i must say i don't understand most of the math. as for sharding, if i understood it correctly, i remember having exactly same idea for 'strata' selection as they show their a year ago. But i think the problem is that you have to run as many MR jobs as the number of strata selected. I.e. if you parallelize it 5 ways (5 maps) then you have to run it at least 5 times. or maybe one can recombine subepochs in reducers and have another run with reducers (so it's 3 times, not 5). Which seems to put fundamental limitations on hadoopified scalability of this (they partly show increased time after some rather low # of mappers which seems to confirm my old concern about this).
it probably makes sense with a lot of data. It probably makes even more sense without MR sort phase. Another thing i did not quite get, how they cope with regularization? it looks like they don't want to use it. How's overfitting handled then? but it's compelling enough for my work so i could try it. Again, i probably did not get some aspects of the algorithm though. Factorization is essentially a quantitative (continuous) target regression, not a classification, so our abstract classifier interfaces probably would not fit here On Tue, May 31, 2011 at 9:45 PM, Ted Dunning <[email protected]> wrote: > After a quick skumming of the paper, it looks vaguely like if you reduced > this to learning logistic regression that you have something roughly the > same as feature sharding. > > (which is still a good idea) > > With matrices, of course, you have two ways to shard, not just one. > > On Tue, May 31, 2011 at 7:19 PM, Dmitriy Lyubimov <[email protected]> wrote: > >> Interesting. >> i'd probably be interested to try it out. >> >> >> >> On Thu, Apr 28, 2011 at 11:31 PM, Stanley Xu <[email protected]> wrote: >> > Thanks Ted and Lance. And sorry for the jargon. >> > >> > For the delay Ted mentioned, we have already considered that, still >> thanks a >> > lot for all the detail ideas, they were pretty helpful. >> > For the parallelized SGD, just found a new paper about using DSGD in >> matrix >> > factorization, it's different from logistic regression, but might helpful >> as >> > well. Put the title here "Large-Scale Matrix Factorization with >> Distributed >> > Stochastic Gradient Descent" if anyone is interested. >> > >> > Best wishes, >> > Stanley Xu >> > On Fri, Apr 29, 2011 at 2:08 PM, Ted Dunning <[email protected]> >> wrote: >> > >> >> Yes. >> >> >> >> Apologies for jargon and TLA< >> >> http://en.wikipedia.org/wiki/Three-letter_acronym> >> >> 's >> >> >> >> On Thu, Apr 28, 2011 at 7:04 PM, Lance Norskog <[email protected]> >> wrote: >> >> >> >> > CTR == Clickthrough Rate >> >> > >> >> > On Thu, Apr 28, 2011 at 12:06 PM, Ted Dunning <[email protected]> >> >> > wrote: >> >> > > On Tue, Apr 26, 2011 at 8:00 PM, Stanley Xu <[email protected]> >> >> wrote: >> >> > > >> >> > >> ... I understood as the algorithm, the time in training only relies >> on >> >> > the >> >> > >> non-zero records, but per our test, there would be some overhead we >> >> > could >> >> > >> not ignore for thoso non-zero records, though the cost is >> sub-linear >> >> or >> >> > >> logit to the length of the hashed vector. >> >> > >> >> >> > > >> >> > > This is pretty close if we say "non-zero values". A record usually >> >> > refers >> >> > > to an entire training >> >> > > example. >> >> > > >> >> > > The extra work refers mostly to deferred regularization that >> eventually >> >> > has >> >> > > to be >> >> > > applied. My guess is that it is even less than log in the feature >> >> vector >> >> > > size. >> >> > > >> >> > > >> >> > >> And in CTR prediction, I am not pretty sure it will converge very >> >> > quickly. >> >> > >> >> >> > > >> >> > > I was saying this purely based on the number of features. >> >> > > >> >> > > >> >> > >> Because we will very possibly see some records has the almost same >> >> > feature >> >> > >> but different result in display ads. >> >> > > >> >> > > >> >> > > The algorithm can still converge to an estimate of the probability >> >> here. >> >> > > >> >> > > >> >> > >> But we will see the result in the >> >> > >> future. >> >> > > >> >> > > >> >> > > You have to be *very* careful about this to avoid prejudicing the >> model >> >> > > against >> >> > > recent impressions. If you have a fast feedback to the ad targeting >> >> > system, >> >> > > you >> >> > > can have severely instability. >> >> > > >> >> > > The key thing that you have to do to avoid these biases is to define >> a >> >> > > maximum >> >> > > delay before click for the purposes of modeling. You need to ignore >> >> all >> >> > > impressions >> >> > > younger than this delay (because they may still get a click) and you >> >> need >> >> > to >> >> > > ignore >> >> > > all clicks after this delay (to avoid bias in favor of old >> >> impressions). >> >> > > For on-line ads >> >> > > you can probably use a maximum delay of a few minutes because most >> >> clicks >> >> > > will >> >> > > happen by then. >> >> > > >> >> > > To find a good value for maximum delay, you should plot the CTR for >> a >> >> > bunch >> >> > > of >> >> > > ads versus delay. This will increase rapidly shortly after zero >> delay, >> >> > but >> >> > > then will >> >> > > level off. The ordering of ads by CTR is what you care about so you >> >> can >> >> > > follow the >> >> > > curves back and find the shortest delay where the ordering is >> clearly >> >> > > preserved. Use >> >> > > that as your maximum delay. Typically this is roughly where your >> CTR >> >> is >> >> > at >> >> > > about >> >> > > 80-90% of the final value. >> >> > > >> >> > > >> >> > > >> >> > > >> >> > >> (We were still working on creating a framework to digg all the >> >> > >> features we need from the log, I would like to share our experience >> by >> >> > >> using >> >> > >> Mahout SGD once we got our CTR prediction model release.) >> >> > >> >> >> > >> And for parallelize SGD, what do you mean for help with sparse >> inputs >> >> > that >> >> > >> exhibit long-tail frequency distribution? Would you like to share >> some >> >> > of >> >> > >> your ideas, Ted? >> >> > >> >> >> > >> Currently, what I could think about is split the data to multiple >> >> mapper >> >> > >> randomly and let every mapper to learn from the local data and get >> an >> >> > >> average on the whole model, or let multiple model to vote for every >> >> > >> feature's weight. A little like the idea of AdaBoost or >> RandomForest. >> >> > But I >> >> > >> am not a scientist or mathematician, so no idea if it is correct or >> >> not. >> >> > >> >> >> > >> >> >> > >> Thanks so much. >> >> > >> Stanley Xu >> >> > >> >> >> > >> >> >> > >> >> >> > >> On Tue, Apr 26, 2011 at 11:16 PM, Ted Dunning < >> [email protected]> >> >> > >> wrote: >> >> > >> >> >> > >> > On Mon, Apr 25, 2011 at 11:46 PM, Stanley Xu < >> [email protected]> >> >> > >> wrote: >> >> > >> > >> >> > >> > > 1 hour is acceptable, but I guess you misunderstand the data >> scale >> >> I >> >> > >> mean >> >> > >> > > here. The 900M records didn't mean 900M Bytes, but 900M lines >> of >> >> > >> training >> >> > >> > > set(900M training example.). If every training data has 1000 >> >> > dimension, >> >> > >> > it >> >> > >> > > means 900 million X 1000 X 16 B = 14TB. If we reduce the logs >> >> > collected >> >> > >> > to >> >> > >> > > 14 days, it would be still 2-3TB data. >> >> > >> > > >> >> > >> > >> >> > >> > Oops. Forgot that last multiplier. >> >> > >> > >> >> > >> > >> >> > >> > > Per our simple test, for 1000 dimension, 10M lines of record, >> it >> >> > will >> >> > >> > take >> >> > >> > > about 1-2 hours to do the training, so 90M lines of data will >> cost >> >> > at >> >> > >> > least >> >> > >> > > 90 hours, is that correct? >> >> > >> > > >> >> > >> > >> >> > >> > 10M x 1000 x 8 = 80 GB. >> >> > >> > >> >> > >> > 1-2 hours = (approx) 5000 seconds. So this is >> >> > >> > >> >> > >> > 80 GB / 5000 s = 80/5 MB /s = 16MB / s >> >> > >> > >> >> > >> > Yes. This is reasonable speed. I think you can get a small >> factor >> >> > >> faster >> >> > >> > than this with SGD. I have seen 100 million records with more >> >> > non-zero >> >> > >> > values than you describe with a training time of 3 hours. I >> would >> >> not >> >> > >> > expect even as much as a factor of 10 speedup here. >> >> > >> > >> >> > >> > >> >> > >> > > >> >> > >> > > And from the PPT you provided >> >> > >> > > http://www.slideshare.net/tdunning/sdforum-11042010 >> >> > >> > > You said it would take less than an hour for 20M data records >> for >> >> > >> > > numeric/category mixed dimensions. I am wondering, how many >> >> > dimensions >> >> > >> > per >> >> > >> > > record? >> >> > >> > > >> >> > >> > >> >> > >> > These are sparse records records with about a thousand non-zero >> >> > elements >> >> > >> > per >> >> > >> > record. >> >> > >> > >> >> > >> > >> >> > >> > But let's step back to your data for a moment. Where do these >> >> > thousand >> >> > >> > dimensions come from? Do you really have a thousand hand-built >> >> > features? >> >> > >> > Do you not have any sparse, text-like features? >> >> > >> > >> >> > >> > If you really only have a thousand dimensional problem, then I >> think >> >> > your >> >> > >> > model might exhibit early convergence. >> >> > >> > >> >> > >> > If not, it is quite possible to parallelize SGD, but this is only >> >> > likely >> >> > >> to >> >> > >> > help with sparse inputs that exhibit long-tail frequency >> >> distribution. >> >> > >> > >> >> > >> >> >> > > >> >> > >> >> > >> >> > >> >> > -- >> >> > Lance Norskog >> >> > [email protected] >> >> > >> >> >> > >> >
