Searn is my baby and I'd like to say it can solve (or at least be applied to) every problem we care about. This is of course not true. But I'd like to understand the boundary between reasonable and unreasonable. One big apparently weakness of Searn as it stands is that it appears applicable only to fully supervised problems. That is, we can't do hidden variables, we can't do unsupervised learning.

I think this is a wrong belief. It's something I've been thinking about for a long time and I think I finally understand what's going on. This post is about showing that you can actually recover forward-backward training of HMMs as an instance of Searn with a particular choice of base classifier, optimal policy, loss function and approximation method. I'll not prove it (I haven't even done this myself), but I think that even at a hand-waving level, it's sufficiently cool to warrant a post.

I'm going to have to assume you know how Searn works in order to proceed. The important aspect is essentially that we train on the basis of an optimal policy (which may be stochastic) and some loss function. Typically I've made the "optimal policy" assumption, which means that when computing the loss for a certain prediction along the way, we approximate the true expected loss with the loss given by the optimal policy. This makes things efficient, but we can't do it in HMMs.

So here's the problem set up. We have a sequence of words, each of which will get a label (for simplicity, say the labels are binary). I'm going to treat the prediction task as predicting both the labels and the words. (This looks a lot like estimating a joint probability, which is what HMMs do.) The search strategy will be to first predict the first label, then predict the first word, then predict the second label and so on. The loss corresponding to an entire prediction (of both labels and words) is just going to be the Hamming loss over the words, ignoring the labels. Since the loss doesn't depend on the labels (which makes sense because they are latent so we don't know them anyway), the optimal policy has to be agnostic about their prediction.

Thus, we set up the optimal policy as follows. For predictions of words, the optimal policy always predicts the correct word. For predictions of labels, the optimal policy is stochastic. If there are K labels, it predicts each with probability 1/K. Other optimal policies are possible and I'll discuss that later.

Now, we have to use a full-blown version of Searn that actually computes expected losses as true expectations, rather than with an optimal policy assumption. Moreover, instead of sampling a single path from the current policy to get to a given state, we sample all paths from the current policy. In other words, we marginalize over them. This is essentially akin to not making the "single sample" assumption on the "left" of the current prediction.

So what happens in the first iteration? Well, when we're predicting the Nth word, we construct features over the current label (our previous prediction) and predict. Let's use a naive Bayes base classifier. But we're computing expectations to the left and right, so we'll essentially have "half" an example for predicting the Nth word from state 0 and half an example for predicting it from state 1. For predicting the Nth label, we compute features over the previous label only and again use a naive Bayes classifier. The examples thus generated will look exactly like a training set for the first maximization in EM (with all the expectations equal to 1/2). We then learn a new base classifier and repeat.

In the second iteration, the same thing happens, except now when we predict a label, there can be an associated loss due to messing up future word predictions. In the end, if you work through it, the weight associated with each example is given by an expectation over previous decisions and an expectation over future decisions, just like in forward-backward training. You just have to make sure that you treat your learned policy as stochastic as well.

So with this particular choice of optimal policy, loss function, search strategy and base learner, we recover something that looks essentially like forward-backward training. It's not identical because in true F-B, we do full maximization each time, while in Searn we instead take baby steps. There are two interesting things here. First, this means that in this particular case, where we compute true expectations, somehow the baby steps aren't necessary in Searn. This points to a potential area to improve the algorithm. Second, and perhaps more interesting, it means that we don't actually have to do full F-B. The Searn theorem holds even if you're not computing true expectations (you'll just wind up with higher variance in your predictions). So if you want to do, eg., Viterbi F-B but are worried about convergence, this shows that you just have to use step sizes. (I'm sure someone in the EM community must have shown this before, but I haven't seen it.)

Anyway, I'm about 90% sure that the above actually works out if you set about to prove it. Assuming its validity, I'm about 90% sure it holds for EM-like structured prediction problems in general. If so, this would be very cool. Or, at least I would think it's very cool :).

No-op: The case of Case and Deaton

4 hours ago

## 5 comments:

酒店經紀PRETTY GIRL 台北酒店經紀人 ,禮服店 酒店兼差PRETTY GIRL酒店公關 酒店小姐 彩色爆米花酒店兼職,酒店工作 彩色爆米花酒店經紀, 酒店上班,酒店工作 PRETTY GIRL酒店喝酒酒店上班 彩色爆米花台北酒店酒店小姐 PRETTY GIRL酒店上班酒店打工PRETTY GIRL酒店打工酒店經紀 彩色爆米花

艾葳酒店經紀公司提供專業的酒店經紀, 酒店上班小姐,八大行業,酒店兼職,傳播妹,或者想要打工兼差、打工,兼差,八大行業,酒店兼職,想去酒店上班, 日式酒店,制服酒店,ktv酒店,禮服店,整天穿得水水漂漂的,還是想去制服店當日領上班小姐,水水們如果想要擁有打工工作、晚上兼差工作、兼差打工、假日兼職、兼職工作、酒店兼差、兼差、打工兼差、日領工作、晚上兼差工作、酒店工作、酒店上班、酒店打工、兼職、兼差、兼差工作、酒店上班等,想了解酒店相關工作和特種行業內容,想兼職工作日領、假日兼職、兼差打工、或晚班兼職想擁有鋼琴酒吧又有保障的工作嗎???又可以現領請找專業又有保障的艾葳酒店經紀公司!

艾葳酒店經紀是合法的公司工作環境高雅時尚，無業績壓力，無脫秀無喝酒壓力，高層次會員制客源，工作輕鬆，可日領、現領。

一般的酒店經紀只會在水水們第一次上班和領薪水時出現而已，對水水們的上班安全一點保障都沒有！艾葳酒店經紀公司的水水們上班時全程媽咪作陪，不需擔心！只提供最優質的酒店上班,酒店上班,酒店打工環境、上班條件給水水們。心動嗎!? 趕快來填寫你的酒店上班履歷表

水水們妳有缺現領、有兼職、缺錢便服店的煩腦嗎?想到日本留學缺錢嗎?妳是傳播妹??想要擁有高時薪又輕鬆的賺錢,酒店和,假日打工,假日兼職賺錢的機會嗎??想實現夢想卻又缺錢沒錢嗎!??

艾葳酒店台北酒店經紀招兵買馬!!徵專業的酒店打工,想要去酒店的水水,想要短期日領,酒店日領,禮服酒店,制服店,酒店經紀,ktv酒店,便服店,酒店工作,禮服店,酒店小姐,酒店經紀人,

等相關服務 幫您快速的實現您的夢想~!!

Really trustworthy blog. Please keep updating with great posts like this one. I have booked marked your site and am about to email it to a few friends of mine that I know would enjoy reading..

sesli sohbetsesli chatkamerali sohbetseslisohbetsesli sohbet sitelerisesli chat siteleriseslichatsesli sohpetseslisohbet.comsesli chatsesli sohbetkamerali sohbetsesli chatsesli sohbetkamerali sohbet

seslisohbetsesli sohbetkamerali sohbetsesli chatsesli sohbetkamerali sohbet

Really trustworthy blog. Please keep updating with great posts like this one. I have booked marked your site and am about to email it

to a few friends of mine that I know would enjoy reading..

seslisohbet

seslichat

sesli sohbet

sesli chat

sesli

sesli site

görünlütü sohbet

görüntülü chat

kameralı sohbet

kameralı chat

sesli sohbet siteleri

sesli chat siteleri

görüntülü sohbet siteleri

görüntülü chat siteleri

kameralı sohbet siteleri

canlı sohbet

sesli muhabbet

görüntülü muhabbet

kameralı muhabbet

seslidunya

seslisehir

sesli sex

Really trustworthy blog. Please keep updating with great posts like this one. I have booked marked your site and am about to email it

to a few friends of mine that I know would enjoy reading..

seslisohbet

seslichat

sesli sohbet

sesli chat

sesli

sesli site

görünlütü sohbet

görüntülü chat

kameralı sohbet

kameralı chat

sesli sohbet siteleri

sesli chat siteleri

sesli muhabbet siteleri

görüntülü sohbet siteleri

görüntülü chat siteleri

görüntülü muhabbet siteleri

kameralı sohbet siteleri

kameralı chat siteleri

kameralı muhabbet siteleri

canlı sohbet

sesli muhabbet

görüntülü muhabbet

kameralı muhabbet

birsesver

birses

seslidunya

seslisehir

sesli sex

Post a Comment