We investigate the efficiency of k-means in terms of both statistical and computational requirements. More precisely, we study a Nystr\"om approach to kernel k-means. We analyze the statistical properties of the proposed method and show that it achieves the same accuracy of exact kernel k-means with only a fraction of computations. Indeed, we prove under basic assumptions that sampling $\sqrt{n}$ Nystr\"om landmarks allows to greatly reduce computational costs without incurring in any loss of accuracy. To the best of our knowledge this is the first result showing in this kind for unsupervised learning.

We consider the problem of anomaly detection in images, and present a new detection technique. Given a sample of images, all known to belong to a ``normal'' class (e.g., dogs), we show how to train a deep neural model that can detect out-of-distribution images (i.e., non-dog objects). The main idea behind our scheme is to train a multi-class model to discriminate between dozens of geometric transformations applied on all the given images. The auxiliary expertise learned by the model generates feature detectors that effectively identify, at test time, anomalous images based on the softmax activation statistics of the model when applied on transformed images. We present extensive experiments using the proposed detector, which indicate that our algorithm improves state-of-the-art methods by a wide margin.

We propose a general, theoretically justified mechanism for processing missing data by neural networks. Our idea is to replace typical neuron's response in the first hidden layer by its expected value. This approach can be applied for various types of networks at minimal cost in their modification. Moreover, in contrast to recent approaches, it does not require complete data for training. Experimental results performed on different types of architectures show that our method gives better results than typical imputation strategies and other methods dedicated for incomplete data.

Modern large-scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computational architectures. A key bottleneck is the communication overhead for exchanging information such as stochastic gradients among different workers. In this paper, to reduce the communication cost, we propose a convex optimization formulation to minimize the coding length of stochastic gradients. The key idea is to randomly drop out coordinates of the stochastic gradient vectors and amplify the remaining coordinates appropriately to ensure the sparsified gradient to be unbiased. To solve the optimal sparsification efficiently, several simple and fast algorithms are proposed for an approximate solution, with a theoretical guarantee for sparseness. Experiments on $\ell_2$ regularized logistic regression, support vector machines, and convolutional neural networks validate our sparsification approaches.

Online learning to rank is a sequential decision-making problem where in each round the learning agent chooses a list of items and receives feedback in the form of clicks from the user. Many sample-efficient algorithms have been proposed for this problem that assume a specific click model connecting rankings and user behavior. We propose a generalized click model that encompasses many existing models, including the position-based and cascade models. Our generalization motivates a novel online learning algorithm based on topological sort, which we call TopRank. TopRank is (a) more natural than existing algorithms, (b) has stronger regret guarantees than existing algorithms with comparable generality, (c) has a more insightful proof that leaves the door open to many generalizations, and (d) outperforms existing algorithms empirically.

Scaling model capacity has been vital in the success of deep learning. For a typical network, necessary compute resources and training time grow dramatically with model size. Conditional computation is a promising way to increase the number of parameters with a relatively small increase in resources. We propose a training algorithm that flexibly chooses neural modules based on the data to be processed. Both the decomposition and modules are learned end-to-end. In contrast to existing approaches, training does not rely on regularization to enforce diversity in module use. We apply modular networks both to image recognition and language modeling tasks, where we achieve superior performance compared to several baselines. Introspection reveals that modules specialize in interpretable contexts.

Link prediction is a key problem for network-structured data. Link prediction heuristics use some score functions, such as common neighbors and Katz index, to measure the likelihood of links. They have obtained wide practical uses due to their simplicity, interpretability, and for some of them, scalability. However, every heuristic has a strong assumption on when two nodes are likely to link, which limits their effectiveness on networks where these assumptions fail. In this regard, a more reasonable way should be learning a suitable heuristic from a given network instead of using predefined ones. By extracting a local subgraph around each target link, we aim to learn a function mapping the subgraph patterns to link existence, thus automatically learning a ``heuristic'' that suits the current network. In this paper, we study this heuristic learning paradigm for link prediction. First, we develop a novel $\gamma$-decaying heuristic theory. The theory unifies a wide range of heuristics in a single framework, and proves that all these heuristics can be well approximated from local subgraphs. Our results show that local subgraphs reserve rich information related to link existence. Second, based on the $\gamma$-decaying theory, we propose a new method to learn heuristics from local subgraphs using a graph neural network (GNN). Its experimental results show unprecedented performance, working consistently well on a wide range of problems.

In many biological and medical contexts, we construct a large labeled corpus by aggregating many sources to use in target prediction tasks. Unfortunately, many of the sources may be irrelevant to our target task, so ignoring the structure of the dataset is detrimental. This work proposes a novel approach, the Multiple Domain Matching Network (MDMN), to exploit this structure. MDMN embeds all data into a shared feature space while learning which domains share strong statistical relationships. These relationships are often insightful in their own right, and they allow domains to share strength without interference from irrelevant data. This methodology builds on existing distribution-matching approaches by assuming that source domains are varied and outcomes multi-factorial. Therefore, each domain should only match a relevant subset. Theoretical analysis shows that the proposed approach can have a tighter generalization bound than existing multiple-domain adaptation approaches. Empirically, we show that the proposed methodology handles higher numbers of source domains (up to 21 empirically), and provides state-of-the-art performance on image, text, and multi-channel time series classification, including clinically relevant data of a novel treatment of Autism Spectrum Disorder.

In dictionary selection, several atoms are selected from finite candidates that successfully approximate given data points in the sparse representation. We propose a novel efficient greedy algorithm for dictionary selection. Not only does our algorithm work much faster than the known methods, but it can also handle more complex sparsity constraints, such as average sparsity. Using numerical experiments, we show that our algorithm outperforms the known methods for dictionary selection, achieving competitive performances with dictionary learning algorithms in a smaller running time.

In this paper, we investigate Dimensionality reduction (DR) maps in an information retrieval setting from a quantitative topology point of view. In particular, we show that no DR maps can achieve perfect precision and perfect recall simultaneously. Thus a continuous DR map must have imperfect precision. We further prove an upper bound on the precision of Lipschitz continuous DR maps. While precision is a natural measure in an information retrieval setting, it does not measure `how' wrong the retrieved data is. We therefore propose a new measure based on Wasserstein distance that comes with similar theoretical guarantee. A key technical step in our proofs is a particular optimization problem of the $L_2$-Wasserstein distance over a constrained set of distributions. We provide a complete solution to this optimization problem, which can be of independent interest on the technical side.