Minimum sum-of-squares clustering (MSSC) is a widely used clustering model, of which the popular K-means algorithm constitutes a local minimizer. It is well known that the solutions of K-means can be arbitrarily distant from the true MSSC global optimum, and dozens of alternative heuristics have been proposed for this problem. However, no other algorithm has been commonly adopted in the literature. This may be related to differences of computational effort, or to the assumption that a better solution of the MSSC has only a minor impact on classification or generalization capabilities. In this article, we dispute this belief. We introduce an efficient population-based metaheuristic that uses K-means as a local search in combination with problem-tailored crossover, mutation, and diversification operators. This algorithm can be interpreted as a multi-start K-means, in which the initial center positions are carefully sampled based on the search history. The approach is scalable and accurate, outperforming all recent state-of-the-art algorithms for MSSC in terms of solution quality, measured by the depth of local minima. This enhanced accuracy leads to classification results which are significantly closer to the ground truth than those of other algorithms, for overlapping Gaussian-mixture datasets with a large number of features and clusters. Therefore, improved global optimization methods appear to be essential to better exploit the MSSC model in high dimension.

In applications of machine learning to particle physics, a persistent challenge is how to go beyond discrimination to learn about the underlying physics. To this end, a powerful tool would be a framework for unsupervised learning, where the machine learns the intricate high-dimensional contours of the data upon which it is trained, without reference to pre-established labels. In order to approach such a complex task, an unsupervised network must be structured intelligently, based on a qualitative understanding of the data. In this paper, we scaffold the neural network's architecture around a leading-order model of the physics underlying the data. In addition to making unsupervised learning tractable, this design actually alleviates existing tensions between performance and interpretability. We call the framework JUNIPR: "Jets from UNsupervised Interpretable PRobabilistic models". In this approach, the set of particle momenta composing a jet are clustered into a binary tree that the neural network examines sequentially. Training is unsupervised and unrestricted: the network could decide that the data bears little correspondence to the chosen tree structure. However, when there is a correspondence, the network's output along the tree has a direct physical interpretation. JUNIPR models can perform discrimination tasks, through the statistically optimal likelihood-ratio test, and they permit visualizations of discrimination power at each branching in a jet's tree. Additionally, JUNIPR models provide a probability distribution from which events can be drawn, providing a data-driven Monte Carlo generator. As a third application, JUNIPR models can reweight events from one (e.g. simulated) data set to agree with distributions from another (e.g. experimental) data set.

Learning the disentangled representation of interpretable generative factors of data is one of the foundations to allow artificial intelligence to think like people. In this paper, we propose the analogical training strategy for the unsupervised disentangled representation learning in generative models. The analogy is one of the typical cognitive processes, and our proposed strategy is based on the observation that sample pairs in which one is different from the other in one specific generative factor show the same analogical relation. Thus, the generator is trained to generate sample pairs from which a designed classifier can identify the underlying analogical relation. In addition, we propose a disentanglement metric called the subspace score, which is inspired by subspace learning methods and does not require supervised information. Experiments show that our proposed training strategy allows the generative models to find the disentangled factors, and that our methods can give competitive performances as compared with the state-of-the-art methods.

Peer reviewing is a central component in the scientific publishing process. We present the first public dataset of scientific peer reviews available for research purposes (PeerRead v1) providing an opportunity to study this important artifact. The dataset consists of 14.7K paper drafts and the corresponding accept/reject decisions in top-tier venues including ACL, NIPS and ICLR. The dataset also includes 10.7K textual peer reviews written by experts for a subset of the papers. We describe the data collection process and report interesting observed phenomena in the peer reviews. We also propose two novel NLP tasks based on this dataset and provide simple baseline models. In the first task, we show that simple models can predict whether a paper is accepted with up to 21% error reduction compared to the majority baseline. In the second task, we predict the numerical scores of review aspects and show that simple models can outperform the mean baseline for aspects with high variance such as 'originality' and 'impact'.

In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two different notions of relational marginals. Second, we show a duality between the resulting relational marginal problems and the maximum likelihood estimation of the parameters of relational models, which generalizes a well-known duality from the propositional setting. Third, by exploiting the relational marginal formulation, we present a statistically sound method to learn the parameters of relational models that will be applied in settings where the number of constants differs between the training and test data. Furthermore, based on a relational generalization of marginal polytopes, we characterize cases where the standard estimators based on feature's number of true groundings needs to be adjusted and we quantitatively characterize the consequences of these adjustments. Fourth, we prove bounds on expected errors of the estimated parameters, which allows us to lower-bound, among other things, the effective sample size of relational training data.

The learning algorithm of a neural network tries to optimize the neural network's weights until some stopping condition has been met. This condition is typically either when the error of the network reaches an acceptable level of accuracy on the training set, when the error of the network on the validation set begins to deteriorate, or when the specified computational budget has been exhausted. The most common learning algorithm for neural networks is back-propagation, an algorithm that uses stochastic gradient descent, which was discussed earlier on in this series. The are some problems with this approach. Adjusting all the weights at once can result in a significant movement of the neural network in weight space, the gradient descent algorithm is quite slow, and the gradient descent algorithm is susceptible to local minima.

Fake news may be intentionally created to promote economic, political and social interests, and can lead to negative impacts on humans beliefs and decisions. Hence, detection of fake news is an emerging problem that has become extremely prevalent during the last few years. Most existing works on this topic focus on manual feature extraction and supervised classification models leveraging a large number of labeled (fake or real) articles. In contrast, we focus on content-based detection of fake news articles, while assuming that we have a small amount of labels, made available by manual fact-checkers or automated sources. We argue this is a more realistic setting in the presence of massive amounts of content, most of which cannot be easily factchecked. To that end, we represent collections of news articles as multi-dimensional tensors, leverage tensor decomposition to derive concise article embeddings that capture spatial/contextual information about each news article, and use those embeddings to create an article-by-article graph on which we propagate limited labels. Results on three real-world datasets show that our method performs on par or better than existing models that are fully supervised, in that we achieve better detection accuracy using fewer labels. In particular, our proposed method achieves 75.43% of accuracy using only 30% of labels of a public dataset while an SVM-based classifier achieved 67.43%. Furthermore, our method achieves 70.92% of accuracy in a large dataset using only 2% of labels.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their applicability remains limited when the problem dimension is large and the projection onto a convex set is costly. Instead, stochastic conditional gradient methods are proposed as an alternative solution relying on (i) Approximating gradients via a simple averaging technique requiring a single stochastic gradient evaluation per iteration; (ii) Solving a linear program to compute the descent/ascent direction. The averaging technique reduces the noise of gradient approximations as time progresses, and replacing projection step in proximal methods by a linear program lowers the computational complexity of each iteration. We show that under convexity and smoothness assumptions, our proposed method converges to the optimal objective function value at a sublinear rate of $O(1/t^{1/3})$. Further, for a monotone and continuous DR-submodular function and subject to a general convex body constraint, we prove that our proposed method achieves a $((1-1/e)OPT-\eps)$ guarantee with $O(1/\eps^3)$ stochastic gradient computations. This guarantee matches the known hardness results and closes the gap between deterministic and stochastic continuous submodular maximization. Additionally, we obtain $((1/e)OPT -\eps)$ guarantee after using $O(1/\eps^3)$ stochastic gradients for the case that the objective function is continuous DR-submodular but non-monotone and the constraint set is down-closed. By using stochastic continuous optimization as an interface, we provide the first $(1-1/e)$ tight approximation guarantee for maximizing a monotone but stochastic submodular set function subject to a matroid constraint and $(1/e)$ approximation guarantee for the non-monotone case.

In this paper, we investigate the potential of estimating the soil-moisture content based on VNIR hyperspectral data combined with IR data. Measurements from a multi-sensor field campaign represent the benchmark dataset which contains measured hyperspectral, IR, and soil-moisture data. We introduce a regression framework with three steps consisting of feature selection, preprocessing, and well-chosen regression models. The latter are mainly supervised machine learning models. An exception are the self-organizing maps which are a combination of unsupervised and supervised learning. We analyze the impact of the distinct preprocessing methods on the regression results. Of all regression models, the extremely randomized trees model without preprocessing provides the best estimation performance. Our results reveal the potential of the respective regression framework combined with the VNIR hyperspectral data to estimate soil moisture. In conclusion, the results of this paper provide a basis for further improvements in different research directions.