Recent advances in optical voltage sensors have brought us closer to a critical goal in cellular neuroscience: imaging the full spatiotemporal voltage on a dendritic tree. However, current sensors and imaging approaches still face significant limitations in SNR and sampling frequency; therefore statistical denoising and interpolation methods remain critical for understanding single-trial spatiotemporal dendritic voltage dynamics. Previous denoising approaches were either based on an inadequate linear voltage model or scaled poorly to large trees. Here we introduce a scalable fully Bayesian approach. We develop a generative nonlinear model that requires few parameters per compartment of the cell but is nonetheless flexible enough to sample realistic spatiotemporal data.

The paper introduces a new algorithm for planning in partially observable Markov decision processes (POMDP) based on the idea of aggregate simulation. The algorithm uses product distributions to approximate the belief state and shows how to build a representation graph of an approximate action-value function over belief space. The algorithm supports large observation spaces using sampling networks, a representation of the process of sampling values of observations, which is integrated into the graph representation. Following previous work in MDPs this approach enables action selection in POMDPs through gradient optimization over the graph representation. This approach complements recent algorithms for POMDPs which are based on particle representations of belief states and an explicit search for action selection.

In this paper, we provide a method to learn the directed structure of a Bayesian network using data. The data is accessed by making conditional probability queries to a black-box model. We introduce a notion of simplicity of representation of conditional probability tables for the nodes in the Bayesian network, that we call low rankness''. We connect this notion to the Fourier transformation of real valued set functions and propose a method which learns the exact directed structure of a low rank Bayesian network using very few queries. We formally prove that our method correctly recovers the true directed structure, runs in polynomial time and only needs polynomial samples with respect to the number of nodes.

Bayesian inference in state-space models is challenging due to high-dimensional state trajectories. A viable approach is particle Markov chain Monte Carlo (PMCMC), combining MCMC and sequential Monte Carlo to form exact approximations'' to otherwise-intractable MCMC methods. The performance of the approximation is limited to that of the exact method. We focus on particle Gibbs (PG) and particle Gibbs with ancestor sampling (PGAS), improving their performance beyond that of the ideal Gibbs sampler (which they approximate) by marginalizing out one or more parameters. This is possible when the parameter(s) has a conjugate prior relationship with the complete data likelihood.

Metamodels offer a cheap statistical representation of complex and/or expensive stochastic simulators that arise in applications ranging from engineering to environmental science and finance [Santner et al., 2013]. Gaussian process (GP) frameworks have emerged as the leading family of metamodels thanks to their flexibility, analytical tractability and superior empirical performance. However, for GP metamodels to be fast, it is imperative to keep the respective design size A manageable. In particular, unless the simulator is truly expensive or the input domain is vast, the typical recommendation is to restrict to hundreds of inputs, A 10 3 . This creates a major tension as frequently the stochastic simulator has low signal-to-noise ratio or a complex noise structure. A prototypical example is where the simulator Y (x) F (X [0, t]) X0 x involves functionals of a continuous-time Markov chain or stochastic differential equation solution (X t), whereby the stochasticity tends to dominate the trend/drift term for short t, and moreover simulation noise is non-Gaussian and state-dependent (heteroskedastic). Both authors are partially supported by NSF DMS-1521743.

Deep Reinforcement Learning (DRL) is vulnerable to small adversarial perturbations on state observations. These perturbations do not alter the environment directly but can mislead the agent into making suboptimal decisions. We analyze the Markov Decision Process (MDP) under this threat model and utilize tools from the neural net-work verification literature to enable robust train-ing for DRL under observational perturbations. Our techniques are general and can be applied to both Deep Q Networks (DQN) and Deep Deterministic Policy Gradient (DDPG) algorithms for discrete and continuous action control problems. We demonstrate that our proposed training procedure significantly improves the robustness of DQN and DDPG agents under a suite of strong white-box attacks on observations, including a few novel attacks we specifically craft. Additionally, our training procedure can produce provable certificates for the robustness of a Deep RL agent.

In many real-world settings, a team of agents must coordinate its behaviour while acting in a decentralised fashion. At the same time, it is often possible to train the agents in a centralised fashion where global state information is available and communication constraints are lifted. Learning joint action-values conditioned on extra state information is an attractive way to exploit centralised learning, but the best strategy for then extracting decentralised policies is unclear. Our solution is QMIX, a novel value-based method that can train decentralised policies in a centralised end-to-end fashion. QMIX employs a mixing network that estimates joint action-values as a monotonic combination of per-agent values. We structurally enforce that the joint-action value is monotonic in the per-agent values, through the use of non-negative weights in the mixing network, which guarantees consistency between the centralised and decentralised policies. To evaluate the performance of QMIX, we propose the StarCraft Multi-Agent Challenge (SMAC) as a new benchmark for deep multi-agent reinforcement learning. We evaluate QMIX on a challenging set of SMAC scenarios and show that it significantly outperforms existing multi-agent reinforcement learning methods.

Redistribution systems iteratively redistribute mass between groups under the control of rules. PRAM is a framework for building redistribution systems. We discuss the relationships between redistribution systems, agent-based systems, compartmental models and Bayesian models. PRAM puts agent-based models on a sound probabilistic footing by reformulating them as redistribution systems. This provides a basis for integrating agent-based and probabilistic models. \pram/ extends the themes of probabilistic relational models and lifted inference to incorporate dynamical models and simulation. We illustrate PRAM with an epidemiological example.

We consider the problem of computing the maximum likelihood multivariate log-concave distribution for a set of points. Specifically, we present an algorithm which, given $n$ points in $\mathbb{R} d$ and an accuracy parameter $\eps 0$, runs in time $\poly(n,d,1/\eps),$ and returns a log-concave distribution which, with high probability, has the property that the likelihood of the $n$ points under the returned distribution is at most an additive $\eps$ less than the maximum likelihood that could be achieved via any log-concave distribution. This is the first computationally efficient (polynomial time) algorithm for this fundamental and practically important task. Our algorithm rests on a novel connection with exponential families: the maximum likelihood log-concave distribution belongs to a class of structured distributions which, while not an exponential family, locally'' possesses key properties of exponential families. This connection then allows the problem of computing the log-concave maximum likelihood distribution to be formulated as a convex optimization problem, and solved via an approximate first-order method.

Knowledge graph reasoning, which aims at predicting missing facts through reasoning with observed facts, is critical for many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent knowledge graph embedding methods. A principled logic rule-based approach is the Markov Logic Network (MLN), which is able to leverage domain knowledge with first-order logic and meanwhile handle uncertainty. However, the inference in MLNs is usually very difficult due to the complicated graph structures. TransE, DistMult) learn effective entity and relation embeddings for reasoning, which are much more effective and efficient.