The success of cancer treatment depends heavily on early diagnosis; unfortunately, modern detection still relies on inaccurate or invasive procedures, and so early detection remains an open problem. We propose a simple, accurate proteomic blood test (a ‘liquid biopsy’) for cancer detection. We conduct experiments on cryogenically preserved plasma from healthy patients from a longitudinal study that were later diagnosed with cancer. These experiments demonstrate that our test achieves diagnostically significant sensitivities and specificities for many types of cancers in their earliest stages using only plasma.

Our biopsy relies on multiplexing observations across thousands of blood proteins and multiple reagents. This yields sparse matrix-valued observations for each patient. We show that `de-noising' this sparse raw data is critical to achieving acceptable diagnostic accuracy levels, and further that traditional approaches to de-noising (algorithms such as PCA) fail. Instead, we rely on a new approach to noisy tensor recovery, we dub `slice learning’. Slice learning admits near-optimal recovery guarantees that in an important regime represent an order improvement over the best available results for tensor recovery. Applied to the design of our biopsy it yields sensitivity and specificity levels that are potentially sufficient for a clinical diagnostic tool.