Numenta NuPIC Tutorials, 17 Oct 2015

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From YouTube: Multiple Fields in NuPIC

Description

with Dr. Subutai Ahmad

A

Whatever, okay, hello.

B

A

And super thigh Matt asked me to talk about multiple.

C

Fields and new pics, so I'd screw together some notes and.

A

I'll just go through that because I know that's. There are a lot of questions about that on the mailing list and and I think thinking about multiple fields in no big. It's it's very different from how you think about it. Normally in machine learning so- and it's often important in practice to understand that so Matt asked me to do that. It's really informal and maybe not too long and it's just threw together some notes. So my agenda is.

D

A

I want to talk about the big picture and then I want talk about the small picture. So here.

E

Are just not really philosophy.

A

In theory and then we'll get into a few new pic details on that and Matt very kindly prepared a few questions that he sees on the mailing list, and so we can go over that near the end of us.

A

C

A

What is the big picture.

A

Here's the big picture, I have an HTM and it gets inputs and, as we all know now, these inputs are basically just sdrs coming in and what does.

E

A

To find common patterns in here so common.

A

Spatial patterns.

A

And then it finds common sequences of those spatial patterns because.

C

That's what this HTM is doing.

A

In the pic it's a drawing like this to point out that the HTM really has no concept of fields. It has no clue that there might be one or more fields in there. It's just seeing a whole bunch of bits coming in and this big, sparse vector and then trying to do these operations. So it's.

E

All about when you think about multiple.

A

Fields that all about you know what can the HTM handle in terms of SDRs coming in and what is the complexity of these STRs coming in? Okay, so in you.

D

A

Typically, we have 2048 columns now at the brain. You can get really big STRs again. So if you think.

E

About like vision for.

A

Example, primary visual cortex gets something like a million bits coming in and there's one to ten million columns in primary visual cortex. So it's way way bigger. It's it's a huge field with lots of complexity in there, but it's also a much bigger HDL. What.

C

A

Do at new pig is we have a bunch of encounters.

C

A

Each previous little SD ours.

A

And we concatenate them into one-day thing and and feed it in there right and.

A

It's kind of tough to do too much with 2048 columns and in general, if you think about finding the common spatial patterns, the space of patterns explodes exponentially, as you add, more and more fields, and so the in general, the space that common spatial patterns are going to explore, explode exponentially as well. So it's kind of hard to do this envision.

E

A

Is that the brain imposes a topology in here, so that you.

E

A

Of columns, only looking at a small set of STRs coming in another nearby set of columns looks at another small set of STRs. In the case of vision, you can do that and the topology really restricts the space that a set of columns is looking, so that really helps in the problem in new paint that we use it. Today we have 2048 columns and typically there's no topology, so the more fields you had every column has to participate in understanding the full richness in this space, and it's just it.

C

Gets hard basically and you're running.

A

Up against the curse of dimensionality and and issues like that, so that's that's the problem, and typically what we found in practice is that in this kind of a scenario we can handle between one and five feels pretty well.

A

C

A

Is of course, just rule of thumb, anything beyond that I think you really need to need to rethink how your database, even you, need more columns or you can impose a topology or use multiple.

E

A

Or something to reduce the space, but we find this is kind of the range where it works: okay and then, if you as you add more fields, so even if you're getting two, you know five fields. If you really want the spatial Pooler to learn common spatial patterns on the temple memory, to learn, common sequences, you're going to also need more data, so you know one field, you need less data and then you know five fields. You're gonna need a lot more data. So that's another confounding factor, often in practice.

A

You don't have enough data to really handle five fields properly, even though, technically that you could here so that's another consideration. So, typically in the the way we have the typical parameters we use one to five fields, it's kind of the range that you should be taking. You know and then you've, if you add more fields, who really need a lot more data for it to learn the common patterns and stuff like that.

B

Finding a hundred thousand rows of data, it's hard enough, finding five feels pretty good get honored as it is.

A

C

Then we found up and then down.

A

Here you can get you know with one field or even two fields you can get by with about 1,000 to you know three thousand rows of data roughly, but you will need quite a bit more here.

F

A

Don't know they don't have a good feel for that. I, don't know the data set where we really had to go through.

F

A

Two or three I mean two is not too different from one, so you can kind.

E

Of say in this range.

A

This kind of an IT and in our anomaly detection we typically have a time of day, as well as the scalar metric and dad, for example. So this range is pretty okay, one and two I. Don't really have a good feel from five. We very rarely really gone to that, but I'm pretty sure you'll need a lot more than this.

F

If their heels are somehow going to door shifts of information, I'm.

A

Gonna get to that. That's a really good point, all right! So, okay.

C

A

One one point I wanted to bring up is that the number of fields in general that you can handle with no topology and with 2048 columns is kind of restricted. Okay. So that's the first point.

A

Okay, so the second big point is you.

G

Know so what is the HTM doing.

A

With all these fields it's coming in well, it's you.

E

Know gets a stream of data, its.

A

Finds these patterns and sequences and that it's making predictions about the future? Okay and that's.

D

A

Highlight what this looks like from an HMS plan of view, so.

C

A

Have a predicted field and then you have some extra field, one an extra field, and here you have time so you have data coming in at different points in time.

A

So here you are hardly at time T, and this is time T plus one. So.

C

E

A

C

They say no, this is look at the full history of what.

A

You've seen to this point, so everything here and uses that to predict with our classifier predicts this one okay, so that is using everything in the past to predict this by now. This is very different from the way it's typically set up nation. It's.

C

Our nation is also internally predicting.

A

All of the fields, but from the classifier standpoint from an external site, one is predicting this one field. This formulation is very different from the typical machine learning formulation. Typically, the machine learning. What you would do is you don't have a concept of a stream of data you just have you know you have your prediction, which is the output up your system and any of the inputs which are these fields. So what you're trying to do is build a function where you predict your predicted.

D

A

T is some function of field, one at time, T and field two at time, T. So.

D

What typically.

A

The way it's done in machine learning is you use these two values to predict this time and the time history is irrelevant. Okay,.

D

So it's a very different.

A

Formulation and.

D

I think this is what humans are doing and.

A

We're looking at the full history- and this is.

G

A

Time here, so you don't really know this stuff until it. Actually that happens at the same time, missus so you're, making predictions of everything and checking against those predictions and so on, but usually in machine learning. You formulate the problems, so you can use for it's. Let's say using energy.

D

Prediction you.

A

Can look at the temperature and try to predict the energy usage? The.

G

A

So what this means going back to your question about correlated deals and so on. Let's.

C

A

C

Predicted field is correlated with.

A

C

Know some feature you.

A

Know f1 there so.

D

In the case of machine learning, you're trying to build this function.

A

And so for in the machine learning case, this is great.

E

A

D

A

Use that feature, because.

D

It's good, you might not even need feature to that, and this is perfectly.

A

Correlated you can just use this feature to make this prediction in.

E

A

E

Is the worst possible scenario.

A

You don't want that feature. The.

C

Reason is that if.

A

F 1 is very correlated with the predicted field. You already have all the information in the history to make this prediction. You don't need that other field. In fact it's making it worse, because if you add another field, you get back to these issues of needing more training data to really understand the common spatial patterns and all that, because.

D

Nothing's going to be a one-to-one match.

A

There's always going to be noise and it's never going to be a perfect correlation. So you have to remember that you have a lot of rich history in this pass when you're predicting here, so actually adding fields that are correlated.

C

B

Really bad for the.

A

Htm making predictions I know.

B

We've seen this before real.

B

A

So the energy example is a great example, so we work with a lot of companies on modeling, their energy data, make predictions and so on. And when we talk to their.

E

Scientists they.

A

Always bring up the fact that things like temperature are very necessary and machine learning to create a good predictive model of energy usage. Whenever we run the HTM, we've got good or better results, as both are better results. We never this one never ended up picking up temperature and they were always puzzled because in in their.

G

A

They required the temperature without temperature. You couldn't do a good prediction and with.

E

The ations, it was always better.

A

Without temperature, because of this reason, if you think about it, energy energy usage is correlated with temperature, that's it's getting warmer and your energy usage is going higher because your air conditioner is being used more you'll, already see an increase in the energy usage here. You'll see the up tectum that and.

E

Htm is using this sequence.

A

To make this prediction, it already knows, and it's better to.

E

Use this because there may be other the reason.

A

Things that affect energy usage, like the number of people in the building- and maybe you have an event in that building that day, so you have temperature, isn't really the predictor of that day. So.

C

You can use.

A

This history, to make this prediction so correlated features and the way up the planet here is bad for you and but good in typical machine learning. So.

C

That's a it's a it's! A mental.

F

C

A

Have to make when dealing with a CMS yeah.

E

Share of invisible vehicles in the standard sliding window approach in machine learning, I mean not just looking at the other variables of this is fine, but looking at its time, stress in the back yeah.

A

So you could do.

C

Something like a TD n n for.

A

Example, which is uses the last n inputs and put that in as well and I bet. In that case, you wouldn't pick up on temperature either so I.

E

Think it'll be similar. It's.

A

Not typically used, but you could yes.

E

I think what I'm saying is.

A

C

To most streaming.

A

Models and and sequence models, not just a CMS but.

E

Yeah, if you, if.

A

You use the past context to predict this as long as.

C

You include the.

E

A

Field and so a TDM is actually often you don't use well, you may or may not use the predicted he'll. So you have to be careful about that as.

E

A

Feeling of predicting is part of the input. There's.

C

Actually, a lot of information.

A

Already embedded I think.

C

It's totally fair point.

F

A

We could saw them in small ring is a pretty good way to figure it out, because it's just an outer loop over the whole HTM process and it'll. Look at the error metric, but.

F

A

You could try to see, you know is there. The thing is correlation is too simplistic of a relationship. So it's not just about correlation. It's also about high over sequences and sequence information, so which is more complicated than correlation.

A

Yeah you could try some like mutual information. Maybe that would work better I don't know. Maybe if there is oh, but you have to always include the predicted field. So if using this, if you look at the mutual information with the next point in time versus including both of these, if you're better with both, maybe you haven't really explored that, like.

C

As the temperature is an example.

A

So one interesting thing, I found out in working with dozens of customer data sets, is that often in the streaming scenario, with HD ng I should need many fewer fields than you would with our traditional machine learning model, because there's already a lot of information in the past and.

E

Most of what these other fields do is give you information.

A

Here, that is you, you don't have access to, because.

A

So then, that sort of begs the question: what are good feels is for evasion.

A

Talk about that so I think is what I kind of came up with it. So a useful field, I.

A

C

There's two conditions: one.

A

Is that so I would say, F is useful.

A

A

You know the predicted field at time, T plus 1,.

A

Ladies in today, F of T can help predict the predicted feel that time, T plus 1 okay. So it's not.

C

A relationship this way it's a relationship.

A

B

One step could be in time yeah.

A

Or you know, or maybe f of t, minus 1 or T or whatever it.

C

A

A time less than T plus 1 looks pretty fancy puts on prey. That's good and.

A

A

A

Not easily found in.

A

The previous stuff, so that would be like P of T P of T, minus 1 and.

E

If you include some other fields, then.

A

You would include that too.

A

This is not the same: F F prime, is useful, hey so.

D

If the information not easily and not.

A

Easily found in the past either in the predictive field and all these other guys so.

D

You have that both of these.

A

Conditions in order for it to be a useful you.

D

A

Just say: oh, it helps predict the future because if it can already be predicted, adding an additional field just makes it worse. So I think you have to have both conditions. It's.

C

Not easy to figure this out intuitively.

A

Kind of your question, so we, the swarm, is a decent way to figure it out. But you know you sometimes get counterintuitive results.

F

F

Yes, that dr. balloon, because this here, if it's useful, to create the bits that will make it differentiable and.

D

Say that it's arrogance to.

F

Differently goes, yeah all right, two different values of the Vinicio. A great feature is the thing that I can connect anything. This is yarn to do my I already had it will make it more also, but also more so.

A

Yeah yeah other vacation, yeah.

C

I think that's it that's true. So let me give you an example of that. So that's.

F

A

This not easily found. Sometimes, if you look at like energy usage seething hour by hour, energy usage, we often find that adding day of the week will help make the prediction now.

D

If you really look at the sequence, the information about day of the week is actually in there because.

A

It repeats you know every seven days you get a repeating cycle roughly repeating so.

E

It's in there, but if.

A

You're doing hourly prediction or every 15 minutes, that's a really higher order, sequence, and so, in order for the HM to learn that you need tons and tons of data so adding day of the week, can't help. But that's why I put this not easily, though so there the week makes it much easier now that HTML only has to learn much shorter sequences. I have.

B

An example that I've been trying and it's the Rhoden fading example where I've got so much data about 3, 1 1, calls for run problems in the otago which I would assume I'm. Sorry, it's not birthday. It's tree debris treated, birdie.

C

B

A

Debris so that should be it's not rodents in trees. It could be that's correct. It could be.

B

Should be directly affected by the Clemente weather and thats data that would not be in the data itself, because that's a.

C

Random sort of cause yeah tree.

B

A

You say like let's say you get some storm and that.

C

Leads to a lot of.

A

Tree debris and then the you get a spike in three one: one calls and shouldn't that be a good feel, I think it it can.

E

It's sort of I found it depends.

A

On the granularity that you're collecting things in so let's say, you're collecting, 3, 1 1 calls every hour or it'd be half an hour on an open in.

D

That case, if there's a.

A

Storm you will start to see an uptick in the 3 1 1 calls shortly after that, yeah.

B

Unfortunately, my granularity is pretty bad. It's only count every day. Yes,.

A

So the daily case I, would you might see that relationship I need.

B

My hat I've run into the problem where I don't have enough dig up. Tell.

A

B

How many rows yeah, but there's not enough history of inclement weather, causing 3 1 100.

E

A

In my dataset, yes, yes, that's exactly this data problem! Yeah! You have to see enough variation here for to pick up yeah. Maybe that could be. Why yeah? Let me give you an example, an abstract example of something.

A

What kind of fields could be helpful? It's very related to what you were saying actually so.

B

A

You have daily retail.

C

A

C

A

You know it's a holiday today, yeah, so you might have 1.2.

E

Million in sales.

A

Point 6 million the next day and you don't there's no holidays.

C

A

There's a holiday to get a sudden uptick in in sales, so you have 4 million in sales and this is a holiday. And then you know we go back to 1.3.

E

A

A

Holiday: okay,.

C

So here's a rent you.

A

Know pretty random thing that happens and it leads to an uptick in sales. Do.

C

You guys think this. This.

A

Feature will help in this warm.

A

That's a no! Why is that? Because.

B

It's a direct correlation in that Eon time slice. Yes,.

A

B

So what I found.

A

In this exact situation is, if you change.

C

This a little bit to say next date.

A

It's a holiday- and you don't like this so now- this is predictive of that guy. That actually does help, so this would get picked up in this form, because this is it's hard.

C

D

Look at the sequence and just.

A

Know that there's going to be an update, but the holiday feel can help predict that the only problem is so similar to what you mentioned. You need to see enough holidays in order to be able to make this correlation. But I have seen stuff like this and there's a gradual increase.

B

In sales or something they never know, yeah because days until next holiday, yeah.

A

Exactly and if you think that this is kind of how humans would reason to if you're trying to plan your store like the staffing at your store, you know you would say: okay is tomorrow holiday, yes, I'm going to pick more people, you wouldn't wait until tomorrow and then do it. So.

C

I think if you just shift it a little bit.

A

But I found that kind of stuff. So once.

C

You understand, what's going on, you can do.

A

Tricks like those too, to help. Okay, that's Lisa clean most of my prepared stuff, so.

C

You had a couple.

A

Of question that and read them out and then you can see if we answered them or not. He said: okay, I'm swarming over several input fields trying to get predictions from one of those fields, but every swarm resolve returns, model params that only encode the predicted field, exclamation mark I, know.

C

D

Be some correlation between the input.

C

A

Is a new pic finding that correlation, okay, so I think we kind of answered that question here, but there's another factor.

A

This is a really little picture factor, but if you're doing a swarm make sure you do a large swarm instead of a medium swarm, because a medium swarm only looks at pairs of field combinations and stops there, whereas large swarm will look at will go beyond pairs, and so very often we see that times then and the value will will help a lot. And so, if one really try to add another field in a medium swarm, only a large swarm will do that. Now, large one will take a lot more time.

A

Larson also looks at a lot more permutation of the parameters that the medium swarm. So it's also more likely to find these correlations. But.

C

Also, remember.

A

This thing that if you're getting a swarm with- and you really want to pick up multiple fields, you may need to swarm over more data as well. That's another.

D

Without writing the last law yeah. So the question: can you set.

A

The appeals manually you can, you can tell it there's a thing in the swarm Jason to force it to include fields, so you can do that.

A

So, if you, if you know you might include a particular, you want to test the effect of a particular field, you can just force it to be there and then see what happens.

C

B

A

B

He was saying manually if you can yeah yeah.

A

Yeah, every every whatever model.

C

A

Will include that field and then you.

C

Can take it out.

A

D

Even so, manually tried the different field.

A

Combinations basically.

D

B

Quit forcing including this worm actually I would run over a different set of permutations that always feel that yeah.

B

A

Okay, protip yeah. I.

D

Think someone on the mailing, let's ask that questions.

A

D

So I want to detect anomalies across several input.

A

Fields at one time, but all your examples feed one input field per model, wouldn't it be better to have one model in many fields that returns and overall anomaly score across all the input. Well, actually, all our most of our examples use two fields which is timestamp n, scalar values. That's really yeah, but.

C

A

If you have feels that.

C

A

And if you have more data, it would be better to have an overall at homee score, see.

E

If you can figure out.

A

Set of additional fields that help the model, then it's perfectly legitimate to use the.

C

Over Minami score will be computed across everything, even.

A

Today so as.

C

Long as the fields are good, it.

A

Should work better and I've.

C

Done tests like that, so.

A

I did a test where the customer, where I would train on four fields, and this was the case where four fields helped and I scrambled somewhere thread that scrambled a couple of the fields.

A

And so, if you plotted the predicted field, you saw no difference but at some point the underlying state space change underlying relationships change because I artificially changed that Detective anomalies there. So.

E

It can detect multivariate you.

A

Know pretty sophisticated multivariate.

E

Anomaly as long as.

B

A

Overall HTM model is good, although.

B

C

That happened since.

A

There is really.

B

No swarming mechanism to find the best detection model yeah.

D

B

Would you suggest instructing the model parameters for multivariate anomaly, detection, yeah.

A

So we don't have a good metric to optimize part, only detection. So what we've been doing is optimize. The prediction error metric so build a prediction model and the same principle is going to apply and then take the best prediction model and just run it as an anomaly model. So.

B

I've got many inputs. I couldn't run a swarm individually for each different input field to get the encoded parameters that are best for predicting that one field and then sort of paste.

A

Them all together in.

B

One model parameters.

A

Well, you could.

C

Run them, maybe you could run a swarm that checks.

A

All the combinations for you so.

B

If you do, a large swarm, I will check more cons, but you're still picking one field to predict in that case. Yes,.

A

Yes, yes, yeah, oh I,.

B

C

A

They said yeah, you could build ooh, it's long to predict each of those fields and then yeah.

B

Maybe the best model to predict that one field and then.

C

You can mix them all together and change.

B

A

Yeah I don't know, though I haven't tried that I don't know if that would or would not work.

D

There's no no assembled models; yeah yeah.

C

So there's sort of two ways to do this: that I've seen there's the one we do with rock.

B

For IT mm-hmm, which is you run them all individually, there's no correlation between any of them and then.

D

You do some post-processing.

B

To decide women, anomaly, wipers right and.

E

Then this other method that we.

B

Have somebody really was trying to do and I've.

C

B

That I've been really curious about how.

A

It would be yeah if you.

B

A

The one one issue we have right now with this forming and there's a github issue file for this is that the range of.

C

A

That the currents warm low sober is not ideal, because we've made changes to the special cooler and we need to update some of those parameters and so you're. Even if you run a swarm, you might find if the manually tweak it until we get that issue resolved and.

D

A

Have a scalar value or a scalar value and the time step I would say, just use the values we have in nab or one of our nominee models and just go with that. Doesn't bother tweaked it even for.

F

F

So 1.2 and 1.6.

F

C

F

First and true, very.

C

F

A

So the end, so you would hope the temporal memory would pick up on that and learn a sequence from that.

F

A

That would be the same. It's not overlap.

F

A

Not large, it's not just the fact that there's a large.

C

Difference in over that, it also has to be predictive.

A

C

Also has to be it also, it has to have these two properties.

F

You could, if I, could have a random variable here that.

A

Would have large overlap and a son.

F

A

That's a little bit snotty.

A

That could help you.

A

Okay last couple of questions: if.

C

A

C

I'm running many anomaly models.

A

Each with one input field: how can I combine all the anomaly outputs together in a way that classifies the nominees across all inputs, so I'd say.

E

A

Five different metrics for monitoring and we're doing anomaly detection on each one independently, so we're getting an anomaly likelihood score for each one and now you're saying how do we combine all of them together? So.

C

I think there's a.

A

Good answer to that so basically.

E

A

Of those metrics shows an anomaly so.

C

The intuitively one of the chosen anomaly: well, that's rare.

A

And interesting, but if two of them show an anomaly at exactly the same point of time, then that's really rare all right and you should pay more attention to that. So one.

E

Suggestion I have is.

A

To take the sum of the log likelihoods.

A

Overall, the metrics and then do a threshold on that. So.

D

Typically, we just usually.

A

We just look at one log likelihood and we use a threshold of 0.5 I. Think if you add up all of the lot of likelihoods and use a slightly larger threshold, you probably get pretty good.

A

C

A

C

This point is, you could have two anomalies that are very.

A

Close together not exactly alive and so.

B

You might want to do this over a window.

B

Explanation so.

A

B

A

Say they know, but.

B

We only get likelihood out of yeah.

A

So we get likelihood, which is when the first one the likelihood is doing, is looking at the anomaly scores and telling you it's a probability. It's telling you what is the likelihood that this anomaly score comes from? This is similar to what we've seen before with anomaly score. So if the metric is.

E

A

Anomaly score is always high, then you need a lot of very high likelihood high on these scores in the road to get a high-end. Omni light be good. So that's what the likelihood is is a probability now. The nominees are really rare. So these probabilities, the threshold we often said, is like point: nine, nine, nine, nine, nine, nine to five nines or something like one in a 10,000 chance or something like that of it of an anomaly. So it's really hard to deal with those numbers.

A

So there's a function in the anomaly likelihood class that just takes the log of that number and returns that it's basically a log and the way it's normalized is that point five on there corresponds to five nines and like and it's a log, and so if you think.

G

A

Things occurring together: what is the probability that both of them will line up? It's the multiplication of the two independent probabilities, so in log space, that's just the Sun! That's why I was saying just to do this on logs. It's.

C

Just an extra function.

A

Call in there I.

D

A

It's easiest to look at the log likelihood. You could just say point: five is your threshold: you can do it if, otherwise, if you look at the likelihood, it's really hard to tell in a chart the difference between 0.99 99.99999, so so you might want to do something like god. Let's say you have two of them in each one. Normally, whatever threshold of 0.5, you could add them up and have a threshold of plate should be lower than one, and so that means, if both of them are four nines instead of five nines.

A

Maybe you should pay attention to them. Where is it one of them individually was at four nines? You might not pay attention to that. So.

C

A

This is a good one and I. Think Lewis's point is really good. You might want to do this in a window. We.

G

D

A

G

A

I think we scaled it. I forgot exact number.

A

C

D

C

A

I get one more. This is nothing to an anomaly models. It's a completely separate question, see how am I supposed to handle data that comes in at different intervals, when swarming or feeding data into nupoc at some time, stamps I don't have input for all fields. What should I do so, I think the you.

C

Can think about it here.

A

Let's say here: that's a field, one only is updated, every other iteration, and so let's.

E

D

A

Every half an hour than every 15 minutes. What should you do here? I think.

G

The socialist thing is.

A

Just to copy this guy over say easiest, if you don't have any other information, because that's basically saying constant for that half an hour and you could have a more complicated model of this. So if you know like, for example, if this is day of the week, let's say so- and this is hourly data. This is what day of the week would only change every 24 rows. So you could.

C

Say this is Monday and this is Tuesday and this is Wednesday, but what we do instead is we.

A

Convert the week into a scalar encoder, so we you know Monday.

E

The different thing Monday and Tuesday.

D

Monday slowly changes.

A

The Tuesday slowly so you could do that to something like that, but.

B

The simplest thing you don't know anything just copy it, you don't know what the next value is going to be can't really gradually hand.

C

It to that this is a common problem with.

B

Riverview because all the.

B

D

Things to copy.

B

Over because that's all you know yeah, that's all you yeah.

D

A

Think that'd be better than leaving it out or something putting.

B

C

But don't put in zero to zero, whatever.

A

You do don't put in zero, that's.

C

A

Thing you can do. Okay, any.

C

More questions and did.

D

I answer all your.

A

Questions: okay, cool.