Distribution matching for transduction

Many transductive inference algorithms assume that distributions over training and test estimates should be related, e.g. by providing a large margin of separation on both sets. We use this idea to design a transduction algorithm which can be used without modification for classification, regression, and structured estimation. At its heart we exploit the fact that for a good learner the distributions over the outputs on training and test sets should match. This is a classical two-sample problem which can be solved efficiently in its most general form by using distance measures in Hilbert Space. It turns out that a number of existing heuristics can be viewed as special cases of our approach.

Compressive Embedding and Visualization using Graphs

Visualizing high-dimensional data has been a focus in data analysis communities for decades, which has led to the design of many algorithms, some of which are now considered references (such as t-SNE for example). In our era of overwhelming data volumes, the scalability of such methods have become more and more important. In this work, we present a method which allows to apply any visualization or embedding algorithm on very large datasets by considering only a fraction of the data as input and then extending the information to all data points using a graph encoding its global similarity. We show that in most cases, using only $\mathcal{O}(\log(N))$ samples is sufficient to diffuse the information to all $N$ data points. In addition, we propose quantitative methods to measure the quality of embeddings and demonstrate the validity of our technique on both synthetic and real-world datasets