| 1. |
- Panahi, Ashkan, 1986, et al.
(author)
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Clustering by Sum of Norms: Stochastic Incremental Algorithm, Convergence and Cluster Recovery
- 2017
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In: Proceedings of Machine Learning Research. - 9781510855144 ; 6, s. 4247-4260
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Conference paper (peer-reviewed)abstract
- Standard clustering methods such as K-means, Gaussian mixture models, and hierarchical clustering, arc beset by local minima, which are sometimes drastically suboptimal. Moreover the number of clusters K must be known in advance. The recently introduced sum-of-norms (SON) or Clusterpath convex relaxation of k-means and hierarchical clustering shrinks cluster centroids toward one another and ensure a unique global minimizer. We give a scalable stochastic incremental algorithm based on proximal iterations to solve the SON problem with convergence guarantees. We also show that the algorithm recovers clusters under quite general conditions which have a similar form to the unifying proximity condition introduced in the approximation algorithms community (that covers paradigm cases such as Gaussian mixtures and planted partition models). We give experimental results to confirm that our algorithm scales much better than previous methods while producing clusters of comparable quality.
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| 2. |
- Shalit, U., et al.
(author)
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Estimating individual treatment effect: generalization bounds and algorithms
- 2017
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In: Proceedings of the 34th International Conference on Machine Learning. - 9781510855144 ; 6, s. 4709-4718
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Conference paper (peer-reviewed)abstract
- There is intense interest in applying machine learning to problems of causal inference in fields such as healthcare, economics and education. In particular, individual-level causal inference has important applications such as precision medicine. We give a new theoretical analysis and family of algorithms for predicting individual treatment effect (ITE) from observational data, under the assumption known as strong ignorability. The algorithms leam a "balanced" representation such that the induced treated and control distributions look similar, and we give a novel and intuitive generalization-error bound showing the expected ITE estimation error of a representation is bounded by a sum of the standard generalization-error of that representation and the distance between the treated and control distributions induced by the representation. We use Integral Probability Metrics to measure distances between distributions, deriving explicit bounds for the Wasserstein and Maximum Mean Discrepancy (MMD) distances. Experiments on real and simulated data show the new algorithms match or outperform the state-of-the-art.
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