Weaknesses: - The authors choose to select \beta based on predictive accuracy. This is sensible, but what other approaches could also be used? And does it make sense to consider predictive accuracy on a separate training dataset? In the SMC community, people usually care more about the efficiency with which you can calculate the likelihood function (in order to estimate the parameters with particle MCMC), the accuracy of the filtered distribution, or ESS. Predictive accuracy is usually not a primary accuracy criterion so does it make sense to select \beta with this metric? From the simulation study, it appears that using predictive accuracy works well, but also seems to be consistently sub-optimal.

Reviewers agree that this is a clear contribution to the HMM and SMC set of methods that allows for robustness in the face of likelihood misspecification. Additionally, the method is both theoretically and empirically justified. While the main reviewer concern is novelty, there is agreement that the work is correct, thorough, and effective. An additional concern is the lack of clear attribution of theoretical results (e.g.

The study of learning causal structure with latent variables has advanced the understanding of the world by uncovering causal relationships and latent factors, e.g., Causal Representation Learning (CRL). However, in real-world scenarios, such as those in climate systems, causal relationships are often nonparametric, dynamic, and exist among both observed variables and latent variables. These challenges motivate us to consider a general setting in which causal relations are nonparametric and unrestricted in their occurrence, which is unconventional to current methods. To solve this problem, with the aid of 3-measurement in temporal structure, we theoretically show that both latent variables and processes can be identified up to minor indeterminacy under mild assumptions. Moreover, we tackle the general nonlinear Causal Discovery (CD) from observations, e.g., temperature, as a specific task of learning independent representation, through the principle of functional equivalence. Based on these insights, we develop an estimation approach simultaneously recovering both the observed causal structure and latent causal process in a nontrivial manner. Simulation studies validate the theoretical foundations and demonstrate the effectiveness of the proposed methodology. In the experiments involving climate data, this approach offers a powerful and in-depth understanding of the climate system.

Feature selection can select important features to address dimensional curses. Subspace learning, a widely used dimensionality reduction method, can project the original data into a low-dimensional space. However, the low-dimensional representation is often transformed back into the original space, resulting in information loss. Additionally, gate function-based methods in Takagi-Sugeno-Kang fuzzy system (TSK-FS) are commonly less discrimination. To address these issues, this paper proposes a novel feature selection method that integrates subspace learning with TSK-FS. Specifically, a projection matrix is used to fit the intrinsic low-dimensional representation. Subsequently, the low-dimensional representation is fed to TSK-FS to measure its availability. The firing strength is slacked so that TSK-FS is not limited by numerical underflow. Finally, the $\ell _{2,1}$-norm is introduced to select significant features and the connection to related works is discussed. The proposed method is evaluated against six state-of-the-art methods on eighteen datasets, and the results demonstrate the superiority of the proposed method.

Inferring the true demand for a product or a service from aggregate data is often challenging due to the limited available supply, thus resulting in observations that are censored and correspond to the realized demand, thereby not accounting for the unsatisfied demand. Censored regression models are able to account for the effect of censoring due to the limited supply, but they don't consider the effect of substitutions, which may cause the demand for similar alternative products or services to increase. This paper proposes Diffusion-aware Censored Demand Models, which combine a Tobit likelihood with a graph diffusion process in order to model the latent process of transfer of unsatisfied demand between similar products or services. We instantiate this new class of models under the framework of GPs and, based on both simulated and real-world data for modeling sales, bike-sharing demand, and EV charging demand, demonstrate its ability to better recover the true demand and produce more accurate out-of-sample predictions.

Model uncertainty quantification involves measuring and evaluating the uncertainty linked to a model's predictions, helping assess their reliability and confidence. Noise injection is a technique used to enhance the robustness of neural networks by introducing randomness. In this paper, we establish a connection between noise injection and uncertainty quantification from a Bayesian standpoint. We theoretically demonstrate that injecting noise into the weights of a neural network is equivalent to Bayesian inference on a deep Gaussian process. Consequently, we introduce a Monte Carlo Noise Injection (MCNI) method, which involves injecting noise into the parameters during training and performing multiple forward propagations during inference to estimate the uncertainty of the prediction. Through simulation and experiments on regression and classification tasks, our method demonstrates superior performance compared to the baseline model.

I found the paper very well presented and enjoyable to read. The basic problem is interesting, and the approach presented as some salient features, notably the fact that one does not have to make parametric assumption on the underlying distribution. The high-level idea of imposing structural assumptions but nonetheless relying on discriminative models was quite elegant. The basic insight in estimating the risk from unlabelled data is that by encoding a certain structural assumption - namely, that the data comprises three independent views - one implicitly gets information about the class-conditional risks by considering the first three moments of the label vectors. This leads to a system of equations which may be solved to infer the class-conditional risks.

I think this paper addresses an important issue and makes valuable contributions, and thus should be published. I have a few concerns, hence my lower rating for the last question above (which I think could be addressed relatively easily, however). I think this is fundamentally *OK* and even perhaps a positive thing. However, I think a bit more discussion needs to be given to how the arguments might be made more formal. For example, in Section 2.1, I think the proof is intended to hold only in the limit of M going to infinity. Please give a stament of what should hold in what limit-- this wasn't clear to me.

The proposed method is very similar to previous work by Nie et al. -- both use k-trees to search for low-treewidth Bayesian networks, both start with a randomly chosen initial clique, and both propose using an A* method for finding the best tree. The differences are that Nie et al. score k-trees using a mutual information score and use BDeu for choosing the final consistent Bayesian network, while this paper proposes using BIC and incrementally building the Bayesian network along with the k-tree, using the BN to score the k-tree. This paper also includes the additional restriction that the complete variable (partial) order is chosen randomly, while in Nie et al. The main justification for these differences is the ability to scale to large treewidths. However, in the experiments, the previous S2 algorithm also can scale to large treewidths.

This paper provides an interesting connection between kernel Bayesian inference and vector valued regression. Based on this, a new regularization method is provided to compute an approximation of the kernel embedding of the posterior distribution. Simulation results look promising, suggesting that the new method gains improvement over many existing methods. However, as a non expert, from reading the current introduction, I'm still confused about the motivation of using kernel Bayesian inference---in order to approximate the kernel embedding of the posterior, a sample of iid draws (x_i, y_i) from the joint distribution of the parameter/hidden variable (X in the paper) and data (Y in the paper) are assumed to be available. First, it is a highly non-trivial problem of obtaining samples (x_i)'s from the posterior.