Energy Based Models: From Relational Regression to Similarity Metric Learning

  • Sumit Chopra | Courant Institute of Mathematical Sciences, New York University

In this talk I will first give a brief introduction to Energy Based Models. I will then discuss in detail the two areas where I have applied these techniques, namely Relational Regression and Similarity Metric Learning.

In a number of real world problems, such as, web-page classification, social networks, and house price prediction, the samples are related to each other in complex ways such that the values of unknown variables associated with one sample depends not only on its individual features but also on other samples. Furthermore, these variables could be continuous and the relationships could be hidden (not given as part of the data). In such situations rather than treating the samples as I.I.D, one must resort to a form of collective prediction. We present a novel factor graph based framework that is capable of doing regression in such relational settings. The method is applied to the problem of real estate price prediction and is shown to be superior than other existing techniques.

Knowledge of an appropriate distance metric over the data which is capable of capturing the complex dependencies exhibited by it, is an important step in designing algorithms for more advanced tasks such as information retrieval, contextual classification, and data visualization. However, most previous techniques either depend on a meaningful and computable distance metric in the input space, or they do not compute a “function” that can accurately map new input points whose relationships to the training data is unknown.
Can we learn a metric that is solely dependent on the arbitrary neighborhood relationships in the data and is also faithful to new unseen samples?
We present a method – called Dimensionality Reduction by Learning an Invariant Mapping (DrLIM) – that answers this question.
We apply this technique for dimensionality reduction and for face verification and show some interesting results.

Speaker Details

Sumit Chopra is a doctoral student under the supervision of Prof. Yann LeCun, at Courant Institute of Mathematical Sciences, New York University. His primary area of interest in Machine Learning and Pattern Recognition. His research involves developing efficient inference and learning algorithms for models that can handle the uncertainties and interdependencies among samples in large scale data sets, with application in computer vision, robotics, and economics. He has published a number of papers in peer-reviewed conferences and journals including NIPS, CVPR, KDD, AISTATS and JPDC. He has also contributed to a chapter in a book titled “Predicting Structured Outputs.” He has been a reviewer of the journals “Transactions on Pattern Analysis and Machine Intelligence,” and “Signal Image and Video Processing.” Sumit was also the recipient of Henry MacCraken fellowship award from New York University.

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