The aim of this comment (set to appear in a formal discussion in JASA) is to draw out some conclusions from an extended back-and-forth I have had with Wang and Blei regarding the deconfounder method proposed in "The Blessings of Multiple Causes" [arXiv:1805.06826]. I will make three points here. First, in my role as the critic in this conversation, I will summarize some arguments about the lack of causal identification in the bulk of settings where the "informal" message of the paper suggests that the deconfounder could be used. This is a point that is discussed at length in D'Amour 2019 [arXiv:1902.10286], which motivated the results concerning causal identification in Theorems 6--8 of "Blessings". Second, I will argue that adding parametric assumptions to the working model in order to obtain identification of causal parameters (a strategy followed in Theorem 6 and in the experimental examples) is a risky strategy, and should only be done when extremely strong prior information is available. Finally, I will consider the implications of the nonparametric identification results provided for a narrow, but non-trivial, set of causal estimands in Theorems 7 and 8. I will highlight that these results may be even more interesting from the perspective of detecting causal identification from observed data, under relatively weak assumptions about confounders.

ABSTRACT W e address the problem of simultaneously learning a k -means clustering and deep feature representation from unlabelle d data, which is of interest due to the potential of deep k -means to outperform traditional two-step feature extraction and shallow-clustering strategies. W e achieve this by develop ing a gradient-estimator for the non-differentiable k -means objective via the Gumbel-Softmax reparameterisation trick. In contrast to previous attempts at deep clustering, our concr ete k -means model can be optimised with respect to the canonical k -means objective and is easily trained end-to-end without resorting to alternating optimisation. W e demonstrate the efficacy of our method on standard clustering benchmarks. Index T erms-- Deep Clustering, Unsupervised Learning, Gradient Estimator 1. INTRODUCTION Clustering is a fundamental task in unsupervised machine learning, and one with numerous applications.

Selecting hyperparameters for unsupervised learning problems is difficult in general due to the lack of ground truth for validation. However, this issue is prevalent in machine learning, especially in clustering problems with examples including the Lagrange multipliers of penalty terms in semidefinite programming (SDP) relaxations and the bandwidths used for constructing kernel similarity matrices for Spectral Clustering. Despite this, there are not many provable algorithms for tuning these hyperparameters. In this paper, we provide a unified framework with provable guarantees for the above class of problems. We demonstrate our method on two distinct models. First, we show how to tune the hyperparameters in widely used SDP algorithms for community detection in networks. In this case, our method can also be used for model selection. Second, we show the same framework works for choosing the bandwidth for the kernel similarity matrix in Spectral Clustering for subgaussian mixtures under suitable model specification. In a variety of simulation experiments, we show that our framework outperforms other widely used tuning procedures in a broad range of parameter settings.

Recent work has shown that the outputs of convolutional neural networks become Gaussian process (GP) distributed when we take the number of channels to infinity. In principle, these infinite networks should perform very well, both because they allow for exact Bayesian inference, and because widening networks is generally thought to improve (or at least not diminish) performance. However, Bayesian infinite networks perform poorly in comparison to finite networks, and our goal here is to explain this discrepancy. We note that the high-level representation induced by an infinite network has very little flexibility; it depends only on network hyperparameters such as depth, and as such cannot learn a good high-level representation of data. In contrast, finite networks correspond to a rich prior over high-level representations, corresponding to kernel hyperparameters. We analyse this flexibility from the perspective of the prior (looking at the structured prior covariance of the top-level kernel), and from the perspective of the posterior, showing that the representation in a learned, finite deep linear network slowly transitions from the kernel induced by the inputs towards the kernel induced by the outputs, both for gradient descent, and for Langevin sampling. Finally, we explore representation learning in deep, convolutional, nonlinear networks, showing that learned representations differ dramatically from the corresponding infinite network. One approach to understanding and improving neural networks is to perform Bayesian inference in an infinitely wide network, which can be done both for fully connected (Lee et al., 2018; Matthews et al., 2018) and convolutional networks (Garriga-Alonso et al., 2019; Novak et al., 2019).

Deep neural networks (DNNs) build high-level intelligence on low-level raw features. Understanding of this high-level intelligence can be enabled by deciphering the concepts they base their decisions on, as human-level thinking. In this paper, we study concept-based explainability for DNNs in a systematic framework. First, we define the notion of completeness, which quantifies how sufficient a particular set of concepts is in explaining a model's prediction behavior. Based on performance and variability motivations, we propose two definitions to quantify completeness. We show that under degenerate conditions, our method is equivalent to Principal Component Analysis. Next, we propose a concept discovery method that considers two additional constraints to encourage the interpretability of the discovered concepts. We use game-theoretic notions to aggregate over sets to define an importance score for each discovered concept, which we call ConceptSHAP. On specifically-designed synthetic datasets and real-world text and image datasets, we validate the effectiveness of our framework in finding concepts that are complete in explaining the decision, and interpretable.

For complex nonlinear supervised learning models, assessing the relevance of input variables or their interactions is not straightforward due to the lack of a direct measure of relevance, such as the regression coefficients in generalized linear models. One can assess the relevance of input variables locally by using the mean prediction or its derivative, but this disregards the predictive uncertainty. In this work, we present a Bayesian method for identifying relevant input variables with main effects and interactions by differentiating the Kullback-Leibler divergence of predictive distributions. The method averages over local measures of relevance and has a conservative property that takes into account the uncertainty in the predictive distribution. Our empirical results on simulated and real data sets with nonlinearities demonstrate accurate and efficient identification of relevant main effects and interactions compared to alternative methods.

--Recently algorithms incorporating second order curvature information have become popular in training neural networks. The Nesterov's Accelerated Quasi-Newton (NAQ) method has shown to effectively accelerate the BFGS quasi-Newton method by incorporating the momentum term and Nesterov's accelerated gradient vector . A stochastic version of NAQ method was proposed for training of large-scale problems. This paper proposes a stochastic variance reduced Nesterov's Accelerated Quasi-Newton method in full (SVR-NAQ) and limited (SVR-LNAQ) memory forms. The performance of the proposed method is evaluated in T ensorflow on four benchmark problems - two regression and two classification problems respectively. The results show improved performance compared to conventional methods.

Machine learning classifiers often stumble over imbalanced datasets where classes are not equally represented. This inherent bias towards the majority class may result in low accuracy in labeling minority class. Imbalanced learning is prevalent in many real world applications, such as medical research, network intrusion detection, and fraud detection in credit card transaction, etc. A good number of research works have been reported to tackle this challenging problem. For example, SMOTE (Synthetic Minority Over-sampling TEchnique) and ADASYN (ADAptive SYNthetic sampling approach) use oversampling techniques to balance the skewed datasets. In this paper, we propose a novel method which combines a Weighted Oversampling Technique and ensemble Boosting method to improve the classification accuracy of minority data without sacrificing the accuracy of majority class. WOTBoost adjust its oversampling strategy at each round of boosting to synthesize more targeted minority data samples. The adjustment is enforced using a weighted distribution. We compared WOTBoost with other 4 classification models (i.e. decision tree, SMOTE + decision tree, ADASYN + decision tree, SMOTEBoost) extensively on 18 public accessible imbalanced datasets. WOTBoost achieved the best G mean on 6 datasets and highest AUC score on 7 datasets.

Our goal is to understand the so-called trade-off between fairness and accuracy. In this work, using a tool from information theory called Chernoff information, we derive fundamental limits on this relationship that explain why the accuracy on a given dataset often decreases as fairness increases. Novel to this work, we examine the problem of fair classification through the lens of a mismatched hypothesis testing problem, i.e., where we are trying to find a classifier that distinguishes between two "ideal" distributions but instead we are given two mismatched distributions that are biased. Based on this perspective, we contend that measuring accuracy with respect to the given (possibly biased) dataset is a problematic measure of performance. Instead one should also consider accuracy with respect to an ideal dataset that is unbiased. We formulate an optimization to find such ideal distributions and show that the optimization is feasible. Lastly, when the Chernoff information for one group is strictly less than another in the given dataset, we derive the information-theoretic criterion under which collection of more features can actually improve the Chernoff information and achieve fairness without compromising accuracy on the available data.

End-to-end learning with deep neural networks, such as con-volutional neural networks (CNNs), has been demonstrated to be very successful for different tasks of image classification. To make decisions of black-box approaches transparent, different solutions have been proposed. LIME is an approach to explainable AI relying on segmenting images into superpixels based on the Quick-Shift algorithm. In this paper, we present an explorative study of how different superpixel methods, namely Felzenszwalb, SLIC and Compact-Watershed, impact the generated visual explanations. We compare the resulting relevance areas with the image parts marked by a human reference. Results show that image parts selected as relevant strongly vary depending on the applied method. Quick-Shift resulted in the least and Compact-Watershed in the highest correspondence with the reference relevance areas.