Generative Adversarial Networks (GANs) are an elegant mechanism for data generation. However, a key challenge when using GANs is how to best measure their ability to generate realistic data. In this paper, we demonstrate that an intrinsic dimensional characterization of the data space learned by a GAN model leads to an effective evaluation metric for GAN quality. In particular, we propose a new evaluation measure, CrossLID, that assesses the local intrinsic dimensionality (LID) of real-world data with respect to neighborhoods found in GAN-generated samples. Intuitively, CrossLID measures the degree to which manifolds of two data distributions coincide with each other. In experiments on 4 benchmark image datasets, we compare our proposed measure to several state-of-the-art evaluation metrics. Our experiments show that CrossLID is strongly correlated with the progress of GAN training, is sensitive to mode collapse, is robust to small-scale noise and image transformations, and robust to sample size. Furthermore, we show how CrossLID can be used within the GAN training process to improve generation quality.

A new generation of manycore processors is on the rise that offers dozens and more cores on a chip and, in a sense, fuses host processor and accelerator. In this paper we target the efficient training of generalized linear models on these machines. We propose a novel approach for achieving parallelism which we call Heterogeneous Tasks on Homogeneous Cores (HTHC). It divides the problem into multiple fundamentally different tasks, which themselves are parallelized. For evaluation, we design a detailed, architecture-cognizant implementation of our scheme on a recent 72-core Knights Landing processor that is adaptive to the cache, memory, and core structure. Experiments for Lasso and SVM with different data sets show a speedup of typically an order of magnitude compared to straightforward parallel implementations in C++.

Recently, a method called the Mutual Information Neural Estimator (MINE) that uses neural networks has been proposed to estimate mutual information and more generally the Kullback-Leibler (KL) divergence between two distributions. The method uses the Donsker-Varadhan representation to arrive at the estimate of the KL divergence and is better than the existing estimators in terms of scalability and flexibility. The output of MINE algorithm is not guaranteed to be a consistent estimator. We propose a new estimator that instead of searching among functions characterized by neural networks searches the functions in a Reproducing Kernel Hilbert Space. We prove that the proposed estimator is consistent. We carry out simulations and show that when the datasets are small the proposed estimator is more reliable than the MINE estimator and when the datasets are large the performance of the two methods are close.

Text embedding representing natural language documents in a semantic vector space can be used for document retrieval using nearest neighbor lookup. In order to study the feasibility of neural models specialized for retrieval in a semantically meaningful way, we suggest the use of the Stanford Question Answering Dataset (SQuAD) in an open-domain question answering context, where the first task is to find paragraphs useful for answering a given question. First, we compare the quality of various text-embedding methods on the performance of retrieval and give an extensive empirical comparison on the performance of various non-augmented base embedding with, and without IDF weighting. Our main results are that by training deep residual neural models, specifically for retrieval purposes, can yield significant gains when it is used to augment existing embeddings. We also establish that deeper models are superior to this task. The best base baseline embeddings augmented by our learned neural approach improves the top-1 paragraph recall of the system by 14%.

Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. The Bayesian optimization routine involves learning a response surface and maximizing a score to select the most valuable inputs to be queried at the next iteration. These key steps are subject to the curse of dimensionality so that Bayesian optimization does not scale beyond 10--20 parameters. In this work, we address this issue and propose a high-dimensional BO method that learns a nonlinear low-dimensional manifold of the input space. We achieve this with a multi-layer neural network embedded in the covariance function of a Gaussian process. This approach applies unsupervised dimensionality reduction as a byproduct of a supervised regression solution. This also allows exploiting data efficiency of Gaussian process models in a Bayesian framework. We also introduce a nonlinear mapping from the manifold to the high-dimensional space based on multi-output Gaussian processes and jointly train it end-to-end via marginal likelihood maximization. We show this intrinsically low-dimensional optimization outperforms recent baselines in high-dimensional BO literature on a set of benchmark functions in 60 dimensions.

This paper advocates against permute-and-predict (PaP) methods for interpreting black box functions. Methods such as the variable importance measures proposed for random forests, partial dependence plots, and individual conditional expectation plots remain popular because of their ability to provide model-agnostic measures that depend only on the pre-trained model output. However, numerous studies have found that these tools can produce diagnostics that are highly misleading, particularly when there is strong dependence among features. Rather than simply add to this growing literature by further demonstrating such issues, here we seek to provide an explanation for the observed behavior. In particular, we argue that breaking dependencies between features in hold-out data places undue emphasis on sparse regions of the feature space by forcing the original model to extrapolate to regions where there is little to no data. We explore these effects through various settings where a ground-truth is understood and find support for previous claims in the literature that PaP metrics tend to over-emphasize correlated features both in variable importance and partial dependence plots, even though applying permutation methods to the ground-truth models do not. As an alternative, we recommend more direct approaches that have proven successful in other settings: explicitly removing features, conditional permutations, or model distillation methods.

Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical correlation analysis (CCA). We show that CCA belongs to a family of statistics for measuring multivariate similarity, but that neither CCA nor any other statistic that is invariant to invertible linear transformation can measure meaningful similarities between representations of higher dimension than the number of data points. We introduce a similarity index that measures the relationship between representational similarity matrices and does not suffer from this limitation. This similarity index is equivalent to centered kernel alignment (CKA) and is also closely connected to CCA. Unlike CCA, CKA can reliably identify correspondences between representations in networks trained from different initializations.

Sparse Subspace Clustering (SSC) is one of the most popular methods for clustering data points into their underlying subspaces. However, SSC may suffer from heavy computational burden. Orthogonal Matching Pursuit applied on SSC accelerates the computation but the trade-off is the loss of clustering accuracy. In this paper, we propose a noise-robust algorithm, Restricted Connection Orthogonal Matching Pursuit for Sparse Subspace Clustering (RCOMP-SSC), to improve the clustering accuracy and maintain the low computational time by restricting the number of connections of each data point during the iteration of OMP. Also, we develop a framework of control matrix to realize RCOMP-SCC. And the framework is scalable for other data point selection strategies. Our analysis and experiments on synthetic data and two real-world databases (EYaleB & Usps) demonstrate the superiority of our algorithm compared with other clustering methods in terms of accuracy and computational time.

Complex or co-existing diseases are commonly treated using drug combinations, which can lead to higher risk of adverse side effects. The detection of polypharmacy side effects is usually done in Phase IV clinical trials, but there are still plenty which remain undiscovered when the drugs are put on the market. Such accidents have been affecting an increasing proportion of the population (15% in the US now) and it is thus of high interest to be able to predict the potential side effects as early as possible. Systematic combinatorial screening of possible drug-drug interactions (DDI) is challenging and expensive. However, the recent significant increases in data availability from pharmaceutical research and development efforts offer a novel paradigm for recovering relevant insights for DDI prediction. Accordingly, several recent approaches focus on curating massive DDI datasets (with millions of examples) and training machine learning models on them. Here we propose a neural network architecture able to set state-of-the-art results on this task---using the type of the side-effect and the molecular structure of the drugs alone---by leveraging a co-attentional mechanism. In particular, we show the importance of integrating joint information from the drug pairs early on when learning each drug's representation.

We present a heuristic algorithm, called recombinator-k-means, that can substantially improve the results of k-means optimization. Instead of using simple independent restarts and returning the best result, our scheme performs restarts in batches, using the results of a previous batch as a reservoir of candidates for the new initial starting values (seeds), exploiting the popular k-means++ seeding algorithm to piece them together into new promising initial configurations. Our scheme is general (it only affects the seeding part of the optimization, thus it could be applied even to k-medians or k-medoids, for example), it has no additional costs and it is trivially parallelizable across the restarts of each batch. In some circumstances, it can systematically find better configurations than the best one obtained after 10^4 restarts of a standard scheme. Our implementation is publicly available at https://github.com/carlobaldassi/RecombinatorKMeans.jl.