Visualizing probabilistic models: Intensive Principal Component Analysis

Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in high-dimensions. Inspired by replica theory from statistical mechanics, we consider replicas of the system to tune the dimensionality and take the limit as the number of replicas goes to zero. The result is the intensive embedding, which is not only isometric (preserving local distances) but allows global structure to be more transparently visualized. We develop the Intensive Principal Component Analysis (InPCA) and demonstrate clear improvements in visualizations of the Ising model of magnetic spins, a neural network, and the dark energy cold dark matter ({\Lambda}CDM) model as applied to the Cosmic Microwave Background.Comment: 6 pages, 5 figure

Learning Edge Representations via Low-Rank Asymmetric Projections

We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information (from social networks, user-item graphs, knowledge bases, etc.) in many machine learning tasks. Unlike previous work, we (1) explicitly model an edge as a function of node embeddings, and we (2) propose a novel objective, the "graph likelihood", which contrasts information from sampled random walks with non-existent edges. Individually, both of these contributions improve the learned representations, especially when there are memory constraints on the total size of the embeddings. When combined, our contributions enable us to significantly improve the state-of-the-art by learning more concise representations that better preserve the graph structure. We evaluate our method on a variety of link-prediction task including social networks, collaboration networks, and protein interactions, showing that our proposed method learn representations with error reductions of up to 76% and 55%, on directed and undirected graphs. In addition, we show that the representations learned by our method are quite space efficient, producing embeddings which have higher structure-preserving accuracy but are 10 times smaller

Bitwise Source Separation on Hashed Spectra: An Efficient Posterior Estimation Scheme Using Partial Rank Order Metrics

This paper proposes an efficient bitwise solution to the single-channel source separation task. Most dictionary-based source separation algorithms rely on iterative update rules during the run time, which becomes computationally costly especially when we employ an overcomplete dictionary and sparse encoding that tend to give better separation results. To avoid such cost we propose a bitwise scheme on hashed spectra that leads to an efficient posterior probability calculation. For each source, the algorithm uses a partial rank order metric to extract robust features that form a binarized dictionary of hashed spectra. Then, for a mixture spectrum, its hash code is compared with each source's hashed dictionary in one pass. This simple voting-based dictionary search allows a fast and iteration-free estimation of ratio masking at each bin of a signal spectrogram. We verify that the proposed BitWise Source Separation (BWSS) algorithm produces sensible source separation results for the single-channel speech denoising task, with 6-8 dB mean SDR. To our knowledge, this is the first dictionary based algorithm for this task that is completely iteration-free in both training and testing