16,201 research outputs found
Exponential-family Random Network Models
Random graphs, where the connections between nodes are considered random
variables, have wide applicability in the social sciences. Exponential-family
Random Graph Models (ERGM) have shown themselves to be a useful class of models
for representing com- plex social phenomena. We generalize ERGM by also
modeling nodal attributes as random variates, thus creating a random model of
the full network, which we call Exponential-family Random Network Models
(ERNM). We demonstrate how this framework allows a new formu- lation for
logistic regression in network data. We develop likelihood-based inference for
the model and an MCMC algorithm to implement it. This new model formulation is
used to analyze a peer social network from the National Lon- gitudinal Study of
Adolescent Health. We model the relationship between substance use and
friendship relations, and show how the results differ from the standard use of
logistic regression on network data
Information Geometry Approach to Parameter Estimation in Markov Chains
We consider the parameter estimation of Markov chain when the unknown
transition matrix belongs to an exponential family of transition matrices.
Then, we show that the sample mean of the generator of the exponential family
is an asymptotically efficient estimator. Further, we also define a curved
exponential family of transition matrices. Using a transition matrix version of
the Pythagorean theorem, we give an asymptotically efficient estimator for a
curved exponential family.Comment: Appendix D is adde
Exponential Family Hybrid Semi-Supervised Learning
We present an approach to semi-supervised learning based on an exponential
family characterization. Our approach generalizes previous work on coupled
priors for hybrid generative/discriminative models. Our model is more flexible
and natural than previous approaches. Experimental results on several data sets
show that our approach also performs better in practice.Comment: 6 pages, 3 figure
Information Aggregation in Exponential Family Markets
We consider the design of prediction market mechanisms known as automated
market makers. We show that we can design these mechanisms via the mold of
\emph{exponential family distributions}, a popular and well-studied probability
distribution template used in statistics. We give a full development of this
relationship and explore a range of benefits. We draw connections between the
information aggregation of market prices and the belief aggregation of learning
agents that rely on exponential family distributions. We develop a very natural
analysis of the market behavior as well as the price equilibrium under the
assumption that the traders exhibit risk aversion according to exponential
utility. We also consider similar aspects under alternative models, such as
when traders are budget constrained
Exponential Family Matrix Completion under Structural Constraints
We consider the matrix completion problem of recovering a structured matrix
from noisy and partial measurements. Recent works have proposed tractable
estimators with strong statistical guarantees for the case where the underlying
matrix is low--rank, and the measurements consist of a subset, either of the
exact individual entries, or of the entries perturbed by additive Gaussian
noise, which is thus implicitly suited for thin--tailed continuous data.
Arguably, common applications of matrix completion require estimators for (a)
heterogeneous data--types, such as skewed--continuous, count, binary, etc., (b)
for heterogeneous noise models (beyond Gaussian), which capture varied
uncertainty in the measurements, and (c) heterogeneous structural constraints
beyond low--rank, such as block--sparsity, or a superposition structure of
low--rank plus elementwise sparseness, among others. In this paper, we provide
a vastly unified framework for generalized matrix completion by considering a
matrix completion setting wherein the matrix entries are sampled from any
member of the rich family of exponential family distributions; and impose
general structural constraints on the underlying matrix, as captured by a
general regularizer . We propose a simple convex regularized
--estimator for the generalized framework, and provide a unified and novel
statistical analysis for this general class of estimators. We finally
corroborate our theoretical results on simulated datasets.Comment: 20 pages, 9 figure
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