BEGIN:VCALENDAR VERSION:2.0 PRODID:-// BEGIN:VTIMEZONE TZID:Europe/London BEGIN:DAYLIGHT TZOFFSETFROM:+0000 TZOFFSETTO:+0100 TZNAME:BST DTSTART:19700329T010000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0100 TZOFFSETTO:+0000 TZNAME:GMT DTSTART:19701025T020000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT CATEGORIES:Isaac Newton Institute Seminar Series SUMMARY:A concentration interval for the Lasso - Sara Anna van de Geer (ETH Zürich) DTSTART;TZID=Europe/London:20180323T090000 DTEND;TZID=Europe/London:20180323T100000 UID:TALK103171AT URL: DESCRIPTION:We consider the linear model and the Lasso estimat or. Our goal is to provide upper and lower bounds for the prediction error that are close to each ot her. We assume that the active components of the v ector of regression coefficients are sufficiently large in absolute value (in a sense that will be s pecified) and that the tuning parameter is suitabl y chosen. The bounds depend on so-called compatib ility constants. We will present the definition of the compatibility constants and discuss their rel ation with restricted eigenvalues. As an example \, we consider the the least squares estimator wi th total variation penalty and present bounds wit h small gap. For the case of random design\, we assume that the rows of the design matrix are i.i .d.copies of a Gaussian random vector. We assume that the largest eigenvalue of the covariance matr ix remains bounded and establish under some mild c ompatibility conditions upper and lower bounds wit h ratio tending to one. LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR