On Universal Features for High-Dimensional Learning and Inference

We consider the problem of identifying universal low-dimensional features from high-dimensional data for inference tasks in settings involving learning. For such problems, we introduce natural notions of universality and we show a local equivalence among them. Our analysis is naturally expressed via information geometry, and represents a conceptually and computationally useful analysis. The development reveals the complementary roles of the singular value decomposition, Hirschfeld-Gebelein-R\'enyi maximal correlation, the canonical correlation and principle component analyses of Hotelling and Pearson, Tishby's information bottleneck, Wyner's common information, Ky Fan $k$-norms, and Brieman and Friedman's alternating conditional expectations algorithm. We further illustrate how this framework facilitates understanding and optimizing aspects of learning systems, including multinomial logistic (softmax) regression and the associated neural network architecture, matrix factorization methods for collaborative filtering and other applications, rank-constrained multivariate linear regression, and forms of semi-supervised learning

Extreme Classification in Log Memory

We present Merged-Averaged Classifiers via Hashing (MACH) for K-classification with ultra-large values of K. Compared to traditional one-vs-all classifiers that require O(Kd) memory and inference cost, MACH only need O(d log K) (d is dimensionality )memory while only requiring O(K log K + d log K) operation for inference. MACH is a generic K-classification algorithm, with provably theoretical guarantees, which requires O(log K) memory without any assumption on the relationship between classes. MACH uses universal hashing to reduce classification with a large number of classes to few independent classification tasks with small (constant) number of classes. We provide theoretical quantification of discriminability-memory tradeoff. With MACH we can train ODP dataset with 100,000 classes and 400,000 features on a single Titan X GPU, with the classification accuracy of 19.28%, which is the best-reported accuracy on this dataset. Before this work, the best performing baseline is a one-vs-all classifier that requires 40 billion parameters (160 GB model size) and achieves 9% accuracy. In contrast, MACH can achieve 9% accuracy with 480x reduction in the model size (of mere 0.3GB). With MACH, we also demonstrate complete training of fine-grained imagenet dataset (compressed size 104GB), with 21,000 classes, on a single GPU. To the best of our knowledge, this is the first work to demonstrate complete training of these extreme-class datasets on a single Titan X

Metric for Automatic Machine Translation Evaluation based on Universal Sentence Representations

Sentence representations can capture a wide range of information that cannot be captured by local features based on character or word N-grams. This paper examines the usefulness of universal sentence representations for evaluating the quality of machine translation. Although it is difficult to train sentence representations using small-scale translation datasets with manual evaluation, sentence representations trained from large-scale data in other tasks can improve the automatic evaluation of machine translation. Experimental results of the WMT-2016 dataset show that the proposed method achieves state-of-the-art performance with sentence representation features only.Comment: NAACL 2018 Student Research Workshop; 6 page

Kernel Mean Embedding of Distributions: A Review and Beyond

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing kernel Hilbert space (RKHS) in which the whole arsenal of kernel methods can be extended to probability measures. It can be viewed as a generalization of the original "feature map" common to support vector machines (SVMs) and other kernel methods. While initially closely associated with the latter, it has meanwhile found application in fields ranging from kernel machines and probabilistic modeling to statistical inference, causal discovery, and deep learning. The goal of this survey is to give a comprehensive review of existing work and recent advances in this research area, and to discuss the most challenging issues and open problems that could lead to new research directions. The survey begins with a brief introduction to the RKHS and positive definite kernels which forms the backbone of this survey, followed by a thorough discussion of the Hilbert space embedding of marginal distributions, theoretical guarantees, and a review of its applications. The embedding of distributions enables us to apply RKHS methods to probability measures which prompts a wide range of applications such as kernel two-sample testing, independent testing, and learning on distributional data. Next, we discuss the Hilbert space embedding for conditional distributions, give theoretical insights, and review some applications. The conditional mean embedding enables us to perform sum, product, and Bayes' rules---which are ubiquitous in graphical model, probabilistic inference, and reinforcement learning---in a non-parametric way. We then discuss relationships between this framework and other related areas. Lastly, we give some suggestions on future research directions.Comment: 147 pages; this is a version of the manuscript after the review proces

A Linear Dynamical System Model for Text

Low dimensional representations of words allow accurate NLP models to be trained on limited annotated data. While most representations ignore words' local context, a natural way to induce context-dependent representations is to perform inference in a probabilistic latent-variable sequence model. Given the recent success of continuous vector space word representations, we provide such an inference procedure for continuous states, where words' representations are given by the posterior mean of a linear dynamical system. Here, efficient inference can be performed using Kalman filtering. Our learning algorithm is extremely scalable, operating on simple cooccurrence counts for both parameter initialization using the method of moments and subsequent iterations of EM. In our experiments, we employ our inferred word embeddings as features in standard tagging tasks, obtaining significant accuracy improvements. Finally, the Kalman filter updates can be seen as a linear recurrent neural network. We demonstrate that using the parameters of our model to initialize a non-linear recurrent neural network language model reduces its training time by a day and yields lower perplexity.Comment: Accepted at International Conference of Machine Learning 201

Deep Learning

Deep learning (DL) is a high dimensional data reduction technique for constructing high-dimensional predictors in input-output models. DL is a form of machine learning that uses hierarchical layers of latent features. In this article, we review the state-of-the-art of deep learning from a modeling and algorithmic perspective. We provide a list of successful areas of applications in Artificial Intelligence (AI), Image Processing, Robotics and Automation. Deep learning is predictive in its nature rather then inferential and can be viewed as a black-box methodology for high-dimensional function estimation.Comment: arXiv admin note: text overlap with arXiv:1602.0656

An Information Theoretic Interpretation to Deep Neural Networks

It is commonly believed that the hidden layers of deep neural networks (DNNs) attempt to extract informative features for learning tasks. In this paper, we formalize this intuition by showing that the features extracted by DNN coincide with the result of an optimization problem, which we call the `universal feature selection' problem, in a local analysis regime. We interpret the weights training in DNN as the projection of feature functions between feature spaces, specified by the network structure. Our formulation has direct operational meaning in terms of the performance for inference tasks, and gives interpretations to the internal computation results of DNNs. Results of numerical experiments are provided to support the analysis.Comment: Accepted to ISIT 201

Stein Variational Gradient Descent as Moment Matching

Stein variational gradient descent (SVGD) is a non-parametric inference algorithm that evolves a set of particles to fit a given distribution of interest. We analyze the non-asymptotic properties of SVGD, showing that there exists a set of functions, which we call the Stein matching set, whose expectations are exactly estimated by any set of particles that satisfies the fixed point equation of SVGD. This set is the image of Stein operator applied on the feature maps of the positive definite kernel used in SVGD. Our results provide a theoretical framework for analyzing the properties of SVGD with different kernels, shedding insight into optimal kernel choice. In particular, we show that SVGD with linear kernels yields exact estimation of means and variances on Gaussian distributions, while random Fourier features enable probabilistic bounds for distributional approximation. Our results offer a refreshing view of the classical inference problem as fitting Stein's identity or solving the Stein equation, which may motivate more efficient algorithms.Comment: Conference on Neural Information Processing Systems (NIPS) 201

GLoMo: Unsupervisedly Learned Relational Graphs as Transferable Representations

Modern deep transfer learning approaches have mainly focused on learning generic feature vectors from one task that are transferable to other tasks, such as word embeddings in language and pretrained convolutional features in vision. However, these approaches usually transfer unary features and largely ignore more structured graphical representations. This work explores the possibility of learning generic latent relational graphs that capture dependencies between pairs of data units (e.g., words or pixels) from large-scale unlabeled data and transferring the graphs to downstream tasks. Our proposed transfer learning framework improves performance on various tasks including question answering, natural language inference, sentiment analysis, and image classification. We also show that the learned graphs are generic enough to be transferred to different embeddings on which the graphs have not been trained (including GloVe embeddings, ELMo embeddings, and task-specific RNN hidden unit), or embedding-free units such as image pixels

Deep Kernel Learning

We introduce scalable deep kernels, which combine the structural properties of deep learning architectures with the non-parametric flexibility of kernel methods. Specifically, we transform the inputs of a spectral mixture base kernel with a deep architecture, using local kernel interpolation, inducing points, and structure exploiting (Kronecker and Toeplitz) algebra for a scalable kernel representation. These closed-form kernels can be used as drop-in replacements for standard kernels, with benefits in expressive power and scalability. We jointly learn the properties of these kernels through the marginal likelihood of a Gaussian process. Inference and learning cost $O(n)$ for $n$ training points, and predictions cost $O(1)$ per test point. On a large and diverse collection of applications, including a dataset with 2 million examples, we show improved performance over scalable Gaussian processes with flexible kernel learning models, and stand-alone deep architectures.Comment: 19 pages, 6 figure