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Through the lens of matrix and tensor factorization, one of the most popular approaches is to employ simple iterative algorithms such as gradient descent to recover the low-rank factors directly, which allow for small memory and computation footprints. However, the convergence rate of gradient descent degenerates quickly with the condition number of the low-rank object, and therefore, slows down painstakingly when the problem is ill-conditioned. This talk introduces an algorithmic approach, dubbed scaled gradient descent (ScaledGD), that provably converges linearly at a constant rate independent of the condition number at near-optimal sample complexities, while maintaining the low per-iteration cost of gradient descent. In addition, ScaledGD continues to admit fast global convergence from a small random initialization when the rank is over-specified, confirming the benign generalization of ScaledGD in learning overparameterized models. In total, ScaledGD highlights the power of appropriate preconditioning in accelerating nonconvex statistical estimation and learning, where the iteration-varying preconditioners promote desirable invariance properties of the trajectory with respect to the symmetry in low-rank factorization. </div> <div class="row lecture__section"> <h2>About this Lecture</h2> <span> <strong>Number of Slides: </strong> 40</span><br/> <span> <strong>Duration: </strong> 45 minutes </span><br/> <span> <strong>Languages Available: </strong> English</span><br/> <span> <strong>Last Updated: </strong> <span id="lecDate"></span> </span> </div> <div class="row lecture__section"> <h2>Request this Lecture</h2> <p>To request this particular lecture, please complete this <a href="https://services.acm.org/public/speakers/request_lecture.cfm?lecture_id=15705" target="_blank">online form.</a> </p> </div> <div class="row lecture__section"> <h2>Request a Tour</h2> <p>To request a tour with this speaker, please complete 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