"NIPS Neural Information Processing Systems 8-11th December 2014, Montreal, Canada",,, "Paper ID:","1694" "Title:","An Integer Polynomial Programming Based Framework for Lifted MAP Inference" Current Reviews First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors propose a new method of performing lifted inference on Markov Logic Networks. The essence of the idea is to encode the MLN as an integer polynomial program, which is then transformed into an integer linear program (which could be solved with a conventional solver such as Gurobi or CPlex). The lifting as preprocessing idea due to Sarkhel et al. is appealing, and this paper extends it using ideas from probabilistic theorem proving. The idea is to extend the list of symmetries recognized by this lifted inference approach (Algorithm 1).

Your skepticism of growBuf may stem from a shortcoming in our presentation of the method. For most real-world applications, the memory in the chain tends to be fairly local (non-unitary second eigenvalue of the transition matrix), especially in the context of our long chains of interest.

V ariational inference algorithms have proven successful for Bayesian analysis in large data settings, with recent advances using stochastic variational inference (SVI). However, such methods have largely been studied in independent or exchangeable data settings. We develop an SVI algorithm to learn the parameters of hidden Markov models (HMMs) in a time-dependent data setting. The challenge in applying stochastic optimization in this setting arises from dependencies in the chain, which must be broken to consider minibatches of observations. We propose an algorithm that harnesses the memory decay of the chain to adaptively bound errors arising from edge effects. We demonstrate the effectiveness of our algorithm on synthetic experiments and a large genomics dataset where a batch algorithm is computationally infeasible.

Neural population activity in cortical circuits is not solely driven by external inputs, but is also modulated by endogenous states which vary on multiple time-scales. To understand information processing in cortical circuits, we need to understand the statistical structure of internal states and their interaction with sensory inputs. Here, we present a statistical model for extracting hierarchically organised neural population states from multi-channel recordings of neural spiking activity. Population states are modelled using a hidden Markov decision tree with state-dependent tuning parameters and a generalised linear observation model. We present a varia-tional Bayesian inference algorithm for estimating the posterior distribution over parameters from neural population recordings. On simulated data, we show that we can identify the underlying sequence of population states and reconstruct the ground truth parameters. Using population recordings from visual cortex, we find that a model with two levels of population states outperforms both a one-state and a two-state generalised linear model. Finally, we find that modelling of state-dependence also improves the accuracy with which sensory stimuli can be decoded from the population response.

Multiple lines of evidence support the notion that the brain performs probabilistic inference in multiple cognitive domains, including perception and decision making. There is also evidence that probabilistic inference may be implemented in the brain through the (quasi-)stochastic activity of neural circuits, producing samples from the appropriate posterior distributions, effectively implementing a Markov chain Monte Carlo algorithm. However, time becomes a fundamental bottleneck in such sampling-based probabilistic representations: the quality of inferences depends on how fast the neural circuit generates new, uncorrelated samples from its stationary distribution (the posterior). We explore this bottleneck in a simple, linear-Gaussian latent variable model, in which posterior sampling can be achieved by stochastic neural networks with linear dynamics. The well-known Langevin sampling (LS) recipe, so far the only sampling algorithm for continuous variables of which a neural implementation has been suggested, naturally fits into this dynamical framework. However, we first show analytically and through simulations that the symmetry of the synaptic weight matrix implied by LS yields critically slow mixing when the posterior is high-dimensional. Next, using methods from control theory, we construct and inspect networks that are optimally fast, and hence orders of magnitude faster than LS, while being far more biologically plausible. In these networks, strong - but transient - selective amplification of external noise generates the spatially correlated activity fluctuations prescribed by the posterior. Intriguingly, although a detailed balance of excitation and inhibition is dynamically maintained, detailed balance of Markov chain steps in the resulting sampler is violated, consistent with recent findings on how statistical irreversibility can overcome the speed limitation of random walks in other domains.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. As a major novelty, the authors propose that the stochasticity of synaptic transmission is directly involved in the implementation of stochasticity necessary for Monte Carlo sampling. The neurons used throughout the paper are binary threshold units and not spiking neurons. These binary neurons are able to provide useful insights into how a neuronal network may solve computational problems, but it is important to distinguish between implementations using binary units and spiking neurons. The authors include a short section about spike-based implementation in the appendix, but they do not demonstrate that the spike based implementation is able to perform the same tasks with similar performance.

We propose a spiking network model capable of performing both approximate inference and learning for any hidden Markov model. The lower layer sensory neurons detect noisy measurements of hidden world states. The higher layer neurons with recurrent connections infer a posterior distribution over world states from spike trains generated by sensory neurons. We show how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in the population of inference neurons represents a sample of a particular hidden world state.

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Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP), based on a single trajectory of Markovian samples induced by a behavior policy.