35 research outputs found
Expectation-maximization for logistic regression
We present a family of expectation-maximization (EM) algorithms for binary
and negative-binomial logistic regression, drawing a sharp connection with the
variational-Bayes algorithm of Jaakkola and Jordan (2000). Indeed, our results
allow a version of this variational-Bayes approach to be re-interpreted as a
true EM algorithm. We study several interesting features of the algorithm, and
of this previously unrecognized connection with variational Bayes. We also
generalize the approach to sparsity-promoting priors, and to an online method
whose convergence properties are easily established. This latter method
compares favorably with stochastic-gradient descent in situations with marked
collinearity
Augment-and-Conquer Negative Binomial Processes
By developing data augmentation methods unique to the negative binomial (NB)
distribution, we unite seemingly disjoint count and mixture models under the NB
process framework. We develop fundamental properties of the models and derive
efficient Gibbs sampling inference. We show that the gamma-NB process can be
reduced to the hierarchical Dirichlet process with normalization, highlighting
its unique theoretical, structural and computational advantages. A variety of
NB processes with distinct sharing mechanisms are constructed and applied to
topic modeling, with connections to existing algorithms, showing the importance
of inferring both the NB dispersion and probability parameters.Comment: Neural Information Processing Systems, NIPS 201
The Hawkes Edge Partition Model for Continuous-time Event-based Temporal Networks
We propose a novel probabilistic framework to model continuously generated interaction events data. Our goal is to infer the \emphimplicit community structure underlying the temporal interactions among entities, and also to exploit how the latent structure influence their interaction dynamics. To this end, we model the reciprocating interactions between individuals using mutually-exciting Hawkes processes. The base rate of the Hawkes process for each pair of individuals is built upon the latent representations inferred using the hierarchical gamma process edge partition model (HGaP-EPM). In particular, our model allows the interaction dynamics between each pair of individuals to be modulated by their respective affiliated communities.Moreover, our model can flexibly incorporate the auxiliary individuals’ attributes, or covariates associated with interaction events. Efficient Gibbs sampling and Expectation-Maximization algorithms are developed to perform inference via Pólya-Gamma data augmentation strategy. Experimental results on real-world datasets demonstrate that our model not only achieves competitive performance compared with state-of-the-art methods, but also discovers interpretable latent structure behind the observed temporal interactions
PG-TS: Improved Thompson Sampling for Logistic Contextual Bandits
We address the problem of regret minimization in logistic contextual bandits,
where a learner decides among sequential actions or arms given their respective
contexts to maximize binary rewards. Using a fast inference procedure with
Polya-Gamma distributed augmentation variables, we propose an improved version
of Thompson Sampling, a Bayesian formulation of contextual bandits with
near-optimal performance. Our approach, Polya-Gamma augmented Thompson Sampling
(PG-TS), achieves state-of-the-art performance on simulated and real data.
PG-TS explores the action space efficiently and exploits high-reward arms,
quickly converging to solutions of low regret. Its explicit estimation of the
posterior distribution of the context feature covariance leads to substantial
empirical gains over approximate approaches. PG-TS is the first approach to
demonstrate the benefits of Polya-Gamma augmentation in bandits and to propose
an efficient Gibbs sampler for approximating the analytically unsolvable
integral of logistic contextual bandits