BEGIN:VCALENDAR PRODID:-//eluceo/ical//2.0/EN VERSION:2.0 CALSCALE:GREGORIAN BEGIN:VEVENT UID:9b6f8e5b25a2a3dab745e413c4e3633c DTSTAMP:20260505T062505Z SUMMARY:Marco Avella Medina and Philip Ernst DESCRIPTION:14:00 – 15:00 Marco Avella Medina:\nTitle: Differentially pr ivate inference via noisy optimization \nAbstract: We propose a general o ptimization-based framework for computing differentially private M-estimat ors and a new method for the construction of differentially private confid ence regions. Firstly\, we show that robust statistics can be used in conj unction with noisy gradient descent and noisy Newton methods in order to o btain optimal private estimators with global linear or quadratic convergen ce\, respectively. We establish global convergence guarantees\, under both local strong convexity and self-concordance\, showing that our private es timators converge with high probability to a neighborhood of the non-priva te M-estimators. The radius of this neighborhood is nearly optimal in the sense it corresponds to the statistical minimax cost of differential priva cy up to a logarithmic term. Secondly\, we tackle the problem of parametri c inference by constructing differentially private estimators of the asymp totic variance of our private M-estimators. This naturally leads to the us e of approximate pivotal statistics for the construction of confidence reg ions and hypothesis testing. We demonstrate the effectiveness of a bias co rrection that leads to enhanced small-sample empirical performance in simu lations. \nThis is joint work with Casey Bradshaw and Po-Ling Loh.\n15:30 – 16:30 Philip Ernst:\nTitle: New frontiers in statistical inference fo r stochastic processes\nAbstract: I will first speak about how we recentl y resolved a longstanding open question in applied probability. Consider t he standard empirical correlation $\\rho_n$\, which is defined for two rel ated series of data of length $n$ using the standard Pearson correlation s tatistic. This empirical correlation is known as Yule’s “nonsense corr elation” in honor of the British statistician G. Udny Yule\, who in 1926 described the phenomenon by which empirical correlation fails to gauge in dependence of data series for random walks and for other time series. For the case of two independent and identically distributed random walks indep endent from each other\, Yule empirically observed that the distribution o f the empirical correlation is not concentrated around 0\; rather\, it is “volatile” in the sense that its distribution is heavily dispersed and is frequently large in absolute value. This well-documented effect was ig nored by many scientists over the decades\, up to the present day\, even s parking recent controversies in climate-change attribution. Since the 1960 s\, some probabilists have wanted to eliminate any possible ambiguity abou t the issue by computing the variance of the continuous-time version $\\rh o$ of Yule’s nonsense correlation\, based on the paths of two independen t Wiener processes. The problem would remain open until we finally closed it in our work entitled “Yule’s `nonsense correlation’ solved!” (T he Annals of Statistics\, 2017). \nI will then turn to speaking about our subsequent success in explicitly calculating all moments of $\\rho$ for tw o independent Wiener processes. Our solution leads to the first approximat ion to the density of Yule’s nonsense correlation. We are also able to e xplicitly compute higher moments of Yule’s nonsense correlation when the two independent Wiener processes are replaced by two correlated Wiener pr ocesses\, two independent Ornstein-Uhlenbeck processes\, and two independe nt Brownian bridges. We then consider extending the definition of $\\rho$ to the time interval $[0\,T]$ for any $T>0$ and prove a Central Limit Theo rem for the case of two independent Ornstein-Uhlenbeck processes. All of t hese aforementioned results appear in our 2022 preprint entitled “Yule ’s `nonsense correlation’ solved: Part II” (under review\, The Annal s of Statistics\, and available via https://www.stat.rice.edu/~pe6/YuleII. pdf).\nTime permitting\, I will then discuss our present work in building asymptotically exact and powerful tests of independence for pairs of indep endent Ornstein-Uhlenbeck processes and for other stationary Gaussian proc esses. Many of the methods of proof are drawn from Wiener chaos analysis\, a simplified way of implementing the so-called Malliavin calculus for ran dom variables depending in a polynomial way on finite or infinite dimensio nal Gaussian vectors such as Wiener processes. I also hope to speak about some initial leads in building tests of independence for pairs of nonstati onary processes\, in particular for processes with long memory such as the so-called fractional Brownian motion.\nI will conclude with some concrete applications of our work to the study of weather and climate extremes. In particular\, one pressing question of interest to our collaboration with the U.S. Office of Naval Research (ONR) and Royal Navy as follows: can the frequency of open ocean “freak wave” events observed by sea-faring ve ssels be correlated to and/or predicted and/or forecasted by sea-level ris e and/or coastal wind extremes? This answer to this question should help i nform the evaluation of risk exposure for Navy installations and vessels\, particularly those based on the Atlantic seaboard\; indeed\, some naval i nstallations may already be experiencing the recurrent effects of Atlantic storms\, and are sure to be affected by major climate disruptions.\n*I ac knowledge\, with thanks\, the support of this research by the Office of Na val Research (ONR) award N00014-21-1-2672 (2021-2024) and a Royal Society Wolfson Fellowship (2022-2027).\n*The first paper mentioned is joint work with Larry Shepp (deceased) and Abraham J. Wyner (The University of Pennsy lvania). The second paper mentioned is joint work with L.C.G. Rogers (Univ ersity of Cambridge) and my former postdoctoral fellow\, Quan Zhou (Texas A&M University). Some of the present work is joint with Frederi Viens (Ric e University).\nRefreshments available between 15:00 – 15:30 URL:https://www.imperial.ac.uk/events/156724/marco-avella-medina-and-philip -ernst/ DTSTART;TZID=Europe/London:20230113T140000 DTEND;TZID=Europe/London:20230113T163000 LOCATION:HXLY 139\, Huxley Building\, South Kensington Campus\, Imperial Co llege London\, London\, SW7 2AZ\, United Kingdom END:VEVENT BEGIN:VTIMEZONE TZID:Europe/London BEGIN:STANDARD DTSTART:20230113T140000 TZNAME:GMT TZOFFSETTO:+0000 TZOFFSETFROM:+0000 END:STANDARD END:VTIMEZONE END:VCALENDAR