The authors study the problem of structure learning for Bayesian networks. The conventional methods for this task include the constraint-based methods or the score-based methods which involve optimizing a discrete score function over the set of DAGs with a combinatorial constraint. Unlike the existing approaches, the authors propose formulating the problem as a continuous optimization problem over real matrices, which performs a global search, and can be solved using standard numerical algorithms. The main idea in this work is using a smooth function for expressing an equality constraint to force acyclicity on the estimated structure. The paper is very well written and enjoyable to read.

Summary: Meta-learning is motivated by the promise of being able to transfer knowledge from previous learning experiences to new task settings, such that a new task can be learned more effectively from few observations. Yet, updating highly parametric models with little amounts of data can easily lead to overfitting. A promising avenue towards overcoming this challenge is a Bayesian treatment of meta-learning. This work, builds on top of recent work that provides a Bayesian interpretation of MAML (model-agnostic-meta-learning). This contribution is a direct extension of (Grant et al 2018) - where the task-train posterior was approximated via a Gaussian distribution. Applying SVGD instead allows for a more flexible and (potentially) more accurate approximation of a highly complex posterior.

The authors propose a marked process latent variable model that leverages Gaussian processes for continuous latent sates, a generalized linear model for discrete latent states and an inference network for efficient inference. Results on real data suggest that the proposed approach is interpretable and outperforms standard baselines on held out data. I really enjoyed reading the paper, it is very well written. That being said, the notation is sloppy and lack of details makes it difficult to appreciate the contributions of the paper. The authors seemed to have assumed that the reader is very familiar with point processes, Gaussian processes, variational inference and deep learning.

This paper proposes a novel learning frame-work for Markov State Models of real valued vectors. This model can handle metastable processes i.e. processes that evolve locally in short time-scales but switch between a few clusters after very long periods. The proposed framework is based on a nice idea to decompose the transition from x1 to x2 to the probability that x1 belongs to a long-lived state and a distribution of x2 given the state. The first conditional probability is modeled using a decoding deep network whereas the second one can be represented either using a network that assigns weights to x2 or using a generative neural network. This is a very interesting manuscript.

The paper addresses the problem of rho-POMDPs non-convex reward functions, proving that indeed under some cases they, and their resulting value functions, are Lipschitz-continuous (LC) for finite horizons. The paper also proposes and uses a more general vector form of LC, too. This result allows value function approximations of the optimal V * to be used, as well as upper and lower bounds (U and L) on value as in HSVI, and a wide array of new algorithms to be developed. This is analogous to the PWLC result for standard POMDPs, as LC is more general, allowing for similar contraction operators with Banach's fixed point theorem as in (PO)MDPs, and finite horizon approximations of the infinite horizon objective criteria. Once the paper establishes the main result, it discusses approximations of U and L using min or max, respectively, over sets of cones.

The authors conduct an analysis of CTC trained acoustic models to determine how information related to phonetic categories is preserved in CTC-based models which directly output graphemes. The work follows a long line of research that has analyzed neural network representations to determine how they model phonemic representations, although to the best of my knowledge this has not been done previously for CTC-based end-to-end architectures. The results and analysis presented by the authors is interesting, although there are some concerns I have with the conclusions that the authors draw that I would like to clarify these points. Please see my detailed comments below. In the paper, the authors conclude that (Line 159--164) "... after the 5th recurrent layer accuracy goes down again. One possible explanation to this may be that higher layers in the model are more sensitive to long distance information that is needed for the speech recognition task, whereas the local information which is needed for classifying phones is better captured in lower layers."

Summary: The paper's goal is to study the minimax rates for learning problems on Markovian data. The author(s) consider an interesting setting where the sequence of data observed follow a Markovian dependency pattern. They consider discrete state Markov chains with a state space [k] and study the minimax error rates for the following two tasks: Prediction: Given a trajectory X_1 - X_2 … - X_n from an unknown chain M, predict the probability distribution of the next state X_n 1, i.e., P(. X_1…n)) ] where the expectation is over the trajectory X_1…X_n. The loss function the paper focuses on is KL-divergence and presents a conjecture for how the L_1 loss should scale with respect to k and n.

The paper describes a novel brain-computer-interface algorithm for controlling movement of a cursor to random locations on a screen using neuronal activity (power in the "spike-spectrum" of intra-cortically implanted selected electrodes). The algorithm uses a dynamic Bayesian network model that encodes possible target location (from a set of possible positions on a 40x40 grid, layed out on the screed). Target changes can only occur once a countdown timer reaches zero (time intervals are drawn at random) at which time the target has a chance of switching location. Observations (power in spike spectrum) are assumed to be drawn from a multi modal distribution (mixture of von Mises functions) as multiple neurons may affect the power recording on a single electrode and are dependent on the current movement direction. The position is simply the integration over time of the movement direction variable (with a bit of decay).

However, five other causal diagrams can also be considered with confounder proxies (see Figure 1 in [Miao et al., 2016]). It would be interesting to check whether the proposed method can be applied to all these causal diagrams or there are some limitations. For instance, why covariates of x_i are independent given z_i? Is it restricting the expressive power of this method? For instance, in Experimental Results section, it is assumed that z is a 20-dimensional variable.

In particular, it establishes that as long as noises are homoscedastic, then under a milder minimality/faithfulness assumptions it is possible to efficiently recover the GBN. Clarity The paper is heavy on notation, but everything is explained and organized clearly.