{"id":606735,"date":"2019-09-02T14:33:59","date_gmt":"2019-09-02T21:33:59","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=606735"},"modified":"2020-08-28T16:59:51","modified_gmt":"2020-08-28T23:59:51","slug":"detecting-activations-over-graphs-using-spanning-tree-wavelet-bases","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/detecting-activations-over-graphs-using-spanning-tree-wavelet-bases\/","title":{"rendered":"Detecting activations over graphs using spanning tree wavelet bases"},"content":{"rendered":"

We consider the detection of activations over graphs under Gaussian noise, where signals are piece-wise constant over the graph. Despite the wide applicability of such a detection algorithm, there has been little success in the development of computationally feasible methods with proveable theoretical guarantees for general graph topologies. We cast this as a hypothesis testing problem, and first provide a universal necessary condition for asymptotic distinguishability of the null and alternative hypotheses. We then introduce the spanning tree wavelet basis over graphs, a localized basis that reflects the topology of the graph, and prove that for any spanning tree, this approach can distinguish null from alternative in a low signal-to-noise regime. Lastly, we improve on this result and show that using the uniform spanning tree in the basis construction yields a randomized test with stronger theoretical guarantees that in many cases matches our necessary conditions. Specifically, we obtain near-optimal performance in edge transitive graphs, k<\/span><\/span><\/span><\/span>-nearest neighbor graphs, and \\(\\)\\epsilon[\\latex]-graphs.<\/p>\n","protected":false},"excerpt":{"rendered":"

We consider the detection of activations over graphs under Gaussian noise, where signals are piece-wise constant over the graph. Despite the wide applicability of such a detection algorithm, there has been little success in the development of computationally feasible methods with proveable theoretical guarantees for general graph topologies. We cast this as a hypothesis testing 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Sharpnack","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Akshay Krishnamurthy","user_id":30913,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Akshay Krishnamurthy"},{"type":"text","value":"Aarti 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