Browsing by Subject "Alternating minimization"
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Item Combining classifier and cluster ensembles for semi-supervised and transfer learning(2012-05) Acharya, Ayan; Ghosh, Joydeep; Mooney, Raymond J.Unsupervised models can provide supplementary soft constraints to help classify new, "target" data since similar instances in the target set are more likely to share the same class label. Such models can also help detect possible differences between training and target distributions, which is useful in applications where concept drift may take place, as in transfer learning settings. This contribution describes two general frameworks that take as input class membership estimates from existing classifiers learnt on previously encountered "source" data, as well as a set of cluster labels from a cluster ensemble operating solely on the target data to be classified, and yield a consensus labeling of the target data. One of the proposed frameworks admits a wide range of loss functions and classification/clustering methods and exploits properties of Bregman divergences in conjunction with Legendre duality to yield a principled and scalable approach. The other approach is built on probabilistic mixture models and provides additional flexibility of distributed computation that is useful when the target data cannot be gathered in a single place for privacy or security concerns. A variety of experiments show that the proposed frameworks can yield results substantially superior to those provided by popular transductive learning techniques or by naively applying classifiers learnt on the original task to the target data.Item Provable alternating minimization for non-convex learning problems(2014-08) Netrapalli, Praneeth Kumar; Sanghavi, Sujay Rajendra, 1979-Alternating minimization (AltMin) is a generic term for a widely popular approach in non-convex learning: often, it is possible to partition the variables into two (or more) sets, so that the problem is convex/tractable in one set if the other is held fixed (and vice versa). This allows for alternating between optimally updating one set of variables, and then the other. AltMin methods typically do not have associated global consistency guarantees; even though they are empirically observed to perform better than methods (e.g. based on convex optimization) that do have guarantees. In this thesis, we obtain rigorous performance guarantees for AltMin in three statistical learning settings: low rank matrix completion, phase retrieval and learning sparsely-used dictionaries. The overarching theme behind our results consists of two parts: (i) devising new initialization procedures (as opposed to doing so randomly, as is typical), and (ii) establishing exponential local convergence from this initialization. Our work shows that the pursuit of statistical guarantees can yield algorithmic improvements (initialization in our case) that perform better in practice.