There is a growing demand for nonparametric conditional density estimators (CDEs) in fields such as astronomy and economics. In astronomy, for example, one can dramatically improve estimates of the parameters that dictate the evolution of the Universe by working with full conditional densities instead of regression (i.e., conditional mean) estimates. More generally, standard regression falls short in any prediction problem where the distribution of the response is more complex with multi-modality, asymmetry or heteroscedastic noise. Nevertheless, much of the work on high-dimensional inference concerns regression and classification only, whereas research on density estimation has lagged behind. Here we propose FlexCode, a fully nonparametric approach to conditional density estimation that reformulates CDE as a non-parametric orthogonal series problem where the expansion coefficients are estimated by regression. By taking such an approach, one can efficiently estimate conditional densities and not just expectations in high dimensions by drawing upon the success in high-dimensional regression. Depending on the choice of regression procedure, our method can adapt to a variety of challenging high-dimensional settings with different structures in the data (e.g., a large number of irrelevant components and nonlinear manifold structure) as well as different data types (e.g., functional data, mixed data types and sample sets). We study the theoretical and empirical performance of our proposed method, and we compare our approach with traditional conditional density estimators on simulated as well as real-world data, such as photometric galaxy data, Twitter data, and line-of-sight velocities in a galaxy cluster.

Word embeddings provide point representations of words containing useful semantic information. We introduce multimodal word distributions formed from Gaussian mixtures, for multiple word meanings, entailment, and rich uncertainty information. To learn these distributions, we propose an energy-based max-margin objective. We show that the resulting approach captures uniquely expressive semantic information, and outperforms alternatives, such as word2vec skip-grams, and Gaussian embeddings, on benchmark datasets such as word similarity and entailment.

In the context of variable selection, ensemble learning has gained increasing interest due to its great potential to improve selection accuracy and to reduce false discovery rate. A novel ordering-based selective ensemble learning strategy is designed in this paper to obtain smaller but more accurate ensembles. In particular, a greedy sorting strategy is proposed to rearrange the order by which the members are included into the integration process. Through stopping the fusion process early, a smaller subensemble with higher selection accuracy can be obtained. More importantly, the sequential inclusion criterion reveals the fundamental strength-diversity trade-off among ensemble members. By taking stability selection (abbreviated as StabSel) as an example, some experiments are conducted with both simulated and real-world data to examine the performance of the novel algorithm. Experimental results demonstrate that pruned StabSel generally achieves higher selection accuracy and lower false discovery rates than StabSel and several other benchmark methods.

Keyphrase boundary classification (KBC) is the task of detecting keyphrases in scientific articles and labelling them with respect to predefined types. Although important in practice, this task is so far underexplored, partly due to the lack of labelled data. To overcome this, we explore several auxiliary tasks, including semantic super-sense tagging and identification of multi-word expressions, and cast the task as a multi-task learning problem with deep recurrent neural networks. Our multi-task models perform significantly better than previous state of the art approaches on two scientific KBC datasets, particularly for long keyphrases.

End-to-end learning refers to training a possibly complex learning system by applying gradient-based learning to the system as a whole. End-to-end learning system is specifically designed so that all modules are differentiable. In effect, not only a central learning machine, but also all "peripheral" modules like representation learning and memory formation are covered by a holistic learning process. The power of end-to-end learning has been demonstrated on many tasks, like playing a whole array of Atari video games with a single architecture. While pushing for solutions to more challenging tasks, network architectures keep growing more and more complex. In this paper we ask the question whether and to what extent end-to-end learning is a future-proof technique in the sense of scaling to complex and diverse data processing architectures. We point out potential inefficiencies, and we argue in particular that end-to-end learning does not make optimal use of the modular design of present neural networks. Our surprisingly simple experiments demonstrate these inefficiencies, up to the complete breakdown of learning.

Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high-dimensional regime where the number of parameters exceeds the number of samples ($p> n$) and assume that the high-dimensional parameters vector is $s_0$ sparse. We develop a general and flexible $\ell_\infty$ projection statistic for hypothesis testing in this model. Our framework encompasses testing whether the parameter lies in a convex cone, testing the signal strength, testing arbitrary functionals of the parameter, and testing adaptive hypothesis. We show that the proposed procedure controls the type I error under the standard assumption of $s_0 (\log p)/\sqrt{n}\to 0$, and also analyze the power of the procedure. Our numerical experiments confirms our theoretical findings and demonstrate that we control false positive rate (type I error) near the nominal level, and have high power.

In recent years, Deep Learning has become the go-to solution for a broad range of applications, often outperforming state-of-the-art. However, it is important, for both theoreticians and practitioners, to gain a deeper understanding of the difficulties and limitations associated with common approaches and algorithms. We describe four types of simple problems, for which the gradient-based algorithms commonly used in deep learning either fail or suffer from significant difficulties. We illustrate the failures through practical experiments, and provide theoretical insights explaining their source, and how they might be remedied.

This paper introduces a generalization of Convolutional Neural Networks (CNNs) from low-dimensional grid data, such as images, to graph-structured data. We propose a novel spatial convolution utilizing a random walk to uncover the relations within the input, analogous to the way the standard convolution uses the spatial neighborhood of a pixel on the grid. The convolution has an intuitive interpretation, is efficient and scalable and can also be used on data with varying graph structure. Furthermore, this generalization can be applied to many standard regression or classification problems, by learning the the underlying graph. We empirically demonstrate the performance of the proposed CNN on MNIST, and challenge the state-of-the-art on Merck molecular activity data set.

Trajectory analysis is essential in many applications. In this paper, we address the problem of representing motion trajectories in a highly informative way, and consequently utilize it for analyzing trajectories. Our approach first leverages the complete information from given trajectories to construct a thermal transfer field which provides a context-rich way to describe the global motion pattern in a scene. Then, a 3D tube is derived which depicts an input trajectory by integrating its surrounding motion patterns contained in the thermal transfer field. The 3D tube effectively: 1) maintains the movement information of a trajectory, 2) embeds the complete contextual motion pattern around a trajectory, 3) visualizes information about a trajectory in a clear and unified way. We further introduce a droplet-based process. It derives a droplet vector from a 3D tube, so as to characterize the high-dimensional 3D tube information in a simple but effective way. Finally, we apply our tube-and-droplet representation to trajectory analysis applications including trajectory clustering, trajectory classification & abnormality detection, and 3D action recognition. Experimental comparisons with state-of-the-art algorithms demonstrate the effectiveness of our approach.

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsity and orthogonality have been two largely incompatible goals. To accommodate both features, in this paper we suggest the method of sparse orthogonal factor regression (SOFAR) via the sparse singular value decomposition with orthogonality constrained optimization to learn the underlying association networks, with broad applications to both unsupervised and supervised learning tasks such as biclustering with sparse singular value decomposition, sparse principal component analysis, sparse factor analysis, and spare vector autoregression analysis. Exploiting the framework of convexity-assisted nonconvex optimization, we derive nonasymptotic error bounds for the suggested procedure characterizing the theoretical advantages. The statistical guarantees are powered by an efficient SOFAR algorithm with convergence property. Both computational and theoretical advantages of our procedure are demonstrated with several simulation and real data examples.