Topic: kernel ridge regression

A hallmark of intelligence is the ability to infer how stimuli in the world are interrelated. Transitive inference (TI) tasks test if subjects can generalize transitively (A">"B and B">"C implies A">"C), an important case of such relational inference. Despite longstanding study, it remains an open question how the brain, or even statistical learning systems more generally, implements TI. Here we show that a wide range of statistical and biological learning models generalizes transitively and replicates key behavioral patterns observed in humans and animals performing TI. Further, we c

This talk examines randomized sampling methods for approximating positive semidefinite matrices. Fast leverage-score approximation combined with the Nystrom method yields provably accurate, linear-time algorithms for kernel ridge regression and kernel principal-component analysis, avoiding the usual quadratic-time cost. Related sampling techniques give relative-error low-rank approximations of positive semidefinite matrices in sublinear time without assumptions about incoherence or condition number. The results illustrate how randomized algorithms can exploit positive semidefinite structure be