Learning with Scalability and Compactness

Artificial Intelligence has been thriving for decades since its birth. Traditional AI features heuristic search and planning, providing good strategy for tasks that are inherently search-based problems, such as games and GPS searching. In the meantime, machine learning, arguably the hottest subfield of AI, embraces data-driven methodology with great success in a wide range of applications such as computer vision and speech recognition. As a new trend, the applications of both learning and search have shifted toward mobile and embedded devices which entails not only scalability but also compactness of the models. Under this general paradigm, we propose a series of work to address the issues of scalability and compactness within machine learning and its applications on heuristic search. We first focus on the scalability issue of memory-based heuristic search which is recently ameliorated by Maximum Variance Unfolding (MVU), a manifold learning algorithm capable of learning state embeddings as effective heuristics to speed up $A^*$ search. Though achieving unprecedented online search performance with constraints on memory footprint, MVU is notoriously slow on offline training. To address this problem, we introduce Maximum Variance Correction (MVC), which finds large-scale feasible solutions to MVU by post-processing embeddings from any manifold learning algorithm. It increases the scale of MVU embeddings by several orders of magnitude and is naturally parallel. We further propose Goal-oriented Euclidean Heuristic (GOEH), a variant to MVU embeddings, which preferably optimizes the heuristics associated with goals in the embedding while maintaining their admissibility. We demonstrate unmatched reductions in search time across several non-trivial $A^*$ benchmark search problems. Through these work, we bridge the gap between the manifold learning literature and heuristic search which have been regarded as fundamentally different, leading to cross-fertilization for both fields. Deep learning has made a big splash in the machine learning community with its superior accuracy performance. However, it comes at a price of huge model size that might involves billions of parameters, which poses great challenges for its use on mobile and embedded devices. To achieve the compactness, we propose HashedNets, a general approach to compressing neural network models leveraging feature hashing. At its core, HashedNets randomly group parameters using a low-cost hash function, and share parameter value within the group. According to our empirical results, a neural network could be 32x smaller with little drop in accuracy performance. We further introduce Frequency-Sensitive Hashed Nets (FreshNets) to extend this hashing technique to convolutional neural network by compressing parameters in the frequency domain. Compared with many AI applications, neural networks seem not graining as much popularity as it should be in traditional data mining tasks. For these tasks, categorical features need to be first converted to numerical representation in advance in order for neural networks to process them. We show that a na\ {i}ve use of the classic one-hot encoding may result in gigantic weight matrices and therefore lead to prohibitively expensive memory cost in neural networks. Inspired by word embedding, we advocate a compellingly simple, yet effective neural network architecture with category embedding. It is capable of directly handling both numerical and categorical features as well as providing visual insights on feature similarities. At the end, we conduct comprehensive empirical evaluation which showcases the efficacy and practicality of our approach, and provides surprisingly good visualization and clustering for categorical features

Kernel Density Metric Learning

This paper introduces a supervised metric learning algorithm, called kernel density metric learning (KDML), which is easy to use and provides nonlinear, probability-based distance measures. KDML constructs a direct nonlinear mapping from the original input space into a feature space based on kernel density estimation. The nonlinear mapping in KDML embodies established distance measures between probability density functions, and leads to correct classification on datasets for which linear metric learning methods would fail. Existing metric learning algorithms, such as large margin nearest neighbors (LMNN), can then be applied to the KDML features to learn a Mahalanobis distance. We also propose an integrated optimization algorithm that learns not only the Mahalanobis matrix but also kernel bandwidths, the only hyper-parameters in the nonlinear mapping. KDML can naturally handle not only numerical features, but also categorical ones, which is rarely found in previous metric learning algorithms. Extensive experimental results on various benchmark datasets show that KDML significantly improves existing metric learning algorithms in terms of kNN classification accuracy

Neural Characteristic Activation Value Analysis for Improved ReLU Network Feature Learning

This work examines the characteristic activation values of individual ReLU units in neural networks. We refer to the set of input locations corresponding to such characteristic activation values as the characteristic activation set of a ReLU unit. We draw an explicit connection between the characteristic activation set and learned features in ReLU networks. This connection leads to new insights into how various neural network normalization techniques used in modern deep learning architectures regularize and stabilize stochastic gradient optimization. Utilizing these insights, we propose geometric parameterization for ReLU networks to improve feature learning, which decouples the radial and angular parameters in the hyperspherical coordinate system. We empirically verify its usefulness with less carefully chosen initialization schemes and larger learning rates. We report significant improvements in optimization stability, convergence speed, and generalization performance for various models on a variety of datasets, including the ResNet-50 network on ImageNet.Comment: 20 pages, 6 figures, 3 tables; code available at: https://github.com/Wenlin-Chen/geometric-parameterizatio

A Reduction of the Elastic Net to Support Vector Machines with an Application to GPU Computing

The past years have witnessed many dedicated open-source projects that built and maintain implementations of Support Vector Machines (SVM), parallelized for GPU, multi-core CPUs and distributed systems. Up to this point, no comparable effort has been made to parallelize the Elastic Net, despite its popularity in many high impact applications, including genetics, neuroscience and systems biology. The first contribution in this paper is of theoretical nature. We establish a tight link between two seemingly different algorithms and prove that Elastic Net regression can be reduced to SVM with squared hinge loss classification. Our second contribution is to derive a practical algorithm based on this reduction. The reduction enables us to utilize prior efforts in speeding up and parallelizing SVMs to obtain a highly optimized and parallel solver for the Elastic Net and Lasso. With a simple wrapper, consisting of only 11 lines of MATLAB code, we obtain an Elastic Net implementation that naturally utilizes GPU and multi-core CPUs. We demonstrate on twelve real world data sets, that our algorithm yields identical results as the popular (and highly optimized) glmnet implementation but is one or several orders of magnitude faster.Comment: 10 page