We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained. Traditional methods for such problems rely on general-purpose sampling techniques such as Markov chain Monte Carlo, which typically requires manual intervention for tuning parameters and does not work efficiently in practice. Instead, SAGD makes use of the Langevin algorithm to construct stochastic gradients that are biased in finite steps but accurate asymptotically, enabling us to theoretically establish the convergence guarantee for SAGD. Inspired by our theoretical analysis, we also provide useful guidelines for its practical implementation. Finally, we show that SAGD performs well experimentally in popular statistical and machine learning problems such as the expectation-maximization algorithm and the variational autoencoders.

Chaotic itinerancy is a frequently observed phenomenon in high-dimensional and nonlinear dynamical systems, and it is characterized by the random transitions among multiple quasi-attractors. Several studies have revealed that chaotic itinerancy has been observed in brain activity, and it is considered to play a critical role in the spontaneous, stable behavior generation of animals. Thus, chaotic itinerancy is a topic of great interest, particularly for neurorobotics researchers who wish to understand and implement autonomous behavioral controls for agents. However, it is generally difficult to gain control over high-dimensional nonlinear dynamical systems. Hence, the implementation of chaotic itinerancy has mainly been accomplished heuristically. In this study, we propose a novel way of implementing chaotic itinerancy reproducibly and at will in a generic high-dimensional chaotic system. In particular, we demonstrate that our method enables us to easily design both the trajectories of quasi-attractors and the transition rules among them simply by adjusting the limited number of system parameters and by utilizing the intrinsic high-dimensional chaos. Finally, we quantitatively discuss the validity and scope of application through the results of several numerical experiments.

Measuring similarity between two objects is the core operation in existing cluster analyses in grouping similar objects into clusters. Cluster analyses have been applied to a number of applications, including image segmentation, social network analysis, and computational biology. This paper introduces a new similarity measure called point-set kernel which computes the similarity between an object and a sample of objects generated from an unknown distribution. The proposed clustering procedure utilizes this new measure to characterize both the typical point of every cluster and the cluster grown from the typical point. We show that the new clustering procedure is both effective and efficient such that it can deal with large scale datasets. In contrast, existing clustering algorithms are either efficient or effective; and even efficient ones have difficulty dealing with large scale datasets without special hardware. We show that the proposed algorithm is more effective and runs orders of magnitude faster than the state-of-the-art density-peak clustering and scalable kernel k-means clustering when applying to datasets of millions of data points, on commonly used computing machines.

In a Content Based Image Retrieval (CBIR) System, the task is to retrieve similar images from a large database given a query image. The usual procedure is to extract some useful features from the query image, and retrieve images which have similar set of features. For this purpose, a suitable similarity measure is chosen, and images with high similarity scores are retrieved. Naturally the choice of these features play a very important role in the success of this system, and high level features are required to reduce the "semantic gap". In this paper, we propose to use features derived from pre-trained network models from a deeplearning convolution network trained for a large image classification problem. This approach appears to produce vastly superior results for a variety of databases, and it outperforms many contemporary CBIR systems. We analyse the retrieval time of the method, and also propose a pre-clustering of the database based on the above-mentioned features which yields comparable results in a much shorter time in most of the cases.

We propose and analyze a novel theoretical and algorithmic framework for structured prediction. While so far the term has referred to discrete output spaces, here we consider more general settings, such as manifolds or spaces of probability measures. We define structured prediction as a problem where the output space lacks a vectorial structure. We identify and study a large class of loss functions that implicitly defines a suitable geometry on the problem. The latter is the key to develop an algorithmic framework amenable to a sharp statistical analysis and yielding efficient computations. When dealing with output spaces with infinite cardinality, a suitable implicit formulation of the estimator is shown to be crucial.

Domain generalization is the problem of machine learning when the training data and the test data come from different data domains. We present a simple theoretical model of learning to generalize across domains in which there is a meta-distribution over data distributions, and those data distributions may even have different supports. In our model, the training data given to a learning algorithm consists of multiple datasets each from a single domain drawn in turn from the meta-distribution. We study this model in three different problem settings---a multi-domain Massart noise setting, a decision tree multi-dataset setting, and a feature selection setting, and find that computationally efficient, polynomial-sample domain generalization is possible in each. Experiments demonstrate that our feature selection algorithm indeed ignores spurious correlations and improves generalization.

We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph structure or adding hard constraints to feature-space algorithms. Following a different path, we define a metric regression scheme where we train metric-constrained linear combinations of dissimilarity matrices. The idea is that the input matrices can be pre-computed dissimilarity measures obtained from any kind of available data (e.g. node attributes or edge structure). As the model inputs are distance measures, we do not need to assume the existence of any underlying feature space. Main challenge is that metric constraints (especially positive-definiteness and sub-additivity), are not automatically respected if, for example, the coefficients of the linear combination are allowed to be negative. Both positive and sub-additive constraints are linear inequalities, but the computational complexity of imposing them scales as O(D3), where D is the size of the input matrices (i.e. the size of the data set). This becomes quickly prohibitive, even when D is relatively small. We propose a new graph-based technique for optimizing under such constraints and show that, in some cases, our approach may reduce the original computational complexity of the optimization process by one order of magnitude. Contrarily to existing methods, our scheme applies to any (possibly non-convex) metric-constrained objective function.

This paper proposes a novel deep learning architecture for semantic segmentation. The proposed Global and Selective Attention Network (GSANet) features Atrous Spatial Pyramid Pooling (ASPP) with a novel sparsemax global attention and a novel selective attention that deploys a condensation and diffusion mechanism to aggregate the multi-scale contextual information from the extracted deep features. A selective attention decoder is also proposed to process the GSA-ASPP outputs for optimizing the softmax volume. We are the first to benchmark the performance of semantic segmentation networks with the low-complexity feature extraction network (FXN) MobileNetEdge, that is optimized for low latency on edge devices. We show that GSANet can result in more accurate segmentation with MobileNetEdge, as well as with strong FXNs, such as Xception. GSANet improves the state-of-art semantic segmentation accuracy on both the ADE20k and the Cityscapes datasets.

Medical images differ from natural images in significantly higher resolutions and smaller regions of interest. Because of these differences, neural network architectures that work well for natural images might not be applicable to medical image analysis. In this work, we extend the globally-aware multiple instance classifier, a framework we proposed to address these unique properties of medical images. This model first uses a low-capacity, yet memory-efficient, network on the whole image to identify the most informative regions. It then applies another higher-capacity network to collect details from chosen regions. Finally, it employs a fusion module that aggregates global and local information to make a final prediction. While existing methods often require lesion segmentation during training, our model is trained with only image-level labels and can generate pixel-level saliency maps indicating possible malignant findings. We apply the model to screening mammography interpretation: predicting the presence or absence of benign and malignant lesions. On the NYU Breast Cancer Screening Dataset, consisting of more than one million images, our model achieves an AUC of 0.93 in classifying breasts with malignant findings, outperforming ResNet-34 and Faster R-CNN. Compared to ResNet-34, our model is 4.1x faster for inference while using 78.4% less GPU memory. Furthermore, we demonstrate, in a reader study, that our model surpasses radiologist-level AUC by a margin of 0.11. The proposed model is available online: https://github.com/nyukat/GMIC.

For multi-valued functions---such as when the conditional distribution on targets given the inputs is multi-modal---standard regression approaches are not always desirable because they provide the conditional mean. Modal regression aims to instead find the conditional mode, but is restricted to nonparametric approaches. Such methods can be difficult to scale, and cannot benefit from parametric function approximation, like neural networks, which can learn complex relationships between inputs and targets. In this work, we propose a parametric modal regression algorithm, by using the implicit function theorem to develop an objective for learning a joint parameterized function over inputs and targets. We empirically demonstrate on several synthetic problems that our method (i) can learn multi-valued functions and produce the conditional modes, (ii) scales well to high-dimensional inputs and (iii) is even more effective for certain uni-modal problems, particularly for high frequency data where the joint function over inputs and targets can better capture the complex relationship between them. We then demonstrate that our method is practically useful in a real-world modal regression problem. We conclude by showing that our method provides small improvements on two regression datasets that have asymmetric distributions over the targets.