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Collaborating Authors

Lengerich, Benjamin J.


Hybrid Subspace Learning for High-Dimensional Data

arXiv.org Machine Learning

The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help distinguish signal from noise. One way to achieve this goal is to perform subspace learning to estimate a small set of latent features that capture the majority of the variance in the original data. Most existing subspace learning models, such as PCA, assume that the data can be fully represented by its embedding in one or more latent subspaces. However, in this work, we argue that this assumption is not suitable for many high-dimensional datasets; often only some variables can easily be projected to a low-dimensional space. We propose a hybrid dimensionality reduction technique in which some features are mapped to a low-dimensional subspace while others remain in the original space. Our model leads to more accurate estimation of the latent space and lower reconstruction error. We present a simple optimization procedure for the resulting biconvex problem and show synthetic data results that demonstrate the advantages of our approach over existing methods. Finally, we demonstrate the effectiveness of this method for extracting meaningful features from both gene expression and video background subtraction datasets.


Retrofitting Distributional Embeddings to Knowledge Graphs with Functional Relations

arXiv.org Machine Learning

Knowledge graphs are a versatile framework to encode richly structured data relationships, but it not always apparent how to combine these with existing entity representations. Methods for retrofitting pre-trained entity representations to the structure of a knowledge graph typically assume that entities are embedded in a connected space and that relations imply similarity. However, useful knowledge graphs often contain diverse entities and relations (with potentially disjoint underlying corpora) which do not accord with these assumptions. To overcome these limitations, we present Functional Retrofitting, a framework that generalizes current retrofitting methods by explicitly modeling pairwise relations. Our framework can directly incorporate a variety of pairwise penalty functions previously developed for knowledge graph completion. We present both linear and neural instantiations of the framework. Functional Retrofitting significantly outperforms existing retrofitting methods on complex knowledge graphs and loses no accuracy on simpler graphs (in which relations do imply similarity). Finally, we demonstrate the utility of the framework by predicting new drug--disease treatment pairs in a large, complex health knowledge graph.


Towards Visual Explanations for Convolutional Neural Networks via Input Resampling

arXiv.org Machine Learning

The predictive power of neural networks often costs model interpretability. Several techniques have been developed for explaining model outputs in terms of input features; however, it is difficult to translate such interpretations into actionable insight. Here, we propose a framework to analyze predictions in terms of the model's internal features by inspecting information flow through the network. Given a trained network and a test image, we select neurons by two metrics, both measured over a set of images created by perturbations to the input image: (1) magnitude of the correlation between the neuron activation and the network output and (2) precision of the neuron activation. We show that the former metric selects neurons that exert large influence over the network output while the latter metric selects neurons that activate on generalizable features. By comparing the sets of neurons selected by these two metrics, our framework suggests a way to investigate the internal attention mechanisms of convolutional neural networks.