If you're in for something I will consider
contributing to the British scholarship

lecturing very hard for Russian
Foreign Ministry I'll start by saying

I suppose and that's what's wrong I said
George if we say we are not of the busiest

Holy Night and Mansons national arts
then you can see three Israelis really

really good at the news
with one aspect of that.

Really is partly the pastoral
operations research and

the writer of the zero zero research
center and I see us being with an amazing

faculty seems not to be a shock to your
city masters and Dr began to find out and

help me to research that myself and he has
brought the interest of research people

in opposition to life probability and
they're likely patients in health care and

has operations management for future use
it has gotten more than fifty percent of

the first three regularly I suppose he has
the fourth book there and we're actually.

Going to see how with this spring.

He has supervised thirty three doctors do
it and you currently supervising nineteen

others leads into the number
zero to let you know economy of

Engineers is two thousand and five and
has received numerous research awards.

Including more spies.

Awarded guys paperwork cation process
price problem price rising opposition and

presidential young versatile word and
he has told us there are several Yes core

values old can be used in areas of
careful services health care and

mediation published in addition off
the Sentinel research from your own he

also has been a great educator and great
inspiration for many young people myself

so we're very happy to have people.

So I just want my friend.

Thank you one thing if you expect to learn
another dive into Type I think you will be

disappointed so I'm very glad to be
here particularly because I see.

The average age in the audience
is exactly what I would like and

this includes George are a.

Great to be here so so today I would
like to tell you about some work that I

have been been pursuing in the last couple
of years in the area of the district and

last in learning but
from a different perspective.

Than you might have expected so

it consists of three
bodies of work including.

Best selection this is work with my.

King who is graduating and
my novice at the time but

soon to be a faculty member at
the might be Muslim they're.

Least median of square
regression with a whole and

algorithmic approach to immigration so.

So typically what I tried to do in the
talks is I would like to make sure that

the message in the Dover publishing
series that has been written

one hundred seventy now a classic book in
the Dover series with a title might mark

a program in statistics and I'm just
quoting one there are many others but.

Continue optimizing undeniable have
been packed into the sticks but

a lot in addition in the last two
decades convex organization methods

of increasing importance titles like
compressed sensing matrix completion and

more many others are hot
subjects at the moment.

However many problems and so this isn't
allowed to convince you of that soon.

Cannot really be expressed as mixed in
the optimization problems in other words

it's not that I do is the problem
to put in the framework

it's a natural way to think about it.

However at least in
this experiment I know.

This mixing that of the musician
is considered impractical.

And the corresponding problems.

Not solvable that's the Karen
belief to the point.

What is the evidence I have of that I have
some empirical evidence of this is that

people that are educated at Stanford
Stanford is one of the top Department

statistics have not taken or
been exposed to what.

Is not know they can of course they don't
know what it is that's a serious matter in

my book I don't know what's
happening in this department.

What is the answer to that actually.

So maybe the Stanford is not
only allowed liar so your other

heuristic heuristic methods are used for
example I mean some of you might know some

of you would know lasso is a method to
develop one thousand nine hundred six for

best subsidy regression or
card classification with aggression.

Is your heuristic methods.

He has a problem and we have.

A method which is your reasoning.

I would like to educate you.

Many of you know but many of you don't
know the progress of mixing those are my

position in the last twenty five years and

I can say this with pride because my
contribution to that is very minimal so

this was done by the community
not only by one person so and.

So these are some some
facts this speed up between

suplex one point two
subjects economy let's.

Get started nine hundred ninety one and

the first version of simplex
simplex one point two.

The company was sold to I log and
then I.B.M. simplex eleven.

Cannot see this truth
until two thousand and

seven is about twenty nine thousand
times this is both Bixby's calculations.

Groby one point No this is
a people from sleepless.

Started a new company called In fact.

Out of this department in the George I
believe in two thousand and nine is

roughly comparable to subjects eleven with
speed up between Groby one point zero and

roughly the current version of the flex
maybe six point zero is it is now it's

about twenty times you multiply it was
about five hundred eighty thousand times

this is just software this is
really the collective intelligence

of people who misuse optimization
who propose are going to restrict

lower bounds cutting planes and
so forth at the same time.

So just will straight what this means.

That would have taken seven years to
solve twenty years ago can now be solved

in the same twenty year old computer in
less than one second that's what it means

this is namely not not considering
hardware just software or

hardware has about the speed up of about
three hundred twenty thousand times

these are Proxima Now if you multiply the
two you have two hundred billion times.

And there are too many fields that I know
what the progress has been in the billions

I hope you realize what it means two
hundred billion it means that something

that you have taken
centuries takes seconds.

OK.

However given that so

what is the motivation of this work given
the dramatically increased power of mixing

the optimization is mixing the able
to solve key multi vital statistics

problems considered intractable
a decade ago that's the question and in

particular how do these kind of solutions
compete with state of our solutions.

Here's an example the most widely used and
I mean this in all sciences not only.

Are there the most widely used
methods scientific method

in today's computers is aggression and
very good includes scientists

you know people in history made this in
engineering everybody uses regression.

A small percentage use of the magazine is
being widely used yet the way we teach it

we teach it as an art I think it's a trick
question of the Mighty we say well we

have these requirements Tyler Moore and
so forth that's not science that's

an art versions the question
is Can we had this process and

most importantly in my view given
the young people in the audience.

What are the implications of
the interests of this sticks

you know if there are positive answers to
these questions should we change the way

with its of these things.

So what are the problems.

I address in this talk that
work is broader But so

I pick some examples that
are simple to state so

the first classical problem is a so-called
subset selection regression So

that's the usual Gaussian
problem where you have some.

Observations Y. X..

Corresponding data recorders.

The problem that Gauss all of the century
said goal is to minimize overbet the.

Problem and now we have a small
complication we want that the number

of distinct variables to use smaller.

Less than K. like let's say for
example we have.

Ten thousand observations
we have a thousand.

Variables What is the best regression
with fifty non-zero components.

Second problem at least median
regression so we are very similar but

instead of the sum we want the median of
the value of where is it to us why is this

relevant because if you say you want
to regress income as a function of for.

Factors that affect income and you have
Bill Gates there are Warren Buffett one of

the invasion of the included here might
actually make things very very unstable.

But if you have the median
It doesn't matter

it's much more robust to where are or
outliers.

And the final part of the talk
is I suppose you want

to get action that has nice properties
sparsity multi-collinearity

categorical variables with many nice
properties how can we achieve that

in a way that we have a guarantee
that we achieve it by the way

I recognise a big audience feel free to
ask me questions when you have a question

ask me even though I'll try to
answer in other words if I know.

So let's start with our first friends.

Subset selection so so this is a problem
that in nine hundred seventy four

was solved by to start this little farm
and Wilson this always by implicitly.

And in fact there is a team in our art for
those who would not know it

is a free package that implements many
algorithms Massillon And so this six and

it's implemented there and

it's called leaps so if you ask clips it
solves that problem in a sense but but

it cannot solve it doesn't scale beyond
the number of variables being about thirty

it doesn't solve Beyond that
I mean check me out on this.

So lasso.

Was proposed by Robert Gibbs here I
mean ninety nine this is done for

a professor and
in parallel by another stand for

group one thousand nine hundred eight and
just to illustrate the impact you know

citations is a measure of impact
reasonable size of impact

how many sections do you think
George Dance a good book.

Dancing is sort of the father of the of
the migration then we are programmed

because.

One would expect to know
how many Any guesses.

Come on and some guess.

Six thousand.

So this was a couple of months ago when
I searched I didn't search in update so

the last row has has
a citation of ten thousand and

growing ten thousand citations.

So you could say many people use last
year which is over twenty years than sex.

Who is over sixty years and
what is the method the method this to take

the original problem are the penalty which
is the absolute value of the baiters.

That's a quadratic optimization model
because this is a nice convex function so

it can be solved reasonably well
with convex optimization codes.

And.

Some theoretical evidence that it produces
solutions namely solutions that have

small number of non-zero baiters and

this is what is being used today this is
what departments around the world teach.

About sparsity that I know of.

I would first like to make an observation
that it's technically stated that is I

believe it's not widely known fact I would
like to ask the students of the audience

whether or not about to say they
know of the next first life

George two.

So I claim that lasso has absolutely
nothing to do with sparsity

I claim that lasso has only
to do with robustness and

here's the statement suppose you
have with the original problem but

your made the execs error in it right.

So what you would like to do you like to
minimize over beta the worst case over

some back to Beijing in Delta that
are bound into now which is exactly

norm since it's also important just that
they don't I would like to have errors but

the errors are not unbounded there
is small bounce on the right so

this is my home article statement
that the minimum overbet as a robust

regression this is equal to is
not empirical statements and

my question is the minimum of the usual.

Last longer times the norm of the beta so
if you used to equals one.

And.
B. equals two.

That's the last.

So in other words this
is that what does lasso.

Mean if you look under this
light it it protects you.

Against arrows on the data sparse
that there is no to be found.

That I can see anyway right so
is this known to people.

Who knows it.

So we don't teach it so

here's a method which is not of this
difficult segment by the way that is.

If you know something about duality
this is not a deep statement but

I believe it belongs to
the classical things we teach right.

So this is an aside has nothing to
the top but I thought to mention so

so I claimed the problems of the nature
of that I suggested can be naturally be

expressed as discrete of my some problems
like this is not like a deep serve

the ration So when how would you model
that thought to be easy and undergraduates

exercise maybe the first lecture of
George's class maybe the second.

Mini might have something that variable
zero or one would have the betas to be

began formulation M. times e I missed
some of the i's is less than K.

So if the I go zero the betas are zero if
the guy calls you on it and it doesn't

constrain by picking a property themselves
tell you how to select the variables so

this is an exact formulation.

Of the problem in question.

And I consider their natural one not
a great formula but a natural formulation.

So the title of the talk is.

Statistics under a modern optimization
LYNCH So what is more than so

I claim modern.

People into this is nothing more
than think first order methods.

This is a popular conflict methods
are popular musicians are known and

in view I have is that you should
use both first order methods

to find good feasible solutions and.

Mixing that optimization methods
to find lower bounds are really

much NG That's the game that is the modern
means two things first order methods

continues methods and discrete ideas that
we have seen huge huge improvements have

been made so there are some concerns here
I don't want to but there is a this am I

can be computed from the data this is
not a magical thing OK so I skipped it.

Another way to formulate problems
with navy don't like Begins is for

those of you that are.

A bit more knowledgeable
optimization this is a way to say

what I really want I want if the eyes.

Big better I is also zero does
the implication and this is a way to

express this with special order sets
that's a way to express if you don't want

to have began methods is another way
of formulating the problem that the.

Major state of the art.

Of my system coach can accommodate.

So let me reiterate before entering
the theory how do is an example

of in the end of the day
what we have achieved.

So so this is time so
this is a problem about diabetes or

your world problem because about any
course three fifty observations patients

sixty four variables and the objective
is to find how to explain how diabetes

what is the effectiveness of diabetes
that's my health care contribution.

For today.

With only sixty six
variables to explain OK So

here's what is happening in these methods
so very quickly using to restrict

methods of the first order kind I'll tell
you which method just really strange.

Steam leak within like two seconds you
find a solution that you don't know it's

optimal but you find a very good solution
and then you it takes in the programming

about four hundred maybe five hundred
seconds to prove optimality right.

Lasso a competitor method takes also
a second to find the solution and

stops doesn't know.

So these methods because of their in
their programming business can solve

right to the best of my knowledge.

I do not know this is not a big problem
by the way but just to illustrate

I do not know any software package
that can solve these problems or

probably manage to get on the right so so.

So the question is Is this an accident
I mean this is the or are we lucky.

So that's a relevant at all but
what I would like to emphasize is that.

If you don't care about guarantees so what
you don't care about that you want high

quality solutions to solve the problem you
aim to solve you can only solve this if

it takes the same amount of time the other
methods we can only teach in our courses

if you want more you want to be
sued then you have to work hard and

you know it.

Illustrate that George Will
patience my friend.

OK So let me out tell you a bit
about the methods right so so

far how are we doing everybody following.

OK so now we go a little bit higher and
we have some.

But not too much higher though so I would
like to illustrate the key methods we use

not the huge mathematics where the used to
say that these are not and if they do this

matters so what is that that's the problem
we want and the function of data.

Is a convex function clearly
convex a quadratic function and

you can bond the function
that the gravy and survival.

Function virtue's So

what this basically says is that the
function of the gradient of the function

is a leap this is a continuous
function with a parameter lambda.

So this implies Taylor series
Elementary things that if you

have data is upper bound it by
the first or the expansion class and

they're out there that it
an exact inequality so

I found what I want to optimize with

an upper bound that is also quadratic So
that's a constant That's a quadratic and

that's a linear function in beta and
that's a quadratic function.

But a quadratic function that.

The variable does not appear with an X.

beta that was beta that's
actually material.

So instead of solving
the original problem I solve.

This is not equivalent I mean I'm using
a heuristic In other words I find I solve

this problem subject to this condition and
this problem I can so we close form.

So this is by way of first order
type method I I find the expansion

optimizing the expansion and it turns out
that this is equivalent if you do this and

you do it a little bit of
mathematics the simple things

you find that this is equivalent
to solving data times a vector.

Subject to I want a chord
in it's non-zero but

this problem beta mine is you square
subject to that is solvable in closed form

in the following way you find you
take the use use are not constants.

You take the use you sort them
from highest to lowest and

the solution is that the Bay
does are equal to the K.

largest and there is that zero was
called the thresholding methodology

these are not difficult observations these
are not rich are also in my opinion so

for more level observation I mean you know
we don't need a Ph D. do this and I would.

OK.

How are we doing.

OK so here's an algorithm.

We missed our lives with a solution
maybe we'll take the solution

of the least West forget about loss or
even misalignment loss.

So we find it a ration So I call this
given the you actually age of H.K.

or you it's just this business sorting
business what is you you is basically this

vector so I basically iterate this
is variation and if I want to be

fun sure I could also line search to
be faster practically and so forth.

And I I continue until no more
improvement in the solution.

OK this is a method that is very fast

very fast all these kind of
methods are very fast moving.

Now what can we say about how good this
method is first that it converges to

something and the something is
a fixed point of the of a duration.

That the method after
it to find an epsilon.

Solution such that the that you
are all within epsilon of a theory

another Was it doesn't improve any further
more than epsilon it takes all the one or

the one of epsilon iterations and
this is the total in other words.

We can say something about how fast it.

Converges.

And at some point the proper method has
a problem that it finds a discrete set and

then in one iteration we find the right
answer your I.Q. is the cancer so

the bottom line of all this I won't bother
you too much there is that if this is

a method that is provably convergent and
it's extremely fast and

you say that it is good but
it is extremely fast and.

Now so let's see some experiments for
the example I gave you.

So.

So one possibility is to now so
we have this method.

Of people that know a little about their
programming know that if you give it

a warm start a good solution it
accelerates into the programming a lot.

So here's an experiment would just use
a heuristic we start mixing the ger

with calls with no we just give it to God
will be the formulation I gave you and

then we give we give it away
with this warm start and

you observe that in five
hundred seconds and

maximum time is five hundred
seconds that you are within.

Thirty percent of optimally deny fifty
percent ninety nine in one seconds.

For various k's the calls.

If you do call start you need five hundred
seconds you are very close but not optimal

but with it work start and in the
programming you close you close the gap.

So this suggests I mean of course
this is not the only of this but but

this suggests that this method is fast and
is useful.

It closes the gaps it helps closing
the gaps This is also true for this is

the case which is the usual regression
case that you have more more data less

factors this is an example this is
harder example you could spot it

is not a luxury anymore you have now let's
say this is this is data genomic data for

fifty patients again a healthcare example
most of my exams are health care anyway so

you have a fifty patients and
two thousand genomic factors and

you would like to understand certain
diseases a function of his exam factors

you don't know if any of them is relevant
right so you need this partial Lucian

because it's a bit of course if you have
fifty two thousand there will be zero

I mean in sample I mean clearly so
you need something that has four factors

if you're going to have anything useful
five factor so and indeed the same.

Think holds true namely if you
use this method for warm starts

boy it is it helps OK.

Back to drug problem the drug is
QUESTION How good is the method.

So so this is now give you some.

Critical evidence sparsity So
last was designed supposedly to be

sparse the community believes is
very easy if you know my cause or.

Who is a top notch our decision I
have work you know this is what

is being taught Lashawn
sparsity this look at that so

they yellow This is a collection of
many problems not just just one so

the yellow is mixing the programming
this is lasso the blue with the stepwise

regression supplies something with
it actually very interesting and

this is State of the art of.

The cone non-convex approach is
in fact who is responsible for

this so.

This is the number of known zeros so
we created problems that their rights pass

this ten this is a bitty thing we
know the answer because so in all and

then we start.

Increasing decreasing the noise
the harder problems are on the left and

the and they become easier and you observe
the normal cases last so found that I had

to parse it a lot of mixing that are found
the right sparsity found the right answer.

And.

The one that we used did not.

Write So now what is interesting is
they found the same answer about

the same amount of time but
the method to clone got to

prove that it is correct but if you just
want a good answer the amount of time

is very comparable because both of them
are solving in essence convex problems and

simple simpler things that will
respond this part of the selection.

Well we are going to see business so now
we say because we know the answer this is

the air or the the algo of makes mine is
the to answer over the top over the truth.

And again you see that the mix in the door
is lower and sizably better this is

in other words and eight percent
there are sixteen percent there or.

So and
this continues even as the noise becomes.

Less because the lower where
are the easier the problem but.

So on and this it was a case for
an bigger than B.

the usual case the unusual case very
much the results are even more dramatic.

Because in this case on
this part of the sides

we design the problem
with you know of five.

Four or four or
in four four correct variables and

you know last is not even close.

On the accuracy also in other words.

So in other words solving problems to
optimality using these methods definitely

not surprisingly but the family
gets you a spark solution provably.

And.

And this is more accurate.

So what do we learn Here's a small summary
of what I have told you so far for

the case of bigger Vampi.

The usual case mix in this organization
would warm starts finds provably of Muslim

nations for an investor thousands and
be in the hundreds in minutes.

In minutes.

And if you want the goods to Lucian but
not provably in seconds for

the case and smaller than P.
This approach.

Find solutions with better prediction
accuracy than last saw for

any cause candidates and
because in the thousand.

In minutes improving optimality now or.

In hours not days I'm using here.

At this two hundred billion business and
I'm using a very powerful in that this is

we're not alone here we have the strength
of a community behind us to be able

to make these statements it's not
like we've found the fantastic.

Another thing that we have found is that
mixing those are solutions have been

a significant lead to be taken sparsity I
would say that's a very clear advantage

and Ed and some advantage they outperform
in predictive I guess about this is not so

decisive.

So Michael Gross was on recently in
the paper has you know many many examples

I mean this is the magic approach that
most of optimization methods namely mixing

desire and one of the first of them is
capable of solving large scale instances

namely problems that we care to solve
practically is not an academic exercise.

Questions comments on that are about
to change gears that's way.

OK.

So let's think about now so now we have
some a scenario that it would give us

promise that these methods could be of
some practical use let's think about

the process of regression so so recently.

Let me give you an example in practice
that I was I care to solve this is not so

so this was a problem I don't
know if you see this work of.

This full of from Freakonomics from
a cargo of economist Francis and

so there's a fellow who
made some claims about.

The correlation of crimes and
abortion he by the way

he wanted to mark out of the award for
his work so it's a very visible work.

And you make of claims so

I set out to play because this will
change that did not sound correct to me.

They did not sound correct and I can
tell you where the claims is he more or

less claim that.

There was a very
significant in this nation

one hundred seventy
three the United States.

Versus Wade that legalized abortion
in this country seventy three and

you observe crimes violent crimes
in one thousand nine hundred

ninety one and there was indeed in
the data a very significant drop from

one thousand nine hundred
ninety nine hundred ninety.

This is a fact kids are to our nation
statistically motivated Was that

a reason that this happens is because
of the UP SO who commit the crimes

I don't believe that statement by the way
but that's a claim who commit the crimes.

These crimes would have been committed by
the unborn children seventeen eighteen

years later but the argument remains.

Series the argument there are many people
who are not born because of legalisation

of abortion this is true it's
also true of the dropped.

Is this correct or not not is a social
implications of this mathematical

I mean think about what you are saying
I want to say so I checked.

This is all based on regression
with all the questions and

the data I mean I was able
to find the data he used.

So but in doing so you have to
have regulations that make sense

namely they have some
characteristics I mean

this is not the whole experiment we
have data and when to explain so

you need the and in doing this
regressions you need to have.

You need to understand are is
there multi-collinearity

you know who the prime suspect here may.

B..

There's another factor
that affects abortion and

that factor affects crime not
that the F.B.I. or correlation so

understanding these correlations matters
it matters also from a from a policy

perspective not only mathematical
perspective so you have to understand if

you Romberg wrestles with these variables
and you don't control form of the column

you have the you can also conclude many
things you might find for example that.

You know there isn't crime
decreased is because

mix on left the White House that the year.

I mean if we're not careful so

what do we do in building is
a question modest at the two days

what with teach our students I teach
a course at MIT called data models and

decisions and this is what we teach the
students first year graduate students and

I'm I don't think we are aware now to the
mighty We do what the practice is we say

start with a model if you if this variable
is not significant take it out put

another one mean if this
multi-collinearity changes and so forth

don't tell them the method would tell
them what these are desirable things but

we never tell them how to achieve
this objective simple to honestly.

And to the best of my knowledge there
is no such method that I'll go to

achieve this because it's not clear
that if you take one variable out

we won't create a problem elsewhere it's
not clear to me in fact this is a crank

a prime candidate in this exam or
when we tried.

So the purpose of his work we have seen
that his approach in the program works

at least in this particular case can we
not journalism in other words can we right

all the desired properties are very good
as a model within the media programming

problem which is very natural for some
of the educated in this way and I'm like

myself it's not natural for people who
have not seen the program in their lives.

So in other words I view this as
an exercise I don't know it has a very.

Because this is a problem I mean
that's actually a very interesting.

Interesting characteristic about research
if you if it's consistent with your

experience it's not that difficult but
it's very difficult it's not.

So here's a formulation of
this problem I'll try to work

way to give you a glimpse.

A bit of that that's the previous business
but now I put a robust mess in the story I

put up with the last two things not
because of sparsity because of robustness

So that's a good property because the data
are estimated they're not exact data So

having got them there is good
that's their business contribution.

So this is part of the business we have
seen right here's another example we want

pairwise So for example let's say we take
the variables compute the correlation

from data we know what the correlation
is what does multi-collinearity means

it means we don't know who should
political relations point nine So we don't

want both variables to be included
only one of them will be included but

I won't impose my human intuition which
one I leave the problem decide so

I write Z.-I plus C.J. these are the
correlated variables be less than one.

Now here's here's another idea suppose
you have known me other people say

affirmations which one

there are many millions of
affirmations well take fifty of them.

Take the log out and have a variable
the square root of a variable the power to

the fourth blah blah blah.

Take this fifty of new variables and
say out of these fifty and only want one.

But I let the problem find
what is there right now me and

reformation which basically says
out of this transform variables

only one of them should be selected.

And so forth and

you can put more things there so this is
a problem of the end of the programming

via Now how about significance what
we say you would I'm very curious.

This is for the statistics part of
the department we cover the health care.

So what do we say very important
is to find our visit music and

what is it is that the six of these
guys is what we tell our students right.

Now this is hard to compute but we can do
what's called the Great idea of blood and

perform some for the so-called
bootstrap So you re sample the data

you compute.

The confidence levels and if you find
that the levels are not good you

can you say this can we measure variables
one two five and seven I want to exclude

only that combination how do we do it with
say out of this selection of variable C.J.

I want there are four I want at most three
so this excludes this vector and only

this vector you put it in and use told you
basically use a simple copy plain idea so

in other words it in this
reprogramming allows you

to to basically accomplish something that.

I needed in that particular
application in many others

it allows you to find models that.

Satisfy all the constrains you can think
of similar to honestly humans cannot do

that is this human cannot do this
I mean we are not engineer for

that and you know for example we did
we gave data to our students we do

on it actually do to
them very tired enough.

But in the program it doesn't retire
it only requires that it's one of

the solutions so how good is this idea for
the is it feasible computational

I would say is very feasible computation
very feasible so you can solve so

we're basically the following there
was there was data in the U.I.C. and

the University of environ
they have a nice.

About two hundred problems
very question type small law.

Large very large and we solve this
problem using this metal imposing all

the constraints.

She is and I mean I want to have
two hundred here some examples and

I didn't pick the best I picked a random
collection of all the problems so

in this example we found for example that
the are squared of the is comparable

to other methods except we were able to
find a good spot solutions must parts

of the other methods but most importantly
they imposed everything that we wanted to

gather whereas all these other solutions
did not have the properties we wanted for

example I could not so here's
an example with airlines where was it

an airline signable small was a big
Here's an elevator example is data of

predicting elevator usage in
big buildings in New York.

So we ask where it was the same but
the but by look at the correlation it had

ninety nine at the moment I was able
I could not find a good solution

from a human perspective of course was you
know eighteen variables nine thousand of

the variations but we start putting
the correlation at point six seven eight

it found the solution to start putting the
correlation more and more less less less

you you baby will fit but
is able to do it humans cannot do that.

So in other words it is possible
with the programming to find

interpretable solutions sparse with
multiple reality significant variables all

of them simultaneously I think
this is a useful tool and

I think this is how we
should be treated right not.

Me not this is a program just put out
the black box with how you run it.

OK.

Last but not least.

So the idea of outliers last
week a problem in which.

When you find when you
do that at least where.

You have issues with outliers.

This is not a minor issue let's say you
do it in legal trial and in this clinical

trial there is one outlier just one and
click out there you don't have thousands

of patients you have a hundred patients
but one patient is you know things did not

work here but if you because you included
in the data you might like you have your

own your conclusions that's actually a
real problem is not any Maginot you want.

So and not your idea has been proposed in
which instead of solving really squares or

the absolute values and

of the rates of the median now the media
has a property Think about it so

is the median of there is the jewels right
now so you have a country that is he joins

there is it just depends on the choice
of beta of course as you change the beta

reordering changes and the only thing that
matters is the media in this huge world so

the large outliers do not matter that's
a good idea in my opinion a lot my and

there has been proposed
in the eighty's by.

The gentleman by the mail from Shaw.

So the question is but

unfortunately this is a very discrete
problem nobody knows how to solve it.

Right that I nor
an enemy exactly that heuristics.

So what what is the state of the art the
state of the art while the problem is and

we have all these problems and behind
them and you know I think this is a not

informative statement so in your marriage
is used roughly we can solve problem

with fifty observations five independent
variables within your marriage and

after that it doesn't work and there are a
few risks so I won't bother you now with

all the details of this is now
more elevated this is now perhaps.

A senior class on modeling
not the not the junior

maybe first year grad Mr So and
I won't cover it because I would.

I mean I want a new
form of easily some but

is the same business first of
the methods for heuristic solutions.

It is a program for lower bounds and use
them in warm starts inside the not only

the root but inside enumeration.

As you will see it really does well
in the problem that's a start.

And I want to cover the details but this
is the exact formulation of this problem

I mean the only thing I would
like to remember it can be done.

And if you follow there's a paper which
has been published actually just a few

months ago in hours of
statistics that does this.

Which by the way I have to admit
to be honest with our media and

most of that is the first person
I have ever submitted to and

most of the districts this is completely.

Not in my home court to say it was
accepted and I would say positively

enthusiastically not which gives me but
in the end of the day people and

most of the dislike was of course was
like Mark programming in optimisation and

that's a corresponding and
it's a strong stronghold so

you might be one of the first in
the programming if not the first

in this program e-mails that this is.

So so we can say and
the same behavior namely that for

some other data right you.

You find a feasible solution fast and
the lower bound takes longer.

That's the same picture in other words.

What time are we.

How much time we have
five minutes ten minutes.

Then.

OK.

So I can tell you about the method and

the mother this I think a nice one in
the sense that So let's look at this so

take the numbers so
this is the wives variable minus X.

beta but this sort of veteran other words
fix a beta sorta guys and this is a Q.

flood just.

By emphasis means after
sorting which depends on data.

So clearly one value is the sum of
the first two plus one minus the.

The other two values Now the nice thing is
that this function is called VIX in beta.

It's nicer let me give you a small
it's an easy proof of that.

Also And they get out of exercise so
I would like to prove to you but

if you take as a function of data.

Take this sorted largest
If you plug two values you

some them up is convex So
now what have we done we expressed one

of the median as a difference
of two convex functions.

Now let's let me convince you that
this problem is equivalent to that so.

We have so we say.

Take six beta for I mean that.

Might surmise the sum of W.I. times these
values subject to some of the equal

them zero is less and less only go to one.

I claim what is the problem with this is
a linear programming problem as far as W's

are concerned what is a problem going
to do is going to sort the numbers and

some of them up so this actually
gives you the sum of the M. largest.

And the w's are not negative numbers.

So this suggests.

Using your programming that
this in fact a convex function.

So the details are not so important but so

deep in my support so if you express
something as a series of convex functions

you can do nice things about it
you can actually the first part is

is already convex the second part in fact
leaving out recently a programming problem

optimizing minimizing bade over this
is linear programming by duality and

this is not this is of course
minimizing a concave function is

tougher but you can do things about if you
restrict methods of what I want more than.

The details.

So again they impact of
warm starts is very very

substantial in fact more important

than before is there is a tougher
problem there's a reason people don't.

Have any for this funny one Wilson you
could do you could solve the problem

with thirty variables in here or not come
out even to five and we see that but

this is the same same story you can solve.

So what have we learned about this
problem that my old classroom starts

to proveable of Kemal of
the problems of medium of media and

regression to about five hundred
bucks in under two hours.

You have to realize that if these are two
hours in today's computer software that is

two hundred billion times
of nine hundred ninety.

Two.

So reason people believed it was
completely impractical at the time.

But the problem is people don't update
their beliefs they form a belief which is

true in life we form a belief and
then rarely will visit.

But if you have a much larger problem and
it was ten thousand a year and we

solve it in under two hour our performance
significantly All State of the opera but

we cannot prove optimality
in a reasonable amount.

Is still not we have some more work to do.

So what I would like not to in very many
few minutes I would like to give you some

remarks of at least my view.

On complexity What is complexity
Here's what we teach our students

this is what we did you
write We teach you.

I'm also guilty as charge
used to not anymore is

is the following we say I believe that the
theory to have the following requirement.

That it's up to it cause to be positively
correlated with empirical evidence.

We have a theory that is negative we
call a because it was not a good theory.

Would you say.

It's an obvious statement but
we don't apply to ourselves.

So an example is the simplest
method the simplest method.

In the complex of the world is not
a good theory it's an exponential method

because indeed there are some examples in
which to measure that it was not done but

imperiously the method
this extremely good.

So this something wrong is either wrong
with a complex emotional when used or with

programming my vote is on
the complexity here is the problem and

what I believe is important is that
the two hundred billion speedup

forces us to consider what distractable.

Perhaps something to do remember that is
what you used to believe in the seventy's

when the carp proposed and
be hardness of Forth

we can solve problems with ten variables
let alone thousands of variables so

to develop a theory of characterizing what
is different of what made great sense.

But we use the same theory today somehow
to speed up the piece of programming

as two hundred billion did not enter the
complex the world reason I find incorrect

I mean if I must proceed
with I mean I it's and

it doesn't in via like
this in other words.

These problems are intractable we
don't even teach the methods yet

empirically control them this does
not make sense to me at least.

Worst we have.

And other thing you will
find about we are given for

him everything scientifically I made.

Up that we have a good about keeping him
out of you know that's another story.

See who is in YOUR of the.

So what is my definition of complexity so

what distractable In other words
in my view what distractable.

Is if it can be solved for sizes and

times that are appropriate for
the application that's what I think.

Blessedly matters right to say I want a
system in which as the input increases and

so forth it has nothing do with
reality in my in my experience

to give you some examples online trading
problems these are all problems and

I have some experience about this I'm not
talking only hearsay online trading terms

may be sold in milliseconds that any of
the clothes not make billions of dollars

by the need to solve
problems like this right so

who cares if you if you have a polynomial
method or a linear method it

doesn't matter the only thing that matters
it has to be solved in milliseconds

it doesn't look for mention method in
fact this sort of men about physically

about this organization many others
there's a sort of Spock relation for

how to optimally schedule the training the
method used is an exponential I work from.

But it throws in milliseconds in the
application in question there are other

problems in which it doesn't
number one number two.

Problems used for
planning need to be solved in minutes or

even hours you don't need to solve it
in milliseconds you're on a bigger

problem to understand the policy
question you can do it in half a year.

Or so therefore you have a lot
of invisible you heated with but

in the galley they all
of you can solve it.

So in my view asymptotic polynomials of
ability or N.P. hardness is not relevant

and there is that in others we have a
theory that in my view has no resemblance

to the practical realities of the world
I see I used to believe I mean I was

educated I was in the mathematics
department of my team we teach them and

we harness complexity one complexity to
advance craft taking all the classes I

used to believe in them when I went
to the real world I said why doesn't

it doesn't add up so
that's my use my definition and

in fact recently Irani been
told was visiting and he.

Only a pair of I like but act double.

Tracked up all right.

And then I also have yes.

Great your name.

OK I made a new friend really.

Yes.

Of

course.

I don't have a my my for my tax cut I have
my heart of solving a real problem as it

does in very our world and for that I will
use whatever I have you know if I need

it and hardware is extremely cheap now not
in the computer with just one other mighty

few months ago is of the order
it's a thousand dollars and

these capabilities could create a computer
in one thousand nine hundred nine that

the great company had it's
that level I mean you could.

Spend fifty million on this so
if this takes more hardware so

cage Well let's use it but these are
executive you know I mean engineering and

engineering department after all at
the moment anyway engineers this sort of

practice that we need to do with computers
and I want you OK that's my view but

I agree with that
statement you said I also.

Take your vote.

But I want to make this comment was for
the use of your name sir

Spiro you're my friend.

So are some other nations.

Are.

Some of the market forces.

And it's also what is the significance
I wonder particularly problems and

source of electricity OK.

OK.

OK.

Yes we have an hour now.

But but unfortunately I believe
interpretations disaster you so much so

we don't do you think there's a problem to
statisticians I find this mind boggling

but I mean you know we cross out fields So
in other words the interpretation

is important because it has implications
of what we do what we teach so

I think that's relevant final comments.

So I believe the problem is
that the six in my opinion

consider intractable to take
a decade ago are now tractable but

obviously examples of another ten I
mean it's not a beach is the ONLY So

the last saw which as I mentioned is not
a detail it's a major thing in statistics

it is a robust of proper notice parts of
the property in comparison to last so

could is the main incumbent in my own
provides a significant role in taking

Sparty as well as a natural predicting
I can see not as much but so

in my view the time to
include my own statics is.

It would be a mistake not to do it this
is the publicity department that has both

you know twenty percent of
the faculty in optimization

in rough numbers twenty
percent it's artistic.

It's an opportunity.

There are too many departments
I have strength in both.

So corresponding so
that you don't think I don't.

I only preach or not do so next year
especially now I have a munition with

a very young so this isn't coming we'll
be teaching a class first year graduate

class of the my to satisfy their
mother might as well let's call

these three lecture these three topics
would be three different lectures and

the other examples and we have I mean
you know hopefully with other people.

I can see that for the young
people in the audience I know for

a fact that this is this is an area

to expand I mean what evidence do I
have of this this year I have four.

First year got the students.

I miscalculated that's why you know I
went much further than when I saw it

on the numbers but but these four people
they are I believe a talented people

each of them had this specific problem of
classic upper arms as this one was caught

the other one was discrete is V.M.
It doesn't matter but

these are problems these are actually four
chapters there's a main book Inside these

things that we have it might be
by Friedman to see it on me and.

One.

Thing I believe the book is called so
I took four chapters of his book.

And all of them have to restrict and
I assigned.

A job for each problem to one of
the students all four we made it

that is in the end of the year these are
not extremely knowledgeable they're very

talented but they're not knowledgeable
they're not people you know just arrived

so I think we made progress A young people
made progress I didn't solve the problem

they did I posed and they solved it so
I think it's doable so

when I think many people can
contribute on that note I think

you.

Could you also mention your name so yes

dear.

Heart

Yes.

That's right.

Yeah.

So this is not a completely automated
process judgement is needed that is and

I believe that's a good idea a human
modern era has intuition about them

that I wouldn't have so
when we solve this problem.

He said eight C. is make would rather use
glow cross Valley that in fact we have

automated this process we use
cross-pollination to select what is

the right age see but but
at some point some judgment is needed I

don't advocate that we would take the day
that we give this black box and then

an hour later we look at it the answer
is only some participation is needed for

example with star formations I made it
to me and affirmation houses sum up some

amount of human interaction
is needed I think.

Yes your name.

Yes.

So.

This is not this there are you can you
just mentioned two levels the first level

is use them as a humoristic
like the rest of my.

This can scale to hundreds of thousands

hundreds of thousands in fact we
have sold the problem emerging that.

The number of observations
were two hundred thousand and

the number of variables were five
six thousand variables right so

in its case as far as humoristic
solutions are concerned is very scalable

ask a level as Muslim if there is
one is we use continuous methods.

If you want provable guarantees I would
say the skill ability to prove all

of the military is in
the maybe ten thousand And

because then thought if you
want further than that we need.

More work.

Right so this is I'm not claiming we have
done what I claim who teach these methods

and they do scale to some sizable.

Yes.

I.

Yes OK Another friend so
even if you have it.

Also fine with me.

When.

I don't know this paper over here we had.

A fantastic.

It pleases me to see the snow
that goes as a positive

not.

Like the hand of a prom motorcycle and.

Projection like waiting structures like
constructing waiting very well for the.

D.J. was the one constraint
I guess a woman needs.

Like opportunity and I'm just curious
with what we have done also I mean

you have written a paper has many things
I just want to give you a glimpse but

what we do also is that there are multiple
ways to have pulled me out of the if it's

possible the two variables have Local me
up but the combination of variables is

actually very calm in the air so what
we do is we again we use what's up with

a good day to day that we would
take the solution for the solution.

We want two three four and five have been
selected we calculated the correlation

matrix of the five variables with
a conditional number of this.

Plea bargain values of this matrix and
then we observed you know we used some.

Value method to say that sets want two
thousand and three should be excluded so

you put Z. one plus two plus if you listen
to another using a meter of method to

do that that's how we do
the what you just said.

Yes by right.

Here worth.

Of question please.

I'm wondering.

Whether.

There might be something going on
where problems there actually arise.

And have some nice structure
that might help your program

where they might be selling in houses.

Rather than.

Simply.

You know yeah now so

you're saying it is possible that problems
are rising the world at a much easier

number compared to what the complex is
here with you know a good having you.

Know although I doubt that I mean it
you know I've been in this business for

about thirty years and in some problems
I've seen for many I don't believe that

the real world problems
are particularly easy or harder so.

This is speculation I don't have
the kind of evidence of this but.

If if if I want to say why is
it that you cannot solve we now

can solve is really the collective
intelligence of a community and

I think that's what changed and
I also believe that scientifically.

I mean science doesn't change
these really in fact the.

Mechanics of many on even those an
approximation we still teach correctly so

by the way so and that and what I'm
trying to point out especially with young

people in the audience that if you
broaden the horizon a little bit.

You might actually have access to things
that you have not thought about and

it's our obligation as educators to
teach the young people what is possible

even if I'm wrong to say I made some
compilation I'm not I don't think I am but

let's say I am I think is worth
knowing that this is a set of methods

that are worth teaching in
our environments and and

I think this would lead to progress
not my me but my my all of us.

Would really want to go with.

You.

And I don't believe
everybody agrees on this.

Critical evidence against.