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UID:www.tcs.tifr.res.in/event/1364
DTSTAMP:20231205T090534Z
SUMMARY:Identifiability of Product of Experts Models
DESCRIPTION:Speaker: Leonard J. Schulman (Caltech)\n\nAbstract: \nProduct o
f experts (PoE) are layered networks in which the value at each node is an
AND (or product) of the values (possibly negated) at its inputs. These we
re introduced as a neural network architecture that can efficiently learn
to generate high-dimensional data which satisfy many low-dimensional const
raints---thereby allowing each individual expert to perform a simple task.
PoEs have found a variety of applications in learning. More recently\, th
ey have arisen in the theory of causal networks.\n \nWe study the problem
of identifiability of a product of experts model having a layer of binary
latent variables\, and a layer of binary observables that are iid conditi
onal on the latents. The previous best upper bound on the number of observ
ables needed to identify the model was exponential in the number of parame
ters. We show: (a) When the latents are uniformly distributed\, the model
is identifiable with a number of observables equal to the number of parame
ters (and hence best possible). (b) In the more general case of arbitraril
y distributed latents\, the model is identifiable for a number of observab
les that is still linear in the number of parameters (and within a factor
of two of best-possible). The proofs rely on root interlacing phenomena fo
r some special three-term recurrences.\n \nBased on joint work with Spenc
er Gordon\, Manav Kant\, Eric Ma and Andrei Staicu.\n
URL:https://www.tcs.tifr.res.in/web/events/1364
DTSTART;TZID=Asia/Kolkata:20231215T110000
DTEND;TZID=Asia/Kolkata:20231215T120000
LOCATION:AG-80
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