Unit 5 21 Answer and Laplace Smoothing knowitvideos English Japanese

Unit 5 21 Answer and Laplace SmoothingYouTube↗ IA↗(long shot)
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And surprisingly, the probability for this message to be spam is 0.

驚いたことにこのメッセージがスパムである確率は0です

It's not 0.001. It's flat 0.

0．001ではなくちょうど0です

In other words, it's impossible, according to our model, that this text could be a spam message.

言い換えると私たちのモデルではこのメッセージはスパムではあり得ないのです

なぜでしょう

When we apply the same rule as before, we get the prior for spam which is 3/8.

前と同様にベイズの定理を用いましょうスパムの事前確率は3／8です

And we multiple the conditional for each word into this.

これに各単語の条件付き確率を掛けていきます

For "secret," we know it to be 1/3. For "is," to be 1/9, but for today, it's 0.

SECRETは1／3でISは1／9ですところがTODAYの条件付き確率は0です

It's 0 because the maximum of the estimate for the probability of "today" in spam is 0.

スパムにTODAYが登場する確率を最尤推定法で算出すると0になるからです

"Today" just never occurred in a spam message so far.

スパムにはTODAYが一切出現していません

Now, this 0 is troublesome because as we compute the outcome--

この0は厄介な存在と言えます

and I'm plugging in all the numbers as before--

前と同様に値を代入して結果を計算すると

none of the words matter anymore, just the 0 matters.

他の単語に一切関係なく0となるからです

So, we get 0 over something which is plain 0.

そうした理由から答えはちょうど0なのです

Are we overfitting? You bet.

これは過学習の影響と言えます

We are clearly overfitting.

明らかな過学習です

It can't be that a single word determines the entire outcome of our analysis.

たった1つの単語が全体の結果を左右することがあってはなりません

The reason is that our model, to assign a probability of 0 for the word "today"

私たちのモデルがスパムにTODAYが出現する割合を

to be in the class of spam is just too aggressive.

強引に0と設定したのが原因です

Let's change this.

ここに手を加えましょう

One technique to deal with the overfitting problem is called Laplace smoothing.

この過学習に対処する手法の1つがラプラススムージングと呼ばれるものです

In maximum likelihood estimation, we assign towards our probability

最尤推定法ではデータ中の全事象と特定の事象の

the quotient of the count of this specific event over all events in our data set.

回数の比を確率に割り当てます

For example, for the prior probability, we found that 3/8 messages are spam.

例えば事前確率では 3／8のメッセージがスパムだったので

Therefore, our maximum likelihood estimate for the prior probability of spam was 3/8.

最尤推定法ではスパムの事前確率は3／8となりました

In Laplace Smoothing, we use a different estimate.

ラプラススムージングでは別の推定を行います

We add the value k to the count

出現回数に特定の値kを加え

and normalize as if we added k to every single class that we've tried to estimate something over.

すべての事象にもkを加えて分母を修正します

This is equivalent to assuming we have a couple of fake training examples

このようにそれぞれの観測回数にkを加えることで

where we add k to each observation count.

偽の訓練例を多少加えることになります

Now, if k equals 0, we get our maximum likelihood estimator.

kが0ならば最尤推定値が得られます

But if k is larger than 0 and n is finite, we get different answers.

しかしkが正の数でNが有限ならば最尤推定値と異なる結果になります

Let's say k equals 1,

k＝1の場合を考えましょう

and let's assume we get one message,

1つのメッセージを受け取った場合に

and that message was spam, so we're going to write it one message, one spam.

それがスパムだったとします 1件のメッセージ中にスパムが1件です

What is p (spam) for the Laplace smoothing of k + 1?

この時k＝1のラプラススムージングを使うとスパムの事前確率はどうなるでしょうか

Let's do the same with 10 messages, and we get 6 spam.

同じことを10件のメッセージ中6件がスパムだった場合と

And 100 messages, of which 60 are spam.

100件のメッセージ中60件がスパムだった場合についても考えます

Please enter your numbers into the boxes over here.

それぞれの確率を求めてください

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