Department of Computer Science,

Royal Holloway, University of London

http://vovk.net/

Time: 15:00-15:45 IST

*Abstract:*
Traditional methods of testing statistical hypotheses have been
developed for the batch setting, in the terminology of machine
learning: given a batch of data, statisticians typically compute
measures of disagreement, such as p-values or Bayes factors, between
a null hypothesis and the data. An alternative that is popular in
machine learning is the online setting, in which the items of data
(*observations *) keep arriving sequentially. In this
introductory lecture I will explain the role of martingales, in the
form of *test martingales,* in online hypothesis testing and
discuss their applications in the foundations of probability and
statistics.

Time: 16:00-16:45 IST

*Abstract:*
It is interesting that test martingales do not trivialize in the case of only one observation.
In fact, they provide a useful alternative, sometimes called *e-values*,
to the standard statistical notion of p-values.
The most important mathematical advantage of e-values over p-values
is that the average of e-values is always an e-value.
This property is valuable in multiple hypothesis testing,
which will be the topic of this lecture.

Time: 15:00-15:45 IST

*Abstract:*
Mainstream machine learning, despite its recent successes, has a
serious drawback: while its state-of-the-art algorithms often
produce excellent predictions, they do not provide measures of their
accuracy and reliability that would be both practically useful and
provably valid. On the other hand, such measures are commonplace in
statistics. Conformal prediction adapts rank tests, popular in
nonparametric statistics, to testing the IID assumption (the
observations being independent and identically distributed), which
is the standard assumption made in machine learning. This gives us
practical measures, provably valid under the IID assumption, of the
accuracy and reliability of predictions produced by traditional and
recent machine-learning algorithms. In this lecture I will give a
brief review of conformal prediction.

Time: 16:00-16:45 IST

*Abstract:*
An interesting application of conformal prediction is the existence
of *exchangeability martingales*, i.e., random processes that
are test martingales under any exchangeable probability measure. In
particular, they are martingales whenever the observations are IID.
The topics of this last lecture in this series will be the
construction of exchangeability martingales and their use for
different kinds of change detection, including detecting a point at
which the IID assumption becomes violated and detecting concept
shift.

https://us02web.zoom.us/j/82689990363?pwd=VnUrRllOZk5ZMnZGcXh3MVpndVB4UT09

Meeting ID: 826 8999 0363

Passcode: 855047

Last modified : January 11th, 2021