We consider the problem of fitting variational posterior approximations using stochastic optimization methods.

We consider the problem of fitting variational posterior approximations using stochastic optimization methods.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper presents a Bayesian approach to state and parameter estimation in nonlinear state-space models, while also learning the transition dynamics through the use of a Gaussian process (GP) prior. The inference mechanism is based on particle Markov chain Monte Carlo (PMCMC) with the recently-introduced idea of ancestor sampling. The paper also discusses computational efficiencies to be had with respect to sparsity and low-rank Cholesky updates. This is a technically sound and strong paper with clear and accessible presentation.

Ideally, we would prefer an estimator that learns any distribution.

An essential aspect of any machine learning system is understanding what the model does not know.

In the framework specified in section 2.2, we use a first-order Markov chain with two states as our Figure S1: For four different cells, the posterior distribution function is computed and depicted. Here, we concentrate only on trials within original environments, where we know the correct environment and hence can assess how well is the decoding. In this approach, instead of using a state-space structure, we use the likelihoods given by Eq. (1) of Each plot shows a histogram of the average probability (over time) of correctly decoding the trials within unambiguous environments. Fig. S3 shows the decoded environment for a few sample trials based on the neural activity of the whole population. In some trials (e. g. trials 65 & 25) we observe few fluctuations, while in other In Eq. 6, we use a history dependent, gamma-distributed generalized linear model with identity link.

Neural Information Processing Systems http://nips.cc/

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper presents a method for learning the structure of stochastic And-Or grammars. The paper suggests that this generalizes previous work on structure learning, but it's actually a special case, which makes the problem tractable. This is a reasonable point on its own, and the paper makes a nice contribution, so I wouldn't try to argue that the problem is more general than the structure learning problem faced in NLP. The basic algorithm is sensible and successful when compared against other methods for inducing grammars.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Reaction to the author feedback: I cannot agree with point (3): The work of Siracusa III and Fisher (AISTATS 2009) does *not* assume the data are iid, and it allows the generating stucture vary (even if only in a small set of graphical models). While the present proposed method is, in some sense, even more flexible, I'd find it misleading to claim that the proposed method is the first to address the problem. The proposed method is specifically targeted to scenarios where the data generating graphical model may change relatively frequently. The performance of the method is demonstrated using both simulated and real data.