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UID:5fdb9d9f-8497-4dcc-9308-de9f6e0fe73a@nexttoyou
DTSTAMP:20261106T172848Z
DTSTART:20261117T211500Z
DTEND:20261117T221500Z
SUMMARY:ORIE Colloquium: Agostino Capponi (Columbia)
LOCATION:Frank H. T. Rhodes Hall 253
DESCRIPTION:Data-Driven Learning of Latent Dynamics\n\nHigh-dimensional ti
 me series often exhibit complex dependencies that can be explained by a f
 ew latent factors. Uncovering these factors and modeling their dynamics i
 s a fundamental challenge in data science\, with applications ranging fro
 m signal processing and forecasting to asset pricing and financial risk m
 anagement.\n\nWe introduce a data-driven framework for modeling and predi
 cting a multivariate response y(t) from a high-dimensional covariate proc
 ess x(t)\, allowing for nonlinear dependencies without imposing a paramet
 ric model on the covariate dynamics. We leverage diffusion maps to uncove
 r low-dimensional representations of the covariate process that retain ex
 planatory power for the response time series (y(t)). We establish concent
 ration inequalities that provide convergence guarantees for time averages
  and show that\, under mild assumptions\, the resulting diffusion map emb
 eddings exhibit approximately linear dynamics. This property enables us t
 o develop a geometric Kalman filter that operates in the learned embeddin
 g space to estimate latent states and predict the response variable.\n\nW
 e demonstrate the effectiveness of our framework in financial stress test
 ing. Using historical data spanning three major financial crises\, we sho
 w that our data-driven approach reduces the mean absolute error of scenar
 io-based portfolio return predictions by up to 52% and 57%\, relative to 
 standard scenario analysis and dynamic principal component anal\n\nhttp:/
 /next-to-u.app/events/5fdb9d9f-8497-4dcc-9308-de9f6e0fe73a
URL:http://next-to-u.app/events/5fdb9d9f-8497-4dcc-9308-de9f6e0fe73a
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