The El Ni\~no Southern Oscillation (ENSO) is a semi-periodic fluctuation in sea surface temperature (SST) over the tropical central and eastern Pacific Ocean that influences interannual variability in regional hydrology across the world through long-range dependence or teleconnections. Recent research has demonstrated the value of Deep Learning (DL) methods for improving ENSO prediction as well as Complex Networks (CN) for understanding teleconnections. However, gaps in predictive understanding of ENSO-driven river flows include the black box nature of DL, the use of simple ENSO indices to describe a complex phenomenon and translating DL-based ENSO predictions to river flow predictions. Here we show that eXplainable DL (XDL) methods, based on saliency maps, can extract interpretable predictive information contained in global SST and discover SST information regions and dependence structures relevant for river flows which, in tandem with climate network constructions, enable improved predictive understanding. Our results reveal additional information content in global SST beyond ENSO indices, develop understanding of how SSTs influence river flows, and generate improved river flow prediction, including uncertainty estimation. Observations, reanalysis data, and earth system model simulations are used to demonstrate the value of the XDL-CN based methods for future interannual and decadal scale climate projections.

It is extensively used for exploratory data analysis. Traditional clustering algorithms typically identify a single partitioning of a given dataset. However, data is often multifaceted and can be both interpreted and clustered through multiple viewpoints (or, views). For example, the same face data can be clustered based on either identity or based on pose. In real applications, partitions generated by a clustering algorithm may not correspond to the view a user is interested in. In this paper, we address the problem of finding an alternative clustering, given a dataset and an existing, pre-computed clustering. Ideally, one would like the alternative clustering to be novel (i.e., non-redundant) w.r.t. the existing clustering to reveal a new viewpoint to the user. Simultaneously, one would like the result to reveal partitions of high clustering quality. Several recent papers propose algorithms for alternativeProceedings of the 21 st International Conference on Artificial Intelligence and Statistics (AISTATS) 2018, Lan-zarote, Spain.

Clustering is used to find structure in unlabeled data by grouping similar objects together. Cluster analysis depends on the definition of similarity in the feature space. In this paper, we propose an Adaptive Nonparametric Variational Autoencoder (AdapVAE) to perform end-to-end feature learning from raw data jointly with cluster membership learning through a Nonparametric Bayesian modeling framework with deep neural networks. It has the advantage of avoiding pre-definition of similarity or feature engineering. Our model relaxes the constraint of fixing the number of clusters in advance by assigning a Dirichlet Process prior on the latent representation in a low-dimensional feature space. It can adaptively detect novel clusters when new data arrives based on a learned model from historical data in an online unsupervised learning setting. We develop a joint online variational inference algorithm to learn feature representations and cluster assignments via iteratively optimizing the evidence lower bound (ELBO). Our experimental results demonstrate the capacity of our modelling framework to learn the number of clusters automatically using data, the flexibility to detect novel clusters with emerging data adaptively, the ability of high quality reconstruction and generation of samples without supervised information and the improvement over state-of-the-art end-to-end clustering methods in terms of accuracy on both image and text corpora benchmark datasets.

An implicit goal in works on deep generative models is that such models should be able to generate novel examples that were not previously seen in the training data. In this paper, we investigate to what extent this property holds for widely employed variational autoencoder (VAE) architectures. VAEs maximize a lower bound on the log marginal likelihood, which implies that they will in principle overfit the training data when provided with a sufficiently expressive decoder. In the limit of an infinite capacity decoder, the optimal generative model is a uniform mixture over the training data. More generally, an optimal decoder should output a weighted average over the examples in the training data, where the magnitude of the weights is determined by the proximity in the latent space. This leads to the hypothesis that, for a sufficiently high capacity encoder and decoder, the VAE decoder will perform nearest-neighbor matching according to the coordinates in the latent space. To test this hypothesis, we investigate generalization on the MNIST dataset. We consider both generalization to new examples of previously seen classes, and generalization to the classes that were withheld from the training set. In both cases, we find that reconstructions are closely approximated by nearest neighbors for higher-dimensional parameterizations. When generalizing to unseen classes however, lower-dimensional parameterizations offer a clear advantage.

Inferring causal relations from observational data is widely used for knowledge discovery in healthcare and economics. To investigate whether a treatment can affect an outcome of interest, we focus on answering counterfactual questions of this type: what would a patient’s blood pressure be had he/she received a different treatment? Nearest neighbor matching (NNM) sets the counterfactual outcome of any treatment (control) sample to be equal to the factual outcome of its nearest neighbor in the control (treatment) group. Although being simple, flexible and interpretable, most NNM approaches could be easily misled by variables that do not affect the outcome. In this paper, we address this challenge by learning subspaces that are predictive of the outcome variable for both the treatment group and control group. Applying NNM in the learned subspaces leads to more accurate estimation of the counterfactual outcomes and therefore treatment effects. We introduce an informative subspace learning algorithm by maximizing the nonlinear dependence between the candidate subspace and the outcome variable measured by the Hilbert-Schmidt Independence Criterion (HSIC). We propose a scalable estimator of HSIC, called HSIC-RFF that reduces the quadratic computational and storage complexities (with respect to the sample size) of the naive HSIC implementation to linear through constructing random Fourier features. We also prove an upper bound on the approximation error of the HSIC-RFF estimator. Experimental results on simulated datasets and real-world datasets demonstrate our proposed approach outperforms existing NNM approaches and other commonly used regression-based methods for counterfactual inference.

Obtaining labels can be costly and time-consuming. Active learning allows a learning algorithm to intelligently query samples to be labeled for efficient learning. Fisher information ratio (FIR) has been used as an objective for selecting queries in active learning. However, little is known about the theory behind the use of FIR for active learning. There is a gap between the underlying theory and the motivation of its usage in practice. In this paper, we attempt to fill this gap and provide a rigorous framework for analyzing existing FIR-based active learning methods. In particular, we show that FIR can be asymptotically viewed as an upper bound of the expected variance of the log-likelihood ratio. Additionally, our analysis suggests a unifying framework that not only enables us to make theoretical comparisons among the existing querying methods based on FIR, but also allows us to give insight into the development of new active learning approaches based on this objective.