Interview with COPSS Award winner Martin Wainwright

_Editor’s note: Martin Wainwright is the winner of the 2014 COPSS Award. This award is the most prestigious award in statistics, sometimes refereed to as the Nobel Prize in Statistics. Martin received the award for: “ For fundamental and groundbreaking contributions to high-dimensional statistics, graphical modeling, machine learning, optimization and algorithms, covering deep and elegant mathematical analysis as well as new methodology with wide-ranging implications for numerous applications.” He kindly agreed to be interviewed by Simply Statistics. _

SS: How did you find out you had received the COPSS prize?

It was pretty informal -– I received an email in February from

Raymond Carroll, who chaired the committee. But it had explicit

instructions to keep the information private until the award ceremony

in August.

SS: You are in Electrical Engineering & Computer Science (EECS) and

Statistics at Berkeley: why that mix of departments?

Just to give a little bit of history, I did my undergraduate degree in

math at the University of Waterloo in Canada, and then my Ph.D. in

EECS at MIT, before coming to Berkeley to work as a postdoc in

Statistics. So when it came time to looking at faculty positions,

having a joint position between these two departments made a lot of

sense. Berkeley has always been at the forefront of having effective

joint appointments of the “Statistics plus X” variety, whether X is

EECS, Mathematics, Political Science, Computational Biology and so on.

For me personally, the EECS plus Statistics combination is terrific,

as a lot of my interests lie at the boundary between these two areas,

whether it is investigating tradeoffs between computational and

statistical efficiency, connections between information theory and

statistics, and so on. I hope that it is also good for my students!

In any case, whether they enter in EECS or Statistics, they graduate

with a strong background in both statistical theory and methods, as

well as optimization, algorithms and so on. I think that this kind of

mix is becoming increasingly relevant to the practice of modern

statistics, and one can certainly see that Berkeley consistently

produces students, whether from my own group or other people at

Berkeley, with this kind of hybrid background.

SS: What do you see as the relationship between statistics and machine

learning?

This is an interesting question, but tricky to answer, as it can

really depend on the person. In my own view, statistics is a very

broad and encompassing field, and in this context, machine learning

can be viewed as a particular subset of it, one especially focused on

algorithmic and computational aspects of statistics. But on the other

hand, as things stand, machine learning has rather different cultural

roots than statistics, certainly strongly influenced by computer

science. In general, I think that both groups have lessons to learn

from each other. For instance, in my opinion, anyone who wants to do

serious machine learning needs to have a solid background in

statistics. Statisticians have been thinking about data and

inferential issues for a very long time now, and these fundamental

issues remain just as important now, even though the application

domains and data types may be changing. On the other hand, in certain

ways, statistics is still a conservative field, perhaps not as quick

to move into new application domains, experiment with new methods and

so on, as people in machine learning do. So I think that

statisticians can benefit from the playful creativity and unorthodox

experimentation that one sees in some machine learning work, as well

as the algorithmic and programming expertise that is standard in

computer science.

SS: What sorts of things is your group working on these days?

I have fairly eclectic interests, so we are working on a range of

topics. A number of projects concern the interface between

computation and statistics. For instance, we have a recent pre-print

(with postdoc Sivaraman Balakrishnan and colleague Bin Yu) that tries

to address the gap between statistical and computational guarantees in

applications of the expectation-maximization (EM) algorithm for latent

variable models. In theory, we know that the global minimizer of the

(nonconvex) likelihood has good properties, but the in practice, the

EM algorithm only returns local optima. How to resolve this gap

between existing theory and actual practice? In this paper, we show

that under pretty reasonable conditions-–that hold for various types

of latent variable models-–the EM fixed points are as good as the

global minima from the statistical perspective. This explains what is

observed a lot in practice, namely that when the EM algorithm is given

a reasonable initialization, it often returns a very good answer.

There are lots of other interesting questions at this

computation/statistics interface. For instance, a lot of modern data

sets (e.g., Netflix) are so large that they cannot be stored on a

single machine, but must be split up into separate pieces. Any

statistical task must then be carried out in a distributed way, with

each processor performing local operations on a subset of the data,

and then passing messages to other processors that summarize the

results of its local computations. This leads to a lot of fascinating

questions. What can be said about the statistical performance of such

distributed methods for estimation or inference? How many bits do the

machines need to exchange in order for the distributed performance to

match that of the centralized “oracle method” that has access to all

the data at once? We have addressed some of these questions in a

recent line of work (with student Yuchen Zhang, former student John

Duchi and colleague Micheel Jordan).

So my students and postdocs are keeping me busy, and in addition, I am

also busy writing a couple of books, one jointly with Trevor Hastie

and Rob Tibshirani at Stanford University on the Lasso and related

methods, and a second solo-authored effort, more theoretical in focus,

on high-dimensional and non-asymptotic statistics.

SS: What role do you see statistics playing in the relationship

between Big Data and Privacy?

Another very topical question: privacy considerations are certainly

becoming more and more relevant as the scale and richness of data

collection grows. Witness the recent controversies with the NSA, data

manipulation on social media sites, etc. I think that statistics

should have a lot to say about data and privacy. There has a long

line of statistical work on privacy, dating back at least to Warner’s

work on survey sampling in the 1960s, but I anticipate seeing more of

it over the next years. Privacy constraints bring a lot of

interesting statistical questions-–how to design experiments, how to

perform inference, how should data be aggregated and what should be

released and so on-–and I think that statisticians should be at the

forefront of this discussion.

In fact, in some joint work with former student John Duchi and

colleague Michael Jordan, we have examined some tradeoffs between

privacy constraints and statistical utility. We adopt the framework

of local differential privacy that has been put forth in the computer

science community, and study how statistical utility (in the form of

estimation accuracy) varies as a function of the privacy level.

Obviously, preserving privacy means obscuring something, so that

estimation accuracy goes down, but what is the quantitative form of

this tradeoff? An interesting consequence of our analysis is that in

certain settings, it identifies optimal mechanisms for preserving a

certain level of privacy in data.

What advice would you give young statisticians getting into the

discipline right now?

It is certainly an exciting time to be getting into the discipline.

For undergraduates thinking of going to graduate school in statistics,

I would encourage them to build a strong background in basic

mathematics (linear algebra, analysis, probability theory and so on)

that are all important for a deep understanding of statistical methods

and theory. I would also suggest “getting their hands dirty”, that is

doing some applied work involving statistical modeling, data analysis

and so on. Even for a person who ultimately wants to do more

theoretical work, having some exposure to real-world problems is

essential. As part of this, I would suggest acquiring some knowledge

of algorithms, optimization, and so on, all of which are essential in

dealing with large, real-world data sets.

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