We
show that using finer time bins increases the quality of the pairwise model. We
offer new ways of deriving the expressions reported in our previous work for
assessing the quality of pairwise models.Comment: 25 pages, 3 figure
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